Websink Prep UKKS2 MathsYear 4 chaptersMaths textbooksYear 1Year 2Year 4Year 5Year 6GCSEBrowse allPast papersFind a tutorBecome a tutor
Primary Maths · Year 4Chapter 3 · Times tables to 12 × 12
Year 4 · Chapter 3

Year 4 Times Tables: worked examples and questions with answers

By the end of this chapter you will be able to

  • Explain multiplication with equal groups, arrays and number lines, and use the fact that 3 × 4 = 4 × 3
  • Multiply by 0 and by 1, and divide by 1
  • Recall every multiplication and division fact up to 12 × 12, using a trick for each table
  • Use inverse (opposite) facts to divide, write fact families and find missing numbers
  • Find factor pairs of a number and multiply three numbers in any order
  • Use a known fact to work out new facts, like 6 × 7 → 60 × 7 and 420 ÷ 7
  • Solve word problems with multiplication and division, and answer quick-fire questions at speed

You should already know

  • The 2, 3, 4, 5, 8 and 10 times tables from Year 3
  • Counting in steps of 2, 3, 4, 5, 8 and 10
  • Adding equal groups (repeated addition)
  • Place value in numbers up to 10,000 (Chapter 1)

Where this leads

  • Multiplying and dividing larger numbers (Chapter 4)
  • Fractions of amounts (Chapter 5)
  • Money and decimals (Chapter 6)
  • Perimeter and area of rectangles (Chapter 7)
  • The Year 4 multiplication tables check
  • Multiples, factors, primes and squares in Year 5

National Curriculum for England, Key Stage 2 mathematics, Year 4. Content: Recall multiplication and division facts for multiplication tables up to 12 × 12, Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1, dividing by 1, and multiplying together three numbers, Recognise and use factor pairs and commutativity in mental calculations, Practise for the Year 4 multiplication tables check (timed, quick-fire practice).

Printable worksheets. Every lesson in this chapter has a free worksheet and an answer sheet to download and print.

Exercise P  Do you remember?

Non-calculator
1
FWork out 5 × 6.
2
FWork out 24 ÷ 3.
3
FFind the missing number.   ? × 4 = 32
4
FWrite the missing numbers when you count in 3s.   3,  6,  ?,  12,  ?,  18
5
FThere are 5 bags. Each bag has 8 apples. How many apples are there altogether?
88888?
3.1

Equal groups, arrays and swapping the order

Year 4
Multiplication as equal groups, Arrays, Commutativity, Multiplying by 0 and 1

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Equal groups, arrays and swapping the orderComing soon

Multiplication is a quick way to add equal groups. Imagine 3 bags with 4 apples in each bag. You could add 4 + 4 + 4 = 12. It is quicker to write 3 × 4 = 12. We read it as “3 groups of 4”, “3 lots of 4” or “3 times 4”. The first number is how many groups. The second number is how many are in each group.

3 groups of 4: 4 + 4 + 4 = 12, so 3 × 4 = 12.

An array puts the objects in neat rows (across) and columns (down). This array has 3 rows with 4 dots in each row. It shows 3 × 4 = 12. Now turn the array on its side. There are 4 rows with 3 dots in each row. That is 4 × 3 = 12. It is the same number of dots! So 3 × 4 = 4 × 3. This is called commutativity: you can multiply in either order and get the same answer. It means that you only need to learn half of the facts.

3 rows of 4: 3 × 4 = 12
4 rows of 3: 4 × 3 = 12
Turning an array round gives the same total.

You can also count in steps on a number line. Each hop is the same size. Six hops of 4 take you to 24, so 6 × 4 = 24. Counting in steps is called skip counting.

0+44+48+412+416+420+424
Six hops of 4: 4, 8, 12, 16, 20, 24. So 6 × 4 = 24.

Two special numbers. Multiplying by 1 means 1 group, or groups of 1. 1 group of 7 is 7, and 7 groups of 1 is 7. So 7 × 1 = 7. Multiplying by 1 does not change a number. Multiplying by 0 means no groups, or groups with nothing in them. 5 plates with 0 biscuits on each plate is 0 biscuits. So 5 × 0 = 0 and 0 × 5 = 0. Anything times 0 is 0.

5 plates with nothing on them: 5 × 0 = 0.

Key words. A product is the answer to a multiplication. The numbers you multiply are called factors. A multiple of a number is in its times table. The inverse of multiplying is dividing, and you will meet it in Section 3.5.

Key ideas

  • Multiplication means adding equal groups: 3 × 4 = 4 + 4 + 4 = 12.
  • An array has rows and columns. r rows with c dots in each row is r × c.
  • Multiplication can be done in either order: 3 × 4 = 4 × 3. (This is called commutativity.)
  • Any number × 1 is that same number.
  • Any number × 0 is 0.
Worked example 3.1.1
The picture shows 4 plates. Each plate has 6 biscuits. Write the total number of biscuits as an addition and as a multiplication.

Key words. Multiplication is a quick way to add equal groups. A group is a set of things together.

Method. Count the groups and how many are in each group. All the groups are equal, so you can add them up or multiply.

  1. Count the groups. Each plate is one group.
    There are 4 plates.
  2. Count how many are in each group. The groups are equal, so count in one group only.
    Each plate has 6 biscuits.
  3. Write it as an addition. Equal groups can be added.
    6 + 6 + 6 + 6 = 24
  4. Write it as a multiplication. 4 groups of 6 is 4 × 6.
    4 × 6 = 24

Check. Count in 6s: 6, 12, 18, 24. The last number is 24. ✓

Watch out. The first number says how many groups. The second number says how many in each group.

Worked example 3.1.2
The array shows 5 rows of 7 dots. Write two multiplication facts and find the total.

Key words. An array is dots or objects in rows and columns. Rows go across and columns go down.

Method. Count the rows and the columns. An array with r rows and c dots in each row has r × c dots.

  1. Count the rows. Rows go across.
    There are 5 rows.
  2. Count the columns. Columns go down. Each row has the same number of dots.
    There are 7 columns.
  3. Write the multiplication. 5 rows of 7 is 5 × 7. Count in 7s, 5 times.
    7, 14, 21, 28, 35
    5 × 7 = 35
  4. Turn the array on its side. Now there are 7 rows of 5. The total is the same.
    7 × 5 = 35

Check. Count in 5s instead: 5, 10, 15, 20, 25, 30, 35. ✓

Watch out. The total is the same both ways round, but the sentence is different. 3 rows of 4 is 3 × 4.

Worked example 3.1.3
Mei knows that 4 × 9 = 36. What is 9 × 4? Explain how you know.

Key words. Commutative means you can swap the order and the answer stays the same.

Method. Multiplication can be done in either order, so 9 × 4 has the same answer as 4 × 9.

  1. Write down the fact Mei knows.
    4 × 9 = 36
  2. Swap the numbers round. 4 groups of 9 and 9 groups of 4 have the same total. You can see this by turning an array on its side.
    9 × 4 = 4 × 9
  3. Write the answer.
    9 × 4 = 36

Check. Count in 9s four times: 9, 18, 27, 36. ✓

Watch out. Swapping the order works for multiplication. It does not work for subtraction or division.

Worked example 3.1.4
Work out 7 × 1.

Method. Multiplying by 1 leaves the number the same.

  1. Swap the numbers round. Order does not matter in multiplication, so 7 × 1 = 1 × 7. Use the 1 times table trick.
    7 × 1 = 1 × 7
  2. Say what the multiplication means. 1 group of 7 is just 7.
    1 group of 7 = 7
  3. Write the answer.
    7 × 1 = 7

Check. 7 groups of 1, or 1 groups of 7: both are 7. ✓

Watch out. Multiplying by 1 does not change the number. It does not make it 0 or 1.

Worked example 3.1.5
Work out 9 × 0.

Method. Zero groups, or groups with nothing in them, always make 0 in total.

  1. Swap the numbers round. Order does not matter in multiplication, so 9 × 0 = 0 × 9. Use the 0 times table trick.
    9 × 0 = 0 × 9
  2. Say what the multiplication means. 0 × 9 means 0 groups of 9. There are no groups, so there is nothing.
    0 groups of 9 = 0
  3. Write the answer. Anything multiplied by 0 is 0.
    9 × 0 = 0

Check. Adding groups: 0 + 0 + ... = 0. ✓

Watch out. Do not write the other number. Multiplying by 0 always gives 0, not the number you started with.

Worked example 3.1.6
Fill in the missing numbers on the number line. Then say what 6 × 4 is.
0+44+48+4?+416+4?+424

Method. Each hop is 4. Add 4 to the number before each box. The last number on the line is 6 × 4.

  1. Find the size of each hop. The labels at the start show it.
    0 to 4: each hop is 4.
  2. Fill the boxes. Add 4 to the number before the box.
    12 + 4 = 16
    20 is the next number, and 20 + 4 = 24
  3. Say what 6 × 4 is. There are 6 hops, so the last number is 6 × 4.
    6 × 4 = 24

Check. Count in 4s: 4, 8, 12, 16, 20, 24. Six numbers. ✓

Watch out. There are 6 hops but 7 numbers on the line, because the line starts at 0.

Watch out

Be careful with 0 and 1. 7 × 1 is 7 (not 1) and 7 × 0 is 0 (not 7). Also, do not mix up rows and columns: 3 rows of 4 is 3 × 4, and 4 rows of 3 is 4 × 3. The answer is the same, but they are different pictures.

Exercise 3A  Groups, arrays, swapping and multiplying by 0 and 1

Non-calculator
1
FEach picture shows equal groups of dots. Write a multiplication for each picture and work out the total.
(a)
(b)
(c)
(d)
2
FEach picture shows an array. Write two multiplication facts and the total for each array.
(a)
(b)
(c)
(d)
3
FWrite each repeated addition as a multiplication and find the total.
(a) 7 + 7 + 7 + 7    (b) 5 + 5 + 5 + 5 + 5 + 5    (c) 9 + 9 + 9    (d) 10 + 10 + 10 + 10 + 10
(a)7 + 7 + 7 + 7
(b)5 + 5 + 5 + 5 + 5 + 5
(c)9 + 9 + 9
(d)10 + 10 + 10 + 10 + 10
4
FWrite the missing numbers in each sequence.
(a)Count in 3s: 3,  6,  ?,  12,  ?,  18
(b)Count in 4s: 4,  ?,  12,  ?,  20,  24
(c)Count in 5s: 5,  10,  15,  ?,  25,  ?,  35,  ?
(d)Count in 2s: 2,  4,  ?,  8,  ?,  12,  ?,  16
5
FUse the fact that you can multiply in any order. Write the missing numbers.
(a)6 × 4 = 4 × ?
(b)7 × ? = 9 × 7
(c)? × 8 = 8 × 3
(d)5 × 12 = ? × 5
6
FQuick-fire! Write the answers.
(a)7 × 1 =
(b)0 × 9 =
(c)1 × 12 =
(d)12 × 0 =
(e)1 × 1 =
(f)8 × 0 =
7
FQuick-fire! Write the answers. These are tables you know.
(a)3 × 2 =
(b)5 × 4 =
(c)10 × 6 =
(d)2 × 9 =
(e)5 × 7 =
(f)10 × 10 =
(g)4 × 5 =
(h)2 × 8 =
8
PSA box holds 6 eggs. How many eggs are in 5 boxes?
66666?
9
PSA spider has 8 legs. How many legs do 4 spiders have altogether?
8888?
10
RZainab sees 3 rows of chairs with 8 chairs in each row. She says, “3 + 8 = 11, so there are 11 chairs.” Zainab has made a mistake. Find her mistake and write the correct number of chairs.
11
RAlways, sometimes or never?   When you multiply a number by 1, the answer is the same number.
12
RWhich one is the odd one out?   A  4 × 6    B  6 × 4    C  4 + 6    D  2 × 12
13
RAmira says, “9 × 0 = 9, because there are nine of something.” Is Amira right? Explain.
14
RDraw as many different rectangular arrays as you can with exactly 12 dots in rows and columns. Write a multiplication fact for each. How many are there if turning an array counts as a different array?
1 × 122 × 63 × 4
3.2

The 2, 4, 8, 5 and 10 times tables

Year 4
2, 4, 5, 8 and 10 times tables up to 12 × 12

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: The 2, 4, 8, 5 and 10 times tablesComing soon

You already know many of these tables from Year 3. Now we go all the way up to 12 × 12, and we use tricks so that you can work out any fact quickly. The first set of tricks uses doubling, halving and tens.

The 2 times table: double. Multiplying by 2 is the same as doubling. 2 × 7 means 7 + 7 = 14. Every answer in the 2 times table is an even number.

2 × 122 × 242 × 362 × 482 × 5102 × 6122 × 7142 × 8162 × 9182 × 10202 × 11222 × 1224
The 2 times table. Every answer is a double.

The 10 times table: move the digits. Multiplying by 10 makes every digit ten times bigger, so every digit moves one place to the left and a 0 goes in the ones place. 10 × 7 = 70. 10 × 12 = 120 (12 tens). Every answer in the 10 times table ends in 0.

10 × 11010 × 22010 × 33010 × 44010 × 55010 × 66010 × 77010 × 88010 × 99010 × 1010010 × 1111010 × 12120
The 10 times table.

The 5 times table: half of the 10 times table. 5 is half of 10, so 5 × 8 is half of 10 × 8. 10 × 8 = 80 and half of 80 is 40. So 5 × 8 = 40. Every answer in the 5 times table ends in 0 or 5.

5 × 155 × 2105 × 3155 × 4205 × 5255 × 6305 × 7355 × 8405 × 9455 × 10505 × 11555 × 1260
The 5 times table. The last digit goes 5, 0, 5, 0...

The 4 times table: double double. 4 × 7: double 7 is 14, and double 14 is 28. So 4 × 7 = 28. The 8 times table: double double double. 8 × 7: double 7 is 14, double 14 is 28, double 28 is 56. So 8 × 7 = 56. The answers in the 4 and 8 times tables are always even.

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100
Multiples of 4
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100
Multiples of 8
On a hundred square, the 8s are some of the 4s. Every number in the 8 times table is also in the 4 times table.

Key words. To double a number is to multiply it by 2. To halve a number is to share it into 2 equal parts. A multiple of a number is an answer in its times table, such as 8, 16, 24 for 8.

Key ideas

  • × 2: double the number.
  • × 10: move every digit one place to the left (10 × 12 = 120).
  • × 5: find × 10 first, then halve it.
  • × 4: double, then double again.
  • × 8: double three times.
  • Use commutativity: 12 × 5 = 5 × 12, so use the table you know best.
Worked example 3.2.1
Work out 12 × 2.

Method. Multiplying by 2 is the same as doubling. Double the number.

  1. Swap the numbers round. Order does not matter in multiplication, so 12 × 2 = 2 × 12. Use the 2 times table trick.
    12 × 2 = 2 × 12
  2. Double the number. Doubling means adding the number to itself.
    double 10 = 20, double 2 = 4, so 20 + 4 = 24
  3. Write the answer.
    12 × 2 = 24

Check. Check by dividing: 24 ÷ 2 = 12. ✓

Watch out. Doubling is not adding 2. To double 7, add 7 + 7, not 7 + 2.

Worked example 3.2.2
Work out 11 × 10.

Method. To multiply by 10, every digit moves one place to the left. The ones become tens.

  1. Swap the numbers round. Order does not matter in multiplication, so 11 × 10 = 10 × 11. Use the 10 times table trick.
    11 × 10 = 10 × 11
  2. Think about tens. 10 × 11 means 11 lots of 10, which is 11 tens.
    11 tens
  3. Move the digits one place to the left. A tens column needs a 0 in the ones place.
    11 → 110
  4. Write the answer.
    11 × 10 = 110

Check. Check by dividing: 110 ÷ 10 = 11. ✓

Watch out. The 10 times table has a 0 in the ones place every time. Put the 0 on the end, but think “tens” so you understand why.

Worked example 3.2.3
Work out 9 × 5.

Method. Five is half of ten. Multiply by 10 first, then halve the answer.

  1. Swap the numbers round. Order does not matter in multiplication, so 9 × 5 = 5 × 9. Use the 5 times table trick.
    9 × 5 = 5 × 9
  2. Multiply by 10. This is easy: move the digits one place to the left.
    10 × 9 = 90
  3. Halve the answer. 5 is half of 10, so 5 lots of a number is half of 10 lots.
    half of 80 = 40, half of 10 = 5, so 40 + 5 = 45
  4. Write the answer. Answers in the 5 times table end in 0 or 5.
    9 × 5 = 45

Check. The digits of 45 add up to 9: 4 + 5 = 9. ✓

Watch out. Halve the answer to 10 × the number. Do not halve the number before you multiply by 10 and then forget to multiply.

Worked example 3.2.4
Work out 7 × 4.

Method. Four is double double. Double the number, then double the answer.

  1. Swap the numbers round. Order does not matter in multiplication, so 7 × 4 = 4 × 7. Use the 4 times table trick.
    7 × 4 = 4 × 7
  2. Double the number. This gives 2 lots.
    7 + 7 = 14
  3. Double the answer again. Doubling twice gives 4 lots.
    double 10 = 20, double 4 = 8, so 20 + 8 = 28
  4. Write the answer.
    7 × 4 = 28

Check. Check by dividing: 28 ÷ 4 = 7. ✓

Watch out. You must double twice. Doubling once gives the 2 times table.

Worked example 3.2.5
Work out 12 × 4.

Method. Four is double double. Double the number, then double the answer.

  1. Swap the numbers round. Order does not matter in multiplication, so 12 × 4 = 4 × 12. Use the 4 times table trick.
    12 × 4 = 4 × 12
  2. Double the number. This gives 2 lots.
    double 10 = 20, double 2 = 4, so 20 + 4 = 24
  3. Double the answer again. Doubling twice gives 4 lots.
    double 20 = 40, double 4 = 8, so 40 + 8 = 48
  4. Write the answer.
    12 × 4 = 48

Check. Check by dividing: 48 ÷ 4 = 12. ✓

Watch out. You must double twice. Doubling once gives the 2 times table.

Worked example 3.2.6
Work out 6 × 8.

Method. Eight is double double double. Double the number three times.

  1. Swap the numbers round. Order does not matter in multiplication, so 6 × 8 = 8 × 6. Use the 8 times table trick.
    6 × 8 = 8 × 6
  2. Double once. This gives 2 lots.
    6 + 6 = 12
  3. Double again. This gives 4 lots.
    double 10 = 20, double 2 = 4, so 20 + 4 = 24
  4. Double a third time. This gives 8 lots.
    double 20 = 40, double 4 = 8, so 40 + 8 = 48
  5. Write the answer.
    6 × 8 = 48

Check. Check by dividing: 48 ÷ 6 = 8. ✓

Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.

Worked example 3.2.7
Work out 12 × 8.

Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.

  1. Multiply by 10. Move the digits one place to the left.
    10 × 8 = 80
  2. Multiply by 2. Double the number.
    8 + 8 = 16
  3. Add the two answers together. 12 = 10 + 2.
    80 + 16 = 96
  4. Write the answer.
    12 × 8 = 96

Check. Check by dividing: 96 ÷ 8 = 12. ✓

Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.

Watch out

Doubling is not adding 2. To double 7 you add 7 + 7 = 14. Also, for the 5 times table, find 10 × the number first, then halve it. And for the 4 and 8 times tables, count your doubles: two doubles for 4, three doubles for 8.

Exercise 3B  The 2, 4, 5, 8 and 10 times tables

Non-calculator
1
FQuick-fire! The 2 and 10 times tables.
(a)2 × 6 =
(b)10 × 7 =
(c)2 × 11 =
(d)10 × 12 =
(e)9 × 2 =
(f)10 × 9 =
(g)12 × 2 =
(h)4 × 10 =
(i)10 × 11 =
(j)2 × 8 =
2
FQuick-fire! The 5 times table.
(a)5 × 6 =
(b)5 × 9 =
(c)5 × 11 =
(d)7 × 5 =
(e)5 × 12 =
(f)8 × 5 =
(g)5 × 4 =
(h)3 × 5 =
(i)5 × 10 =
(j)5 × 7 =
3
FQuick-fire! The 4 times table. Double and double again.
(a)4 × 6 =
(b)4 × 9 =
(c)7 × 4 =
(d)4 × 11 =
(e)4 × 12 =
(f)8 × 4 =
(g)4 × 3 =
(h)5 × 4 =
4
FQuick-fire! The 8 times table. Double three times.
(a)8 × 6 =
(b)8 × 9 =
(c)7 × 8 =
(d)8 × 11 =
(e)8 × 12 =
(f)8 × 8 =
(g)8 × 3 =
(h)4 × 8 =
5
FMixed quick-fire! Choose the best trick for each one.
(a)8 × 7 =
(b)12 × 5 =
(c)4 × 8 =
(d)10 × 8 =
(e)6 × 4 =
(f)9 × 8 =
(g)2 × 12 =
(h)11 × 5 =
(i)12 × 4 =
(j)5 × 8 =
(k)7 × 10 =
(l)8 × 2 =
6
FFind the missing number in each sum.
(a)8 × ? = 56
(b)? × 4 = 36
(c)5 × ? = 45
(d)? × 10 = 120
(e)4 × ? = 48
(f)? × 8 = 72
7
FThe number line shows counting in 8s. Write the missing numbers.
0+88+8?+824+832+8?+848+8?+864
8
PSStart with 7. Double it. Double the answer. Double that answer again. What number do you get? Which times table fact is this?
9
PSPens come in packs of 4. Amira buys 9 packs. How many pens does she buy?
444444444?
10
PSA cinema ticket costs £5. Noah buys 8 tickets. How much does he spend?
£5£5£5£5£5£5£5£5?
11
PSThere are 12 boxes of pencils. Each box has 8 pencils. How many pencils are there altogether?
888888888888?
12
RNoor says, “8 × 6 is double 4 × 6.” Is Noor right? Show how you know.
13
RAlways, sometimes or never?
(a)A number in the 10 times table ends in 0.
(b)A number in the 5 times table ends in 5.
14
RI am a number in the 4 times table and in the 5 times table. I am between 30 and 50. What number am I?
3.3

The 3, 6, 9 and 12 times tables

Year 4
3, 6, 9 and 12 times tables up to 12 × 12

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: The 3, 6, 9 and 12 times tablesComing soon

These tables are a bit harder, but each one has a good trick.

The 3 times table: double and one more. 3 × 7: double 7 is 14, and one more 7 makes 21. So 3 × 7 = 21. A pattern to spot: the digits of every answer add up to 3, 6 or 9. For example, 24 gives 2 + 4 = 6, and 33 gives 3 + 3 = 6.

3 × 133 × 263 × 393 × 4123 × 5153 × 6183 × 7213 × 8243 × 9273 × 10303 × 11333 × 1236
The 3 times table.

The 6 times table: 5 lots and one more. 6 × 7: 5 × 7 = 35, and one more 7 makes 42. You can also double the 3 times table: 3 × 7 = 21, and double 21 is 42. Every answer in the 6 times table is even.

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100
Multiples of 3
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100
Multiples of 6
Every multiple of 6 is also a multiple of 3, but not the other way round.

The 9 times table: ten lots, take away one lot. 9 × 7: 10 × 7 = 70, and 70 − 7 = 63. Look for the pattern in the answers: the tens digit goes up by 1 each time and the ones digit goes down by 1. The two digits always add up to 9.

9 × 1 =099 × 2 =189 × 3 =279 × 4 =369 × 5 =459 × 6 =549 × 7 =639 × 8 =729 × 9 =819 × 10 =90tens digit goes up by 1ones digit goes down by 1tens + ones = 9(except 9 × 10 = 90)
The 9 times table up to 9 × 10: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90.

The finger trick for 9 × 1 to 9 × 10. Hold up all ten fingers and number them 1 to 10 from the left. To work out 9 × 7, fold down finger 7. There are 6 fingers on the left (6 tens) and 3 fingers on the right (3 ones). The answer is 63.

12345678910tens: 6ones: 3Finger 7 is folded down. Left of it: 6. Right of it: 3.
9 × 7 = 63: 6 fingers on the left and 3 on the right of the folded finger.

The 12 times table: ten lots and two lots. 12 × 7: 10 × 7 = 70 and 2 × 7 = 14, so 70 + 14 = 84. A dozen is 12, so a dozen eggs is 12 eggs.

12 × 11212 × 22412 × 33612 × 44812 × 56012 × 67212 × 78412 × 89612 × 910812 × 1012012 × 1113212 × 12144
The 12 times table.

Key ideas

  • × 3: double the number, then add the number once more.
  • × 6: do × 5 and add one more group (or double the 3 times table).
  • × 9: do × 10, then take away the number once. The digits of the answer add up to 9.
  • × 12: do × 10 and × 2, then add.
  • Finger trick for 9s: fold down the finger you are multiplying by. Fingers on the left are tens, fingers on the right are ones.
Worked example 3.3.1
Work out 3 × 8.

Method. Three is double and one more. Double the number, then add the number once.

  1. Double the number. This gives 2 lots.
    8 + 8 = 16
  2. Add one more group. 3 = 2 + 1, so add the number once more.
    16 + 8 = 24
  3. Write the answer.
    3 × 8 = 24

Check. Check by dividing: 24 ÷ 3 = 8. ✓

Watch out. Add the number itself, not 3, as the extra group.

Worked example 3.3.2
Work out 7 × 6.

Method. Six is five and one more. Work out 5 lots, then add one more group.

  1. Swap the numbers round. Order does not matter in multiplication, so 7 × 6 = 6 × 7. Use the 6 times table trick.
    7 × 6 = 6 × 7
  2. Work out 5 lots. The 5 times table is half of the 10 times table: 70 halved.
    5 × 7 = 35
  3. Add one more group. 6 = 5 + 1, so add the number once more.
    35 + 7 = 42
  4. Write the answer.
    7 × 6 = 42

Check. Check by dividing: 42 ÷ 6 = 7. ✓

Watch out. Add one more group, not six more. 6 lots = 5 lots + 1 lot.

Worked example 3.3.3
Work out 9 × 6.

Method. Nine is one less than ten. Multiply by 10, then take away one group.

  1. Multiply by 10. 10 lots of the number first.
    10 × 6 = 60
  2. Take away one group. 9 = 10 − 1, so take away the number itself once.
    60 − 6 = 54
  3. Write the answer. Answers in the 9 times table have digits that add up to 9 (or 18).
    9 × 6 = 54

Check. The digits of 54 add up to 9: 5 + 4 = 9. ✓

Watch out. Take away 6, the other number, not 9. For 9 × 6 you work out 10 × 6 − 6.

Worked example 3.3.4
Work out 9 × 11.

Method. Eleven is ten and one more. Multiply by 10, then add one more group.

  1. Swap the numbers round. Order does not matter in multiplication, so 9 × 11 = 11 × 9. Use the 11 times table trick.
    9 × 11 = 11 × 9
  2. Multiply by 10. 10 lots of the number first.
    10 × 9 = 90
  3. Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 99.
    90 + 9 = 99
  4. Write the answer.
    9 × 11 = 99

Check. The digits of 99 add up to 9: 9 + 9 = 18. ✓

Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.

Worked example 3.3.5
Work out 12 × 7.

Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.

  1. Multiply by 10. Move the digits one place to the left.
    10 × 7 = 70
  2. Multiply by 2. Double the number.
    7 + 7 = 14
  3. Add the two answers together. 12 = 10 + 2.
    70 + 14 = 84
  4. Write the answer.
    12 × 7 = 84

Check. Check by dividing: 84 ÷ 7 = 12. ✓

Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.

Worked example 3.3.6
Work out 12 × 6.

Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.

  1. Multiply by 10. Move the digits one place to the left.
    10 × 6 = 60
  2. Multiply by 2. Double the number.
    6 + 6 = 12
  3. Add the two answers together. 12 = 10 + 2.
    60 + 12 = 72
  4. Write the answer.
    12 × 6 = 72

Check. Check by dividing: 72 ÷ 6 = 12. ✓

Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.

Worked example 3.3.7
Use the finger trick to work out 9 × 7.

Method. Hold up all ten fingers. Fold down the finger that matches the number you are multiplying 9 by. The fingers either side give the answer.

  1. Hold up ten fingers and number them 1 to 10. Number the fingers from left to right. Fold down finger 7.
    12345678910tens: 6ones: 3Finger 7 is folded down. Left of it: 6. Right of it: 3.
  2. Count the fingers on the left of the folded finger. This is the number of tens.
    6 fingers on the left = 6 tens
  3. Count the fingers on the right of the folded finger. This is the number of ones.
    3 fingers on the right = 3 ones
  4. Write the tens and ones together.
    9 × 7 = 63

Check. Use the other method: 10 × 7 = 70, then 70 − 7 = 63. ✓

Watch out. The folded finger is not counted. Count only the fingers that are still up.

Worked example 3.3.8
Is 54 in the 9 times table? Add the digits to find out.

Method. Add up the digits. If they make 9 (or add to 9 again), the number is in the 9 times table.

  1. Split the number into digits. The digit test looks at each digit on its own.
    5,  4
  2. Add the digits. Every number in the 9 times table has digits that add up to 9 (or to 18, which adds to 9 again).
    5 + 4 = 9
  3. Decide. The digits add up to 9.
    Yes, 54 is in the 9 times table.

Check. 9 × 6 = 54. ✓

Watch out. Add the digits and look for 9. It is not enough for the digits to be big or for the number to be odd.

Watch out

For the 9 times table, take away the other number, not 9. 9 × 6 is 60 − 6 = 54, not 60 − 9. For the 6 times table add one more group to the 5 times table, not six more. And for the finger trick, do not count the folded finger.

Exercise 3C  The 3, 6, 9 and 12 times tables

Non-calculator
1
FQuick-fire! The 3 times table. Double and add one more.
(a)3 × 4 =
(b)3 × 6 =
(c)7 × 3 =
(d)3 × 9 =
(e)3 × 11 =
(f)12 × 3 =
(g)3 × 8 =
(h)5 × 3 =
(i)3 × 10 =
(j)3 × 12 =
2
FQuick-fire! The 6 times table.
(a)6 × 4 =
(b)6 × 6 =
(c)7 × 6 =
(d)6 × 9 =
(e)6 × 11 =
(f)12 × 6 =
(g)8 × 6 =
(h)6 × 5 =
(i)6 × 10 =
(j)6 × 3 =
3
FQuick-fire! The 9 times table. Use × 10 and take away.
(a)9 × 3 =
(b)9 × 6 =
(c)7 × 9 =
(d)9 × 9 =
(e)9 × 11 =
(f)12 × 9 =
(g)9 × 8 =
(h)5 × 9 =
(i)9 × 10 =
(j)9 × 4 =
4
FQuick-fire! The 12 times table. Use × 10 and × 2.
(a)12 × 3 =
(b)12 × 6 =
(c)7 × 12 =
(d)12 × 9 =
(e)12 × 11 =
(f)12 × 12 =
(g)8 × 12 =
(h)12 × 4 =
5
FMixed quick-fire!
(a)3 × 7 =
(b)6 × 8 =
(c)9 × 7 =
(d)12 × 8 =
(e)3 × 12 =
(f)6 × 6 =
(g)9 × 5 =
(h)12 × 10 =
(i)7 × 6 =
(j)11 × 9 =
(k)4 × 12 =
(l)8 × 3 =
6
FFind the missing number in each sum.
(a)3 × ? = 27
(b)? × 6 = 48
(c)9 × ? = 72
(d)? × 12 = 96
(e)6 × ? = 54
(f)? × 3 = 33
7
FUse the finger trick to work out each answer.
(a)9 × 4
(b)9 × 6
(c)9 × 8
(d)9 × 9
8
FWrite the missing numbers in the 9 times table.   9,  18,  27,  ?,  45,  ?,  63,  ?,  81,  90
9
FIs each number in the 9 times table? Add the digits to find out. Write Yes or No.
(a)45
(b)54
(c)62
(d)72
(e)85
(f)36
10
PSA box has a dozen eggs. A shop has 6 boxes. How many eggs is that?
121212121212?
11
PSA concert ticket costs £9. A family buys 7 tickets. How much do the tickets cost altogether?
£9£9£9£9£9£9£9?
12
PSA tricycle has 3 wheels. There are 11 tricycles in a playground. How many wheels is that altogether?
33333333333?
13
RAisha works out 9 × 6 like this: “10 × 6 = 60. 60 − 9 = 51.” Her answer is wrong. What mistake did she make? What is the correct answer?
14
RTom says, “Every answer in the 6 times table is an even number.” Prove it.
15
RWhich one is the odd one out? Explain.   18    27    36    40    45
16
RI am in the 3 times table and in the 4 times table. I am between 20 and 30. What number am I?
3.4

The 7 and 11 times tables, square numbers and the whole grid

Year 4
7 and 11 times tables, Square numbers, The 12 × 12 grid

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: The 7 and 11 times tables, square numbers and the whole gridComing soon

The 7 times table. This is often called the hardest table, but you already know almost all of it! 7 × 2, 7 × 3, 7 × 4, 7 × 5, 7 × 9, 7 × 10 and 7 × 12 come from tricks you know. The ones to practise are 6 × 7 = 42, 7 × 7 = 49 and 7 × 8 = 56. To remember 56 = 7 × 8, notice the digits in order: 5, 6, 7, 8. If you forget a fact, build it: 7 × 7 = 5 × 7 + 2 × 7 = 35 + 14 = 49.

7 × 177 × 2147 × 3217 × 4287 × 5357 × 6427 × 7497 × 8567 × 9637 × 10707 × 11777 × 1284
The 7 times table.

The 11 times table. From 11 × 1 to 11 × 9, write the digit twice: 11 × 4 = 44 and 11 × 7 = 77. After that, use ten lots and one more lot: 11 × 10 = 110, 11 × 11 = 110 + 11 = 121 and 11 × 12 = 120 + 12 = 132.

11 × 11111 × 22211 × 33311 × 44411 × 55511 × 66611 × 77711 × 88811 × 99911 × 1011011 × 1112111 × 12132
The 11 times table.

Square numbers. When you multiply a number by itself, such as 5 × 5 = 25, the dots in the array make a perfect square. 1, 4, 9, 16, 25, ... are called square numbers. The first twelve are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144.

1×1=12×2=43×3=94×4=165×5=256×6=367×7=498×8=64
The first eight square numbers drawn as arrays. Each array has the same number of rows and columns.

The whole grid. Here is the complete multiplication grid up to 12 × 12. The square numbers form a diagonal line (orange). The grid is a mirror image across this line, because 7 × 8 = 8 × 7 (blue). There are 144 facts in the grid, but because of commutativity only 78 of them are different. And you already know all of the × 0, × 1, × 2, × 5 and × 10 facts.

×123456789101112112345678910111222468101214161820222433691215182124273033364481216202428323640444855101520253035404550556066121824303642485460667277142128354249566370778488162432404856647280889699182736455463728190991081010203040506070809010011012011112233445566778899110121132121224364860728496108120132144
The 12 × 12 grid. Orange = square numbers. Blue = 7 × 8 and 8 × 7, the same fact.

Key words. A square number is what you get when you multiply a whole number by itself. A grid is rows and columns of boxes.

Key ideas

  • × 7: 5 lots + 2 lots. Learn 6 × 7 = 42, 7 × 7 = 49 and 7 × 8 = 56 (5, 6, 7, 8).
  • × 11 (up to 11 × 9): write the digit twice. After that: × 10 and add one more lot.
  • Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
  • There are 144 facts in the grid but only 78 different ones, because 7 × 8 = 8 × 7.
Worked example 3.4.1
Work out 6 × 7.

Method. Six is five and one more. Work out 5 lots, then add one more group.

  1. Work out 5 lots. The 5 times table is half of the 10 times table: 70 halved.
    5 × 7 = 35
  2. Add one more group. 6 = 5 + 1, so add the number once more.
    35 + 7 = 42
  3. Write the answer.
    6 × 7 = 42

Check. Check by dividing: 42 ÷ 6 = 7. ✓

Watch out. Add one more group, not six more. 6 lots = 5 lots + 1 lot.

Worked example 3.4.2
Work out 7 × 7.

Method. Seven is five and two. Work out 5 lots and 2 lots, then add them.

  1. Work out 5 lots. The 5 times table is half of the 10 times table.
    5 × 7 = 35
  2. Work out 2 lots. Double the number.
    7 + 7 = 14
  3. Add them. 7 = 5 + 2.
    35 + 14 = 49
  4. Write the answer.
    7 × 7 = 49

Check. Check by dividing: 49 ÷ 7 = 7. ✓

Watch out. Do not forget the 2 lots. 7 lots = 5 lots + 2 lots.

Worked example 3.4.3
Work out 7 × 8.

Method. Eight is double double double. Double the number three times.

  1. Swap the numbers round. Order does not matter in multiplication, so 7 × 8 = 8 × 7. Use the 8 times table trick.
    7 × 8 = 8 × 7
  2. Double once. This gives 2 lots.
    7 + 7 = 14
  3. Double again. This gives 4 lots.
    double 10 = 20, double 4 = 8, so 20 + 8 = 28
  4. Double a third time. This gives 8 lots.
    double 20 = 40, double 8 = 16, so 40 + 16 = 56
  5. Write the answer.
    7 × 8 = 56

Check. Check by dividing: 56 ÷ 7 = 8. ✓

Watch out. Count your doubles. Three doubles give 8 lots. Two doubles only give 4.

Worked example 3.4.4
Work out 12 × 7.

Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.

  1. Multiply by 10. Move the digits one place to the left.
    10 × 7 = 70
  2. Multiply by 2. Double the number.
    7 + 7 = 14
  3. Add the two answers together. 12 = 10 + 2.
    70 + 14 = 84
  4. Write the answer.
    12 × 7 = 84

Check. Check by dividing: 84 ÷ 7 = 12. ✓

Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.

Worked example 3.4.5
Work out 11 × 6.

Method. Eleven is ten and one more. Multiply by 10, then add one more group.

  1. Multiply by 10. 10 lots of the number first.
    10 × 6 = 60
  2. Add one more group. 11 = 10 + 1, so add the number itself once more. You can also write the digit twice: 66.
    60 + 6 = 66
  3. Write the answer.
    11 × 6 = 66

Check. Check by dividing: 66 ÷ 6 = 11. ✓

Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.

Worked example 3.4.6
Work out 11 × 12.

Method. Eleven is ten and one more. Multiply by 10, then add one more group.

  1. Multiply by 10. 10 lots of the number first.
    10 × 12 = 120
  2. Add one more group. 11 = 10 + 1, so add the number itself once more.
    120 + 12 = 132
  3. Write the answer.
    11 × 12 = 132

Check. Check by dividing: 132 ÷ 11 = 12. ✓

Watch out. The “write the digit twice” trick only works from 11 × 1 to 11 × 9. For 11 × 12 it does not give 1212. Use 10 lots + 1 lot.

Worked example 3.4.7
Work out 12 × 12.

Method. Twelve is ten and two. Multiply by 10, multiply by 2, then add.

  1. Multiply by 10. Move the digits one place to the left.
    10 × 12 = 120
  2. Multiply by 2. Double the number.
    double 10 = 20, double 2 = 4, so 20 + 4 = 24
  3. Add the two answers together. 12 = 10 + 2.
    120 + 24 = 144
  4. Write the answer.
    12 × 12 = 144

Check. Check by dividing: 144 ÷ 12 = 12. ✓

Watch out. Do both parts, 10 lots and 2 lots, then add. Do not stop after 10 lots.

Worked example 3.4.8
Is 49 a square number? Use an array to explain.

Method. A square number makes a square array: the same number of rows and columns.

  1. Find a pair of equal numbers that multiply to 49. Try the times tables. 7 × 7 is 49.
    7 × 7 = 49
  2. Check the array. The array has 7 rows and 7 columns. It is a square.
    7 rows of 7 dots
  3. Answer.
    Yes. 49 is a square number because 7 × 7 = 49.

Check. The square numbers in order: 1, 4, 9, 16, 25, 36, 49, 64. ✓

Watch out. The array must be a square. 7 × 8 = 56 is a rectangle, not a square, so 56 is not a square number.

Watch out

The “write the digit twice” trick for 11 only works up to 11 × 9. 11 × 12 is not 1212. It is 120 + 12 = 132. Also, 7 × 8 is 56, not 54 or 58. If you forget a fact, build it from ones you know, such as 5 lots and 3 lots of 7.

Exercise 3D  The 7 and 11 times tables, squares and the grid

Non-calculator
1
FQuick-fire! The 7 times table.
(a)7 × 3 =
(b)7 × 6 =
(c)7 × 7 =
(d)7 × 8 =
(e)9 × 7 =
(f)7 × 11 =
(g)12 × 7 =
(h)7 × 4 =
(i)5 × 7 =
(j)10 × 7 =
2
FQuick-fire! The 11 times table.
(a)11 × 2 =
(b)11 × 5 =
(c)11 × 9 =
(d)3 × 11 =
(e)11 × 10 =
(f)11 × 11 =
(g)12 × 11 =
(h)7 × 11 =
(i)11 × 8 =
(j)4 × 11 =
3
FWrite each square number.
(a)3 × 3
(b)5 × 5
(c)6 × 6
(d)8 × 8
(e)9 × 9
(f)10 × 10
(g)11 × 11
(h)12 × 12
4
FQuick-fire! These are the trickiest facts.
(a)6 × 6 =
(b)6 × 7 =
(c)6 × 8 =
(d)7 × 7 =
(e)7 × 8 =
(f)8 × 8 =
(g)6 × 9 =
(h)7 × 9 =
(i)8 × 9 =
(j)9 × 9 =
(k)6 × 12 =
(l)8 × 12 =
5
FFind the missing number in each sum.
(a)7 × ? = 63
(b)? × 11 = 88
(c)8 × ? = 56
(d)? × 7 = 84
(e)12 × ? = 144
(f)? × 9 = 81
6
FPart of the multiplication grid is below. Work out the numbers in the boxes A, B, C and D.
×789642A547B56C85664D
(a)Box A: row 6, column 8
(b)Box B: row 7, column 7
(c)Box C: row 7, column 9
(d)Box D: row 8, column 9
7
FWrite all the square numbers that are between 30 and 100.
8
PSThere are 7 days in one week. How many days are there in 8 weeks?
77777777?
9
PSA football team has 11 players. There are 9 teams in a tournament. How many players are there altogether?
111111111111111111?
10
PSA square garden has 9 rows of 9 plants. How many plants are in the garden?
11
PSA pizza costs £7. Priya buys 6 pizzas for a party. How much do the pizzas cost altogether?
£7£7£7£7£7£7?
12
RRavi says, “7 × 8 = 54.” Show that Ravi is wrong. What is 7 × 8?
13
RAlways, sometimes or never?
(a)When you multiply 11 by a number from 1 to 9, both digits of the answer are the same.
(b)A square number is an even number.
14
RWhich one is the odd one out?   49    64    56    81
15
RThe 12 × 12 grid has 144 boxes. Because 7 × 8 = 8 × 7, many of the facts are repeats. How many different facts are in the grid? (3 × 4 and 4 × 3 count as the same fact.)
×123456789101112112345678910111222468101214161820222433691215182124273033364481216202428323640444855101520253035404550556066121824303642485460667277142128354249566370778488162432404856647280889699182736455463728190991081010203040506070809010011012011112233445566778899110121132121224364860728496108120132144
3.5

Division facts, fact families and missing numbers

Year 4
Division facts up to 12 × 12, Inverse operations and fact families, Dividing by 1, Missing number problems

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Division facts, fact families and missing numbersComing soon

Division is the inverse (opposite) of multiplication. It has two meanings. Sharing: 12 sweets are shared equally between 3 children, so each child gets 12 ÷ 3 = 4. Grouping: 12 sweets are put into bags of 3, so there are 12 ÷ 3 = 4 bags. Both are the same calculation.

12 ÷ 3 = 4. Sharing 12 between 3 groups gives 4 in each group.

The best way to divide is to use the times tables. To work out 56 ÷ 7, think: 7 times what is 56? You know 7 × 8 = 56, so 56 ÷ 7 = 8. The tricks work backwards too: to divide by 2 halve, to divide by 4 halve twice, to divide by 8 halve three times, to divide by 10 move the digits one place to the right.

Fact families. Three numbers can make four facts. The array below has 4 rows and 6 columns, so it shows 4 × 6 = 24 and 6 × 4 = 24. If you split the 24 dots into 4 equal rows you get 6 in each row, so 24 ÷ 4 = 6. If you split them into 6 equal columns you get 4, so 24 ÷ 6 = 4. In the fact triangle, the product is always at the top.

24 dots in an array
2446
Fact triangle
4 × 6 = 24   6 × 4 = 24   24 ÷ 4 = 6   24 ÷ 6 = 4

Special cases. Any number divided by 1 stays the same: 9 ÷ 1 = 9. Any number divided by itself is 1: 9 ÷ 9 = 1. 0 divided by any number is 0: 0 ÷ 6 = 0. But you can never divide by 0. There is no answer to 6 ÷ 0.

Missing number problems. Use the inverse. For ? ÷ 6 = 7, the opposite of dividing by 6 is multiplying by 6, so ? = 7 × 6 = 42. For 54 ÷ ? = 6, ask: how many 6s make 54? That is 54 ÷ 6 = 9.

Key words. The inverse of a calculation undoes it. A fact family is the multiplication and division facts that use the same three numbers.

Key ideas

  • Division is the inverse of multiplication: if 7 × 8 = 56 then 56 ÷ 7 = 8.
  • To work out 56 ÷ 7, ask “7 times what is 56?”
  • Three numbers make a fact family: 2 multiplication facts and 2 division facts.
  • A number ÷ 1 is the same number. A number ÷ itself is 1. 0 ÷ a number is 0.
  • You can never divide by 0.
  • Missing numbers: use the opposite operation.
Worked example 3.5.1
Work out 56 ÷ 7.

Method. Use the 7 times table. Count up in 7s until you reach 56.

  1. Turn the division into a missing multiplication. 56 ÷ 7 asks: what do we multiply 7 by to get 56?
    56 ÷ 7 = ? means ? × 7 = 56
  2. Count up in 7s until you reach 56. Each number you say is one more group of 7.
    7, 14, 21, 28, 35, 42, 49, 56
  3. Count how many numbers you said. The number of jumps is the answer.
    I said 8 numbers, so 8 × 7 = 56
  4. Write the answer.
    56 ÷ 7 = 8

Check. Multiply back: 8 × 7 = 56. ✓

Watch out. Know your 7 times table facts, then division is quick.

Worked example 3.5.2
Work out 96 ÷ 8.

Method. Dividing by 8 is halving three times.

  1. Turn the division into a missing multiplication. 96 ÷ 8 asks: what do we multiply 8 by to get 96?
    96 ÷ 8 = ? means ? × 8 = 96
  2. Halve the number. 8 = 2 × 2 × 2, so we halve three times.
    half of 80 = 40, half of 16 = 8, so 40 + 8 = 48
  3. Halve again.
    half of 40 = 20, half of 8 = 4, so 20 + 4 = 24
  4. Halve a third time.
    half of 20 = 10, half of 4 = 2, so 10 + 2 = 12
  5. Write the answer.
    96 ÷ 8 = 12

Check. Multiply back: 12 × 8 = 96. ✓

Watch out. Count your halves. Three halves divide by 8.

Worked example 3.5.3
Work out 132 ÷ 11.

Method. Use the 11 times table. Count up in 11s until you reach 132.

  1. Turn the division into a missing multiplication. 132 ÷ 11 asks: what do we multiply 11 by to get 132?
    132 ÷ 11 = ? means ? × 11 = 132
  2. Count up in 11s until you reach 132. Each number you say is one more group of 11.
    11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132
  3. Count how many numbers you said. The number of jumps is the answer.
    I said 12 numbers, so 12 × 11 = 132
  4. Write the answer.
    132 ÷ 11 = 12

Check. Multiply back: 12 × 11 = 132. ✓

Watch out. Know your 11 times table facts, then division is quick.

Worked example 3.5.4
Work out 35 ÷ 5.

Method. To divide by 5, double the number first and then divide by 10.

  1. Turn the division into a missing multiplication. 35 ÷ 5 asks: what do we multiply 5 by to get 35?
    35 ÷ 5 = ? means ? × 5 = 35
  2. Double the number. Doubling then dividing by 10 is the same as dividing by 5.
    double 30 = 60, double 5 = 10, so 60 + 10 = 70
  3. Divide by 10. Move the digits one place to the right.
    70 ÷ 10 = 7
  4. Write the answer.
    35 ÷ 5 = 7

Check. Multiply back: 7 × 5 = 35. ✓

Watch out. Remember to do both steps: double, then divide by 10.

Worked example 3.5.5
Write the fact family for 6, 8 and 48.

Key words. A fact family is a group of multiplication and division facts that use the same three numbers.

Method. A fact family uses three numbers. Two multiplication facts and two division facts use the same three numbers.

  1. Put the numbers in a fact triangle. The product goes at the top and the two factors at the bottom.
    4868
  2. Write the two multiplication facts. Multiply the bottom numbers in either order.
    6 × 8 = 48
    8 × 6 = 48
  3. Write the two division facts. Start at the top and divide by one factor to get the other.
    48 ÷ 6 = 8
    48 ÷ 8 = 6

Check. Check one fact: 6 × 8 = 48, so 48 ÷ 8 = 6. ✓

Watch out. In a division fact, the biggest number (the product) always comes first.

Worked example 3.5.6
Write the fact family for 7, 7 and 49. Why are there only two facts?

Key words. A fact family is a group of multiplication and division facts that use the same three numbers.

Method. A fact family uses three numbers. Both factors are 7, so there are only two facts.

  1. Put the numbers in a fact triangle. The product goes at the top and the factors at the bottom.
    4977
  2. Write the multiplication fact. Multiply the two numbers at the bottom to get the top.
    7 × 7 = 49
  3. Write the division fact. Start at the top and divide by the factor.
    49 ÷ 7 = 7

Check. Check one fact: 7 × 7 = 49, so 49 ÷ 7 = 7. ✓

Watch out. In a division fact, the biggest number (the product) always comes first.

Worked example 3.5.7
Work out 9 ÷ 1.

Method. Dividing by 1 does not change the number. Sharing between 1 person leaves everything with that person.

  1. Say what the division means. 9 ÷ 1 means: share 9 into 1 equal group.
    1 group gets all 9
  2. Think of a small example. Imagine sharing sweets with just one person.
    6 sweets shared with 1 person: they get all 6, so 6 ÷ 1 = 6
  3. Write the answer. One group means no sharing happens.
    9 ÷ 1 = 9

Check. Multiply back: 9 × 1 = 9. ✓

Watch out. Dividing by 1 does not give 1. It gives the same number.

Worked example 3.5.8
Work out 9 ÷ 9.

Method. Any number divided by itself is 1. There is exactly one group of that size.

  1. Say what the division means. 9 ÷ 9 asks: how many groups of 9 fit into 9?
    one group of 9 fits
  2. Think of a small example. Imagine putting sweets into bags that each hold the whole amount.
    6 sweets in bags of 6: you fill 1 bag, so 6 ÷ 6 = 1
  3. Write the answer.
    9 ÷ 9 = 1

Check. Multiply back: 1 × 9 = 9. ✓

Watch out. The answer is 1, not 9 and not 0.

Worked example 3.5.9
Work out 0 ÷ 6.

Method. Zero shared between any number of groups is 0. There is nothing to share.

  1. Say what the division means. 0 ÷ 6 means: share 0 things between 6 groups.
    nothing to share
  2. Think of a small example. Imagine sharing an empty bag of sweets between 3 children.
    0 sweets shared between 3 children: each gets 0, so 0 ÷ 3 = 0
  3. Write the answer. Every group gets nothing.
    0 ÷ 6 = 0

Check. Multiply back: 0 × 6 = 0. ✓

Watch out. 0 ÷ 5 is 0. But you can never divide by 0: 5 ÷ 0 has no answer.

Worked example 3.5.10
Find the missing number.   ? ÷ 6 = 7

Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.

Method. Use the inverse operation. Multiplication and division undo each other.

  1. Say what the sentence means. A number divided by 6 gives 7.
    ? ÷ 6 = 7
  2. Use the inverse (opposite) operation. The opposite of dividing by 6 is multiplying by 6.
    7 × 6 = 42
  3. Write the missing number.
    42 ÷ 6 = 7

Check. Put it back: 42 ÷ 6 = 7. ✓

Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.

Worked example 3.5.11
Find the missing number.   54 ÷ ? = 6

Key words. A missing number is a number you have to find. Division and multiplication are inverses (opposites): they undo each other.

Method. Use the inverse operation. Multiplication and division undo each other.

  1. Say what the sentence means. 54 divided by the missing number makes 6.
    54 ÷ ? = 6
  2. Turn it into a multiplication. 6 lots of the missing number make 54.
    6 × ? = 54, so ? = 54 ÷ 6
  3. Work out the division. Count up in 6s, or use the 6 times table.
    54 ÷ 6 = 9
  4. Write the missing number.
    54 ÷ 9 = 6

Check. Put it back: 54 ÷ 9 = 6. ✓

Watch out. Do not just put the numbers in the box in the order you see them. Think about what the sentence means.

Watch out

Division is not commutative: 56 ÷ 7 = 8, but 7 ÷ 56 is not 8. The biggest number always comes first in a division fact. And do not mix up the special cases: 9 ÷ 1 is 9 (not 1), and 9 ÷ 9 is 1 (not 9 or 0).

Exercise 3E  Division facts, fact families and missing numbers

Non-calculator
1
FQuick-fire! Halve, double then divide by 10, or move the digits.
(a)18 ÷ 2 =
(b)70 ÷ 10 =
(c)45 ÷ 5 =
(d)120 ÷ 10 =
(e)50 ÷ 5 =
(f)24 ÷ 2 =
(g)110 ÷ 10 =
(h)60 ÷ 5 =
(i)16 ÷ 2 =
(j)100 ÷ 10 =
2
FQuick-fire! Divide by 3 and by 4.
(a)21 ÷ 3 =
(b)36 ÷ 4 =
(c)27 ÷ 3 =
(d)48 ÷ 4 =
(e)33 ÷ 3 =
(f)32 ÷ 4 =
(g)36 ÷ 3 =
(h)44 ÷ 4 =
(i)15 ÷ 3 =
(j)40 ÷ 4 =
3
FQuick-fire! Divide by 6, 7, 8 and 9.
(a)42 ÷ 6 =
(b)56 ÷ 7 =
(c)72 ÷ 8 =
(d)81 ÷ 9 =
(e)54 ÷ 6 =
(f)63 ÷ 7 =
(g)64 ÷ 8 =
(h)108 ÷ 9 =
(i)84 ÷ 7 =
(j)96 ÷ 8 =
(k)72 ÷ 6 =
(l)90 ÷ 9 =
4
FQuick-fire! Divide by 11 and by 12.
(a)66 ÷ 11 =
(b)84 ÷ 12 =
(c)121 ÷ 11 =
(d)144 ÷ 12 =
(e)99 ÷ 11 =
(f)60 ÷ 12 =
(g)132 ÷ 11 =
(h)108 ÷ 12 =
5
FMixed quick-fire!
(a)45 ÷ 9 =
(b)72 ÷ 12 =
(c)35 ÷ 7 =
(d)88 ÷ 8 =
(e)66 ÷ 6 =
(f)48 ÷ 4 =
(g)55 ÷ 11 =
(h)36 ÷ 12 =
(i)49 ÷ 7 =
(j)80 ÷ 10 =
(k)63 ÷ 9 =
(l)30 ÷ 5 =
6
FWrite the answers. Take care with the special cases!
(a)12 ÷ 1
(b)7 ÷ 7
(c)0 ÷ 9
(d)100 ÷ 1
(e)12 ÷ 12
(f)8 ÷ 1
7
FWrite the fact family for each set of numbers.
(a)3, 8 and 24
(b)6, 9 and 54
(c)7, 7 and 49
(d)12, 5 and 60
8
FEach fact triangle has a number missing. Find the missing number.
(a)
639?
(b)
56?8
(c)
726?
9
FFind the missing number in each sum.
(a)? ÷ 7 = 6
(b)72 ÷ ? = 9
(c)6 × ? = 54
(d)? ÷ 12 = 5
(e)63 ÷ ? = 7
(f)96 = 8 × ?
(g)? ÷ 4 = 11
(h)110 ÷ ? = 10
10
FUse multiplication to check each division. Write “Correct” or “Wrong”. If it is wrong, write the right answer.
(a)63 ÷ 7 = 8
(b)56 ÷ 8 = 6
(c)72 ÷ 9 = 8
(d)45 ÷ 5 = 8
11
PSPriya shares 48 stickers equally between 6 friends. How many stickers does each friend get?
??????48
12
PSBiscuits are packed into boxes of 12. A factory has 84 biscuits. How many boxes can it fill?
1212121212121284
13
PSNine friends win £72 in a raffle. They share the money equally. How much does each friend get?
?????????£72
14
RTom says, “36 ÷ 4 = 8, because 4 × 8 = 32.” Tom has made a mistake. What is the correct answer?
15
RAlways, sometimes or never?   When you divide a number by 2, the answer is an even number.
16
RThree of these divisions have the answer 8. Which three?   Tick three boxes.
A   56 ÷ 7
B   64 ÷ 9
C   72 ÷ 9
D   96 ÷ 12
E   80 ÷ 8
17
RTwo numbers multiply to make 36. The same two numbers add to make 13. What are the two numbers?
3.6

Factor pairs and multiplying three numbers

Year 4
Factor pairs, Multiplying three numbers

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Factor pairs and multiplying three numbersComing soon

A factor of a number is a whole number that divides into it exactly, with nothing left over. A factor pair is two numbers that multiply to make the number. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4. Each pair makes a different array of 12 squares.

1 × 122 × 63 × 4
The three factor pairs of 12 as arrays. The factors of 12 are 1, 2, 3, 4, 6 and 12.

How to find all the factor pairs. Start at 1 and test each number in turn using the times tables: does it fit into the number exactly? Write down every pair you find. You can stop when the numbers meet in the middle, because after that you would only find the same pairs the other way round. Then write the factors in order. Every number has the pair 1 and itself.

Square numbers have a pair with the same number twice, like 6 × 6 = 36. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Notice that 6 is only written once.

Factors and multiples. Factors are smaller than (or equal to) the number. Multiples are bigger than (or equal to) the number. The factors of 12 are 1, 2, 3, 4, 6, 12. The multiples of 12 are 12, 24, 36, 48...

Multiplying three numbers. Suppose a baker has 2 trays. Each tray has 3 rows of 4 buns. The number of buns is 2 × 3 × 4. You can multiply in any order and the answer is the same: (2 × 3) × 4 = 6 × 4 = 24, or 2 × (3 × 4) = 2 × 12 = 24. So look for a pair that is easy to multiply first. A great pair to look for is one that makes 10: 2 × 5. For 2 × 5 × 7, do 2 × 5 = 10, then 10 × 7 = 70.

2 trays with 3 rows of 4 buns: 2 × 3 × 4 = 24.

Key words. A factor divides into a number exactly. A factor pair is two factors that multiply to make the number. A multiple is in the times table of a number.

Key ideas

  • A factor pair is two numbers that multiply to make the number: 3 × 4 = 12.
  • Test 1, 2, 3, ... in order. Stop when the numbers meet in the middle.
  • Every number has 1 and itself as a factor pair.
  • You can multiply three numbers in any order. Look for a pair that makes 10.
  • Factors are small and multiples are big: factors of 12: 1, 2, 3, 4, 6, 12. Multiples of 12: 12, 24, 36...
Worked example 3.6.1
Find all the factor pairs of 12.

Key words. A factor of a number is a whole number that divides into it exactly. A factor pair is two factors that multiply to make the number.

Method. A factor pair is two numbers that multiply to make 12. Test 1, 2, 3, ... in order, and write down every pair you find.

  1. Start at 1 and try each number in turn. A factor pair is two numbers that multiply to make the number. We test 1, 2, 3, ... using the times tables.
    1 × 12 = 12  (a pair: 1 and 12)
    2 × 6 = 12  (a pair: 2 and 6)
    3 × 4 = 12  (a pair: 3 and 4)
  2. Stop when the numbers meet. After 3, the next factors would just be pairs we have already found the other way round.
    We can stop at 3.
  3. Write the factor pairs.
    1 × 12 = 12
    2 × 6 = 12
    3 × 4 = 12
  4. Picture them. Each pair makes a different array of the same number of squares.
    1 × 122 × 63 × 4
  5. List all the factors in order. Each number in a pair is a factor.
    1, 2, 3, 4, 6, 12

Check. There are 6 factors: 1, 2, 3, 4, 6, 12. Every factor pairs up with another. ✓

Watch out. Do not forget 1 and the number itself. Every number has the pair 1 and itself.

Worked example 3.6.2
Find all the factor pairs of 24.

Key words. A factor of a number is a whole number that divides into it exactly. A factor pair is two factors that multiply to make the number.

Method. A factor pair is two numbers that multiply to make 24. Test 1, 2, 3, ... in order, and write down every pair you find.

  1. Start at 1 and try each number in turn. A factor pair is two numbers that multiply to make the number. We test 1, 2, 3, ... using the times tables.
    1 × 24 = 24  (a pair: 1 and 24)
    2 × 12 = 24  (a pair: 2 and 12)
    3 × 8 = 24  (a pair: 3 and 8)
    4 × 6 = 24  (a pair: 4 and 6)
  2. Stop when the numbers meet. After 4, the next factors would just be pairs we have already found the other way round.
    We can stop at 4.
  3. Write the factor pairs.
    1 × 24 = 24
    2 × 12 = 24
    3 × 8 = 24
    4 × 6 = 24
  4. Picture them. Each pair makes a different array of the same number of squares.
    1 × 242 × 123 × 84 × 6
  5. List all the factors in order. Each number in a pair is a factor.
    1, 2, 3, 4, 6, 8, 12, 24

Check. There are 8 factors: 1, 2, 3, 4, 6, 8, 12, 24. Every factor pairs up with another. ✓

Watch out. Do not forget 1 and the number itself. Every number has the pair 1 and itself.

Worked example 3.6.3
Find all the factor pairs of 36.

Key words. A factor of a number is a whole number that divides into it exactly. A factor pair is two factors that multiply to make the number.

Method. A factor pair is two numbers that multiply to make 36. Test 1, 2, 3, ... in order, and write down every pair you find.

  1. Start at 1 and try each number in turn. A factor pair is two numbers that multiply to make the number. We test 1, 2, 3, ... using the times tables.
    1 × 36 = 36  (a pair: 1 and 36)
    2 × 18 = 36  (a pair: 2 and 18)
    3 × 12 = 36  (a pair: 3 and 12)
    4 × 9 = 36  (a pair: 4 and 9)
    5 × 7 = 35 and 5 × 8 = 40: 36 is in between, so 5 is not a factor
    6 × 6 = 36  (6 is paired with itself)
  2. Stop when the numbers meet. After 6, the next factors would just be pairs we have already found the other way round.
    We can stop at 6.
  3. Write the factor pairs.
    1 × 36 = 36
    2 × 18 = 36
    3 × 12 = 36
    4 × 9 = 36
    6 × 6 = 36
  4. Picture them. Each pair makes a different array of the same number of squares.
    1 × 362 × 183 × 124 × 96 × 6
  5. List all the factors in order. Each number in a pair is a factor.
    1, 2, 3, 4, 6, 9, 12, 18, 36

Check. There are 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. Every factor pairs up with another. ✓

Watch out. Do not forget 1 and the number itself. Every number has the pair 1 and itself.

Worked example 3.6.4
Find all the factor pairs of 30.

Key words. A factor of a number is a whole number that divides into it exactly. A factor pair is two factors that multiply to make the number.

Method. A factor pair is two numbers that multiply to make 30. Test 1, 2, 3, ... in order, and write down every pair you find.

  1. Start at 1 and try each number in turn. A factor pair is two numbers that multiply to make the number. We test 1, 2, 3, ... using the times tables.
    1 × 30 = 30  (a pair: 1 and 30)
    2 × 15 = 30  (a pair: 2 and 15)
    3 × 10 = 30  (a pair: 3 and 10)
    4 × 7 = 28 and 4 × 8 = 32: 30 is in between, so 4 is not a factor
    5 × 6 = 30  (a pair: 5 and 6)
  2. Stop when the numbers meet. After 5, the next factors would just be pairs we have already found the other way round.
    We can stop at 5.
  3. Write the factor pairs.
    1 × 30 = 30
    2 × 15 = 30
    3 × 10 = 30
    5 × 6 = 30
  4. Picture them. Each pair makes a different array of the same number of squares.
    1 × 302 × 153 × 105 × 6
  5. List all the factors in order. Each number in a pair is a factor.
    1, 2, 3, 5, 6, 10, 15, 30

Check. There are 8 factors: 1, 2, 3, 5, 6, 10, 15, 30. Every factor pairs up with another. ✓

Watch out. Do not forget 1 and the number itself. Every number has the pair 1 and itself.

Worked example 3.6.5
Is 7 a factor of 42?

Method. Check if 42 is in the 7 times table. If it is, 7 is a factor.

  1. Say what we need to check. A factor divides into the number exactly, with nothing left over. So 7 is a factor of 42 only if 42 is in the 7 times table.
    Is 42 in the 7 times table?
  2. Count up in 7s. Find the multiples of 7 close to 42.
    7 × 6 = 42
  3. Answer.
    Yes. 7 × 6 = 42, so 7 is a factor of 42.

Check. 42 ÷ 7 = 6 exactly, with nothing left over. ✓

Watch out. A factor must divide in exactly, with nothing left over.

Worked example 3.6.6
Is 5 a factor of 42?

Method. Check if 42 is in the 5 times table. If it is, 5 is a factor.

  1. Say what we need to check. A factor divides into the number exactly, with nothing left over. So 5 is a factor of 42 only if 42 is in the 5 times table.
    Is 42 in the 5 times table?
  2. Count up in 5s. Find the multiples of 5 on each side of 42.
    5 × 8 = 40
    5 × 9 = 45
  3. Answer. 42 is between those two multiples, so it is not in the 5 times table.
    No. 5 is not a factor of 42.

Check. 42 ÷ 5 = 8 remainder 2. There is something left over. ✓

Watch out. A factor must divide in exactly, with nothing left over.

Worked example 3.6.7
Work out 2 × 3 × 4.

Key words. You can multiply three numbers in any order and the answer is the same.

Method. Multiplication can be done in any order, so look for two numbers that are easy to multiply first.

  1. Choose two numbers to multiply first. 2 × 3 is a times table fact.
    2 × 3 = 6
  2. Multiply the answer by the last number, 4. 6 × 4 is a times table fact.
    6 + 6 = 12
    double 10 = 20, double 2 = 4, so 20 + 4 = 24
    6 × 4 = 24
  3. Write the answer.
    2 × 3 × 4 = 24

Check. Try a different order: 3 × 4 = 12, then 12 × 2 = 24. ✓

Watch out. You can multiply in any order. Pick the pair that gives an easy answer, like a pair that makes 10.

Worked example 3.6.8
Work out 2 × 5 × 7.

Key words. You can multiply three numbers in any order and the answer is the same.

Method. Multiplication can be done in any order, so look for two numbers that are easy to multiply first.

  1. Choose two numbers to multiply first. 2 × 5 = 10, and multiplying by 10 is easy.
    2 × 5 = 10
  2. Multiply the answer by the last number, 7. 10 × 7 is a times table fact.
    7 tens
    7 → 70
    10 × 7 = 70
  3. Write the answer.
    2 × 5 × 7 = 70

Check. Try a different order: 5 × 7 = 35, then 35 × 2 = 70. ✓

Watch out. You can multiply in any order. Pick the pair that gives an easy answer, like a pair that makes 10.

Worked example 3.6.9
Work out 4 × 3 × 5.

Key words. You can multiply three numbers in any order and the answer is the same.

Method. Multiplication can be done in any order, so look for two numbers that are easy to multiply first.

  1. Choose two numbers to multiply first. 4 × 5 = 20, a multiple of 10, which is easy to multiply.
    4 × 5 = 20
  2. Multiply the answer by the last number, 3. 20 is 2 tens. Work out 2 × 3, then say that many tens.
    2 × 3 = 6, so 2 tens × 3 = 6 tens
    6 tens = 60
  3. Write the answer.
    4 × 3 × 5 = 60

Check. Try a different order: 5 × 3 = 15, then 15 × 4 = 60. ✓

Watch out. You can multiply in any order. Pick the pair that gives an easy answer, like a pair that makes 10.

Watch out

Do not forget 1 and the number itself! They are always a factor pair. Also, a factor pair must multiply to make the number exactly: 3 × 5 = 15, but 3 and 5 are not a factor pair of 16. When you multiply three numbers, only multiply two at a time. Do the first pair, then multiply the answer by the third number.

Exercise 3F  Factor pairs and multiplying three numbers

Non-calculator
1
FFind all the factor pairs of each number.
(a)8
(b)15
(c)20
(d)28
2
FList all the factors of each number, in order.
(a)10
(b)16
(c)18
(d)21
3
FIs the first number a factor of the second number? Write Yes or No.
(a)Is 6 a factor of 24?
(b)Is 5 a factor of 36?
(c)Is 8 a factor of 56?
(d)Is 9 a factor of 72?
(e)Is 7 a factor of 50?
(f)Is 12 a factor of 96?
4
FSquare numbers have a factor pair with the same number twice. Find all the factors of each square number.
(a)36
(b)49
(c)25
5
FMultiply the three numbers. Look for an easy pair to multiply first.
(a)2 × 5 × 7
(b)4 × 3 × 5
(c)2 × 3 × 4
(d)5 × 2 × 9
(e)6 × 3 × 2
(f)2 × 5 × 8
(g)3 × 3 × 4
(h)4 × 5 × 5
6
PSFactor pairs of 24. Mr Ali has 24 chairs. He puts them in equal rows. Write all the ways he could arrange them in rows with the same number in each row.
7
PSA baker makes 3 trays of buns. Each tray has 4 rows with 6 buns in each row. How many buns is that altogether?
8
PSA shop has 4 crates. Each crate has 5 rows of 6 bottles. How many bottles are there altogether?
9
RAmira says, “Every number has exactly two factors: 1 and the number itself.” Is Amira right? Give an example to explain.
10
ROne of these numbers is not a factor of 24. Which one?   1   2   3   4   6   8   9   12
11
RAlways, sometimes or never?
(a)1 is a factor of every number.
(b)A factor of 12 is also a factor of 24.
(c)A factor of a number is smaller than the number.
12
RZoe says, “30 has more factors than 24 because 30 is bigger.” Is Zoe right?
13
RSome numbers have exactly three factors. 9 is one: its factors are 1, 3 and 9. Find all the numbers up to 50 that have exactly three factors. (Hint: they are all square numbers.)
14
RChoose three different numbers from 2, 3, 4 and 5. Multiply them together. Which three numbers make 60?
3.7

Using known facts, word problems and the times table check

Year 4
Known and derived facts, Multiplication and division problems, Times tables check practice

Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page

Video lesson: Using known facts, word problems and the times table checkComing soon

Use a fact you know to work out new facts. Suppose you know 6 × 7 = 42. Then 60 is 6 tens, so 60 × 7 is 6 tens × 7 = 42 tens = 420. In the same way, 6 × 70 = 420 (6 groups of 7 tens) and 600 × 7 = 4,200 (42 hundreds). The digits stay the same and the zeros move along. Division works the same way: 420 ÷ 7 = 60 and 4,200 ÷ 7 = 600.

6 groups of 7 tens: 6 × 7 tens = 42 tens = 420. Each green rod is one ten.

You can also get a new fact from a nearby fact. Add or take away one group: 7 × 7 is 6 × 7 plus one more 7, which is 42 + 7 = 49. Double: 12 × 7 is double 6 × 7, so double 42 is 84. Halve: 3 × 7 is half of 6 × 7, so half of 42 is 21.

5 × 7 and 1 × 7
6 × 7 = 5 × 7 + 1 × 7
6 × 7 and 1 × 7
7 × 7 = 6 × 7 + 1 × 7
Blue dots are the fact you know. Orange dots are the extra group. Each extra row of 7 dots adds 7.

Word problems. Read the problem twice. Draw a bar model. If you know the size of each group and the number of groups, multiply to find the total. If you know the total and want to share it equally, or find how many groups, divide. Write the unit (like £, cm or “pens”) in your answer.

9999?
Multiply: 4 bags of 9. Total?
????36
Divide: 36 shared by 4. Each?
In a bar model, equal bars mean equal groups. The bracket shows the total.

The times tables check. In Year 4 you take a short check on the computer. There are 25 questions like 7 × 8 = ?, and you get 6 seconds for each one. The best preparation is a little practice every day. Make sure you know the ten tricky facts where both numbers are from 6 to 9 (shaded below), and use the tricks in this chapter to build any fact in a flash. The practice sets in this section use the same style: 25 questions, 6 seconds each. Cover the answers and see how many you can do in time!

×123456789101112112345678910111222468101214161820222433691215182124273033364481216202428323640444855101520253035404550556066121824303642485460667277142128354249566370778488162432404856647280889699182736455463728190991081010203040506070809010011012011112233445566778899110121132121224364860728496108120132144
The 16 shaded boxes are the trickiest. Because 7 × 8 = 8 × 7, there are only 10 different facts to learn.

Key words. A known fact is a fact you can recall. A derived fact is a new fact that you work out from a known fact.

Key ideas

  • Use a known fact and place value: 6 × 7 = 42, so 60 × 7 = 420, 6 × 70 = 420 and 600 × 7 = 4,200.
  • Division too: 42 ÷ 7 = 6, so 420 ÷ 7 = 60.
  • Nearby facts: add or take away one group. Double or halve the number of groups.
  • Equal groups with a total to find: multiply. A total to share or split into groups: divide.
  • Times tables check: 25 questions, 6 seconds each.
Worked example 3.7.1
Use the fact 6 × 7 = 42 to work out 60 × 7.

Key words. A known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 6 × 7 = 42, and place value. 60 is 6 tens, so the answer is 42 tens.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    6 × 7 = 42
  2. Say the bigger number in tens. 60 is 6 tens.
    60 = 6 tens
  3. Multiply, using the known fact. 6 tens × 7 = 42 tens, because 6 × 7 = 42.
    6 × 7 = 42, so 6 tens × 7 = 42 tens
  4. Change 42 tens back to a number. 1 ten is 10, so 42 tens is 42 × 10.
    42 tens = 420
  5. Write the answer.
    60 × 7 = 420

Check. Divide back: 420 ÷ 7 = 60. ✓

Watch out. The answer is 42 tens, which has 1 zero on the end. Count the zeros carefully.

Worked example 3.7.2
Use the fact 4 × 8 = 32 to work out 4 × 80.

Key words. A known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 4 × 8 = 32, and place value. 80 is 8 tens, so the answer is 32 tens.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    4 × 8 = 32
  2. Say the bigger number in tens. 80 is 8 tens.
    80 = 8 tens
  3. Multiply, using the known fact. 8 tens × 4 = 32 tens, because 8 × 4 = 32.
    8 × 4 = 32, so 8 tens × 4 = 32 tens
  4. Change 32 tens back to a number. 1 ten is 10, so 32 tens is 32 × 10.
    32 tens = 320
  5. Write the answer.
    4 × 80 = 320

Check. Divide back: 320 ÷ 80 = 4. ✓

Watch out. The answer is 32 tens, which has 1 zero on the end. Count the zeros carefully.

Worked example 3.7.3
Use the fact 9 × 5 = 45 to work out 900 × 5.

Key words. A known fact is a multiplication fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 9 × 5 = 45, and place value. 900 is 9 hundreds, so the answer is 45 hundreds.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    9 × 5 = 45
  2. Say the bigger number in hundreds. 900 is 9 hundreds.
    900 = 9 hundreds
  3. Multiply, using the known fact. 9 hundreds × 5 = 45 hundreds, because 9 × 5 = 45.
    9 × 5 = 45, so 9 hundreds × 5 = 45 hundreds
  4. Change 45 hundreds back to a number. 1 hundred is 100, so 45 hundreds is 45 × 100.
    45 hundreds = 4,500
  5. Write the answer.
    900 × 5 = 4,500

Check. Divide back: 4,500 ÷ 5 = 900. ✓

Watch out. The answer is 45 hundreds, which has 2 zeros on the end. Count the zeros carefully.

Worked example 3.7.4
Use the fact 56 ÷ 8 = 7 to work out 560 ÷ 8.

Key words. A known fact is a fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 56 ÷ 8 = 7, and place value. 560 is 56 tens, so the answer is 7 tens.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    56 ÷ 8 = 7
  2. Say the big number in tens. 560 is 56 tens.
    560 = 56 tens
  3. Divide, using the known fact. 56 tens ÷ 8 = 7 tens, because 56 ÷ 8 = 7.
    56 ÷ 8 = 7, so 56 tens ÷ 8 = 7 tens
  4. Change 7 tens back to a number. Put the zeros back.
    7 tens = 70
  5. Write the answer.
    560 ÷ 8 = 70

Check. Multiply back: 70 × 8 = 560. ✓

Watch out. Keep the zeros. 420 ÷ 7 is 60, not 6.

Worked example 3.7.5
Use the fact 36 ÷ 9 = 4 to work out 3,600 ÷ 9.

Key words. A known fact is a fact you can already recall. A derived fact is a new fact you work out from a known fact.

Method. Use the fact you know, 36 ÷ 9 = 4, and place value. 3,600 is 36 hundreds, so the answer is 4 hundreds.

  1. Spot the fact you know. Take away the zeros and look at the digits that are left.
    36 ÷ 9 = 4
  2. Say the big number in hundreds. 3,600 is 36 hundreds.
    3,600 = 36 hundreds
  3. Divide, using the known fact. 36 hundreds ÷ 9 = 4 hundreds, because 36 ÷ 9 = 4.
    36 ÷ 9 = 4, so 36 hundreds ÷ 9 = 4 hundreds
  4. Change 4 hundreds back to a number. Put the zeros back.
    4 hundreds = 400
  5. Write the answer.
    3,600 ÷ 9 = 400

Check. Multiply back: 400 × 9 = 3,600. ✓

Watch out. Keep the zeros. 420 ÷ 7 is 60, not 6.

Worked example 3.7.6
You know that 6 × 8 = 48. Use this fact to work out 7 × 8.

Key words. A derived fact is a new fact you work out from a fact you already know.

Method. 7 is one more than 6, so add one more group of 8 to the answer to 6 × 8.

  1. Write the fact you know. We start from the fact we know.
    6 × 8 = 48
  2. Compare 7 with 6. 7 is one more than 6, so we need one more group of 8.
    7 = 6 + 1
  3. Add one more group. One group is 8.
    48 + 8 = 56
  4. Write the answer.
    7 × 8 = 56

Check. Check by dividing: 56 ÷ 8 = 7. ✓

Watch out. Add 8, the size of one group, not 7 or 1.

Worked example 3.7.7
You know that 6 × 7 = 42. Use this fact to work out 12 × 7.

Key words. A derived fact is a new fact you work out from a fact you already know.

Method. 12 is double 6, so double the answer to 6 × 7.

  1. Write the fact you know. We start from the fact we know.
    6 × 7 = 42
  2. Compare 12 with 6. 12 is double 6, so 12 groups of 7 are double 6 groups of 7.
    12 = 2 × 6
  3. Double the known answer.
    double 40 = 80, double 2 = 4, so 80 + 4 = 84
  4. Write the answer.
    12 × 7 = 84

Check. Check by dividing: 84 ÷ 7 = 12. ✓

Watch out. Doubling the number of groups doubles the total. Do not double the other number as well.

Worked example 3.7.8
Leo buys 6 packs of pencils. Each pack has 12 pencils. He gives 15 pencils to his friends. How many pencils does Leo have left?

Method. Two steps. First find how many pencils Leo buys by multiplying. Then take away the pencils he gives away.

  1. Draw a bar model for step 1. 6 equal packs of 12. We want the total.
    121212121212?
  2. Step 1: multiply. Equal groups, so multiply.
    10 × 6 = 60
    6 + 6 = 12
    60 + 12 = 72
    6 × 12 = 72
  3. Step 2: take away. Leo gives 15 pencils away. Take 10 first, then 5.
    72 − 10 = 62, then 62 − 5 = 57
  4. Write the answer.
    57 pencils

Check. Add back: 57 + 15 = 72 and 72 ÷ 6 = 12. ✓

Watch out. The answer to step 1 (72) is not the final answer. Check what the question asks for.

Worked example 3.7.9
72 apples are shared equally between 8 bags. How many apples are in each bag?

Method. Dividing is the opposite of multiplying. Use the times table to find how many times the number fits.

  1. Draw a bar model. The whole is 72. It is split into 8 equal parts. We want the size of one part.
    ????????72
  2. Choose the operation. Sharing equally means dividing.
    72 ÷ 8
  3. Use the times tables. Think: what do we multiply 8 by to get 72?
    9 × 8 = 72, so 72 ÷ 8 = 9
  4. Write the answer. Include the unit.
    9 apples

Check. Multiply back: 9 × 8 = 72. ✓

Watch out. Read the question carefully. Does it ask for the size of each group, or for how many groups?

Watch out

Keep the zeros! 60 × 7 is 420, not 42. Write the known fact first, then say how many tens or hundreds you have. In word problems, do not choose multiply or divide because of one word in the question. Draw a bar model and decide if you know the total or the size of each group.

Exercise 3G  Using known facts

Non-calculator
1
FUse the fact 6 × 4 = 24 to work out each answer.
(a)60 × 4
(b)6 × 40
(c)600 × 4
(d)240 ÷ 4
(e)2,400 ÷ 4
(f)240 ÷ 6
2
FUse the fact 8 × 7 = 56 to work out each answer.
(a)80 × 7
(b)8 × 70
(c)800 × 7
(d)560 ÷ 7
(e)560 ÷ 8
(f)5,600 ÷ 8
3
FQuick-fire! Use a times table fact and place value.
(a)30 × 8
(b)7 × 50
(c)90 × 6
(d)4 × 700
(e)110 × 3
(f)8 × 90
4
FDivide. Use a times table fact and place value.
(a)360 ÷ 6
(b)480 ÷ 8
(c)2,100 ÷ 7
(d)5,400 ÷ 9
(e)880 ÷ 11
(f)1,200 ÷ 12
5
FYou know that 5 × 8 = 40. Use this fact to work out each answer.
(a)6 × 8
(b)4 × 8
(c)10 × 8
6
FDouble or halve a fact you know.
(a)6 × 9.   You know 3 × 9 = 27.
(b)6 × 5.   You know 12 × 5 = 60.
(c)8 × 7.   You know 4 × 7 = 28.
(d)6 × 6.   You know 12 × 6 = 72.
7
PSA stamp costs 60p. Hana buys 8 stamps. How much do the stamps cost altogether?
60p60p60p60p60p60p60p60p?
8
PSA bus holds 70 passengers. There are 6 full buses. How many passengers is that altogether?
707070707070?
9
PSA school orders 540 pencils. They are packed in boxes of 9. How many boxes does the school get?
10
RZoe says, “6 × 7 = 42, so 60 × 7 = 42 too.” What mistake did Zoe make? What is 60 × 7?
11
RWhich one is the odd one out?   A  6 × 70    B  60 × 7    C  42 × 10    D  600 × 7
12
RAlways, sometimes or never?   When you multiply a whole number by a multiple of 10, the answer ends in 0.
13
RUse the fact 7 × 8 = 56 to write down four more facts about 5,600.

Exercise 3H  Multiplication and division problems

Non-calculator
1
FThere are 12 months in one year. How many months are there in 7 years?
12121212121212?
2
FSam has 60 stickers. He shares them equally between 5 friends. How many stickers does each friend get?
?????60
3
FA book costs £8. A school buys 12 books. How much do the books cost altogether?
£8£8£8£8£8£8£8£8£8£8£8£8?
4
FA teacher has 99 pencils. She puts 9 pencils in each pot. How many pots does she fill?
9999999999
5
PSAisha buys 4 packs of stickers. There are 12 stickers in each pack. She gives 15 stickers to her cousin. How many stickers does Aisha have left?
6
PSCakes cost £6 each. Leo buys 7 cakes. He pays with a £50 note. How much change does he get?
£6£6£6£6£6£6£6?
7
PSMr Khan buys 5 boxes of 8 markers and 3 boxes of 12 markers. How many markers does he buy altogether?
8
PSMei reads 7 pages every day for 12 days. Ben reads 9 pages every day for 9 days. Who reads more pages? How many more?
9
PSThe table shows the price of a pack of cards.
CardsPrice of one pack
Football£4
Animals£7

Sam buys 8 packs of football cards and 6 packs of animal cards. How much does he spend?
10
RThere are 9 rows of seats in a hall, with 7 seats in each row. Which bar model, A or B, matches this? Do the two bar models give the same total? Explain why.
A
777777777?
B
9999999?
11
RAnil says, “8 packs of 6 buns is the same number of buns as 6 packs of 8 buns.” Is Anil right? Prove it.
8 rows of 6
6 rows of 8
12
RWhich two of these problems need division? Tick two boxes. You do not need to work out the answers.
A   6 bags have 9 apples in each bag. How many apples are there?
B   42 pens are shared equally between 6 children. How many pens does each child get?
C   A rope 56 m long is cut into pieces that are each 7 m long. How many pieces are there?
D   A train has 8 carriages with 12 seats in each carriage. How many seats are there?
13
RA farmer has 10 animals. Some are chickens and some are cows. There are 28 legs altogether. A chicken has 2 legs and a cow has 4 legs. How many chickens and how many cows are there?

Exercise 3I  Times tables check practice: 25 questions, 6 seconds each

Non-calculator
1
FSet A (25 questions): a warm-up with the easier tables. Give yourself 6 seconds for each question (2 minutes 30 seconds in total). Cover the answers and write your answers on paper.
(a)9 × 2 =
(b)5 × 4 =
(c)3 × 3 =
(d)4 × 11 =
(e)11 × 2 =
(f)3 × 5 =
(g)10 × 5 =
(h)3 × 10 =
(i)7 × 5 =
(j)8 × 4 =
(k)5 × 11 =
(l)10 × 11 =
(m)4 × 2 =
(n)3 × 4 =
(o)2 × 5 =
(p)10 × 9 =
(q)3 × 7 =
(r)9 × 3 =
(s)6 × 4 =
(t)5 × 9 =
(u)11 × 3 =
(v)4 × 4 =
(w)12 × 10 =
(x)8 × 11 =
(y)4 × 12 =
2
FSet B (25 questions): a mix of all the tables. Give yourself 6 seconds for each question (2 minutes 30 seconds in total). Cover the answers and write your answers on paper.
(a)3 × 7 =
(b)11 × 9 =
(c)8 × 10 =
(d)2 × 8 =
(e)2 × 3 =
(f)10 × 9 =
(g)11 × 7 =
(h)5 × 10 =
(i)5 × 9 =
(j)7 × 7 =
(k)10 × 11 =
(l)2 × 5 =
(m)11 × 8 =
(n)6 × 3 =
(o)7 × 5 =
(p)3 × 8 =
(q)12 × 6 =
(r)6 × 7 =
(s)9 × 2 =
(t)8 × 6 =
(u)11 × 3 =
(v)8 × 5 =
(w)9 × 4 =
(x)4 × 10 =
(y)3 × 3 =
3
FSet C (25 questions): the tricky tables 6, 7, 8, 9 and 12. Give yourself 6 seconds for each question (2 minutes 30 seconds in total). Cover the answers and write your answers on paper.
(a)7 × 3 =
(b)2 × 9 =
(c)8 × 2 =
(d)9 × 6 =
(e)12 × 6 =
(f)12 × 7 =
(g)7 × 10 =
(h)6 × 7 =
(i)6 × 8 =
(j)12 × 11 =
(k)12 × 12 =
(l)11 × 8 =
(m)8 × 10 =
(n)12 × 4 =
(o)12 × 8 =
(p)7 × 8 =
(q)7 × 9 =
(r)9 × 5 =
(s)2 × 12 =
(t)12 × 9 =
(u)6 × 5 =
(v)4 × 9 =
(w)6 × 6 =
(x)9 × 3 =
(y)5 × 7 =
4
FSet D (20 questions): division facts and missing numbers. Try to answer each one in 10 seconds.
(a)56 ÷ 7 =
(b)6 × ? = 36
(c)? × 6 = 24
(d)? ÷ 7 = 10
(e)132 ÷ ? = 12
(f)30 ÷ 6 =
(g)11 × ? = 121
(h)? × 3 = 21
(i)? ÷ 3 = 10
(j)30 ÷ ? = 6
(k)99 ÷ 11 =
(l)5 × ? = 40
(m)? × 8 = 32
(n)? ÷ 4 = 11
(o)77 ÷ ? = 11
(p)60 ÷ 10 =
(q)6 × ? = 36
(r)? × 4 = 16
(s)? ÷ 6 = 11
(t)120 ÷ ? = 12
5
PSIn the times tables check there are 25 questions and you have 6 seconds for each. How many seconds is that altogether? Write your answer in minutes and seconds too.
6
RShow two different ways to work out 7 × 8.
7
RDev says, “There are 16 tricky facts to learn, because the grid below has 16 boxes.” Explain why Dev only needs to learn 10 facts.
×6789636424854742495663848566472954637281

Chapter summary

SkillMethod
MultiplicationEqual groups: 3 × 4 = 4 + 4 + 4. An array has rows and columns. 3 × 4 = 4 × 3 (order does not matter).
× 0 and × 1Any number × 0 = 0. Any number × 1 = the same number. Any number ÷ 1 = the same number.
2, 4, 8Double (× 2). Double double (× 4). Double three times (× 8).
10 and 5× 10: digits move one place left. × 5: do × 10 and halve.
3, 6, 12× 3 = double + one more. × 6 = × 5 + one more. × 12 = × 10 + × 2.
9× 9 = × 10 take away one lot. The digits of the answer add to 9. Finger trick.
7 and 11× 7 = × 5 + × 2 (learn 56 = 7 × 8). × 11: write the digit twice up to 9, then × 10 + one more.
Square numbers1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
Division factsUse the inverse: 56 ÷ 7 = ? means 7 × ? = 56. A fact family has 4 facts (2 if the factors are equal).
Special divisionn ÷ 1 = n. n ÷ n = 1. 0 ÷ n = 0. Never divide by 0.
Factor pairsTest 1, 2, 3, ... Write every pair that multiplies to make the number. 1 and the number itself are always a pair.
Three numbersMultiply in any order. Look for a pair that makes 10 (like 2 × 5).
Known facts6 × 7 = 42 gives 60 × 7 = 420, 6 × 70 = 420 and 420 ÷ 7 = 60. Add or take away one group; double or halve.
Word problemsDraw a bar model. Total to find: multiply. Total to share or split: divide. Write the unit.

Can you…?

  • I can use arrays, equal groups and number lines to show multiplication.
  • I know that 3 × 4 = 4 × 3, and I can multiply by 0 and 1 and divide by 1.
  • I can recall every multiplication fact up to 12 × 12 and use a trick if I forget.
  • I can recall the division facts that go with them.
  • I can write a fact family and find missing numbers.
  • I can find factor pairs of a number.
  • I can multiply three numbers by choosing an easy pair first.
  • I can use a known fact to work out facts like 60 × 7 and 420 ÷ 7.
  • I can solve multiplication and division word problems with a bar model.
  • I can answer times table questions quickly, in 6 seconds each.

Key terms

Multiply
To find the total of equal groups. 3 × 4 means 3 groups of 4.
Product
The answer to a multiplication.
Factor
A number that divides exactly into another number. Also, the numbers you multiply are called factors.
Factor pair
Two factors that multiply to make a number, such as 3 and 4 for 12.
Multiple
A number in a times table. The multiples of 4 are 4, 8, 12, 16...
Array
Objects in rows and columns.
Commutative
You can swap the order and the answer stays the same. 3 × 4 = 4 × 3.
Square number
A number multiplied by itself, such as 5 × 5 = 25.
Double / Halve
Double means × 2. Halve means ÷ 2.
Inverse
The opposite operation. Multiplying and dividing undo each other.
Fact family
The multiplication and division facts that use the same three numbers.
Divide
To share equally or to split into equal groups.
Known fact
A fact you can recall without working it out.
Derived fact
A new fact worked out from a known fact.
Bar model
A drawing of bars that shows the numbers in a problem.

Exercise 3Z  Check-up (non-calculator)

Non-calculator
1
Work out 8 × 7.
2
Work out 9 × 12.
3
Work out 72 ÷ 9.
4
Find the missing number.   ? × 6 = 54
5
Write the fact family for 4, 9 and 36.
6
Use the fact 7 × 6 = 42 to work out 70 × 6.
7
Write all the factor pairs of 18.
8
Work out 2 × 5 × 6.
9
A box holds 6 cupcakes. A bakery fills 9 boxes. How many cupcakes is that?
666666666?
10
Sweets are put into bags of 8. There are 96 sweets. How many bags can be filled?
8888888896

Total 17 marks. Allow about 17 minutes.

Exercise 3X  SATs-style questions

Non-calculator
1
FWork out 9 × 6.[1 mark]
2
FWork out 96 ÷ 12.[1 mark]
3
FWrite the missing number.   ? ÷ 7 = 9[1 mark]
4
F6 × 8 = 48.   Use this fact to work out 60 × 8.[1 mark]
5
PSA pack has 12 pencils. A teacher buys 9 packs. How many pencils does the teacher buy?   Show your working.[2 marks]
121212121212121212?
6
RWhich two multiplications have the same answer as 6 × 8?   Tick two boxes.    A  4 × 12    B  7 × 7    C  8 × 6    D  9 × 5[2 marks]
7
FWrite all the factor pairs of 28.[2 marks]
8
RShow that 4 × 5 × 7 = 140.   Show your working.[2 marks]
9
RLeo says, “9 × 7 = 62.” Use the digits of his answer to show that Leo is wrong. Then write the correct answer.[2 marks]
10
PSPens come in packs of 8. Pencils come in packs of 6. Mr Khan buys 7 packs of pens and 9 packs of pencils. How many pens and pencils does he buy altogether?   Show your working.[3 marks]
← Chapter 2: Adding and subtractingChapter 4: Multiplying and dividing →

Websink Prep UK is an independent site. It is not affiliated with, endorsed by or sponsored by AQA, Pearson Edexcel, OCR, WJEC, Eduqas, CCEA, SQA, GL Assessment, CEM or the Department for Education. All exam board names and trademarks belong to their owners. Past papers are linked from the exam boards' own websites and are not hosted here.

About Websink Prep UK · Find a tutor · Privacy · Terms · Cookie settings