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Step-by-step practice: Maths · Level 5Chapter 4 · Long multiplication of two-digit by one-digit numbers
Level 5 · Chapter 4

Long multiplication of two-digit by one-digit numbers

By the end of this chapter you will be able to

  • Multiply a two-digit number by a one-digit number in columns
  • Carry tens into the next column
  • Multiply a three-digit number by a one-digit number
  • Estimate a product by rounding, and check an answer
  • Solve multiplication word problems with equal groups and scaling

You should already know

  • Times tables to 12 times 12 (chapter 3)
  • Column addition with carrying (chapter 2)

Where this leads

  • Short division with remainders (chapter 5)
  • Multiplying by two-digit numbers (a later level)

Step-by-step practice: maths (Level 5). Small steps, repeated until fluent. Content: Multiply a two-digit number by a one-digit number using a formal written method, with carrying (Y5 paraphrase), Multiply a three-digit number by a one-digit number where carrying is needed (Y5 paraphrase), Use estimation and checking to decide whether an answer is sensible (Y5 paraphrase), Solve problems involving multiplication, including scaling and equal groups (Y5 paraphrase).

Exercise P  Do you remember?

Non-calculator
1
FWhat is 12 × 6?
2
FWhat is 11 × 9?
3
FWhat is 10,000 more than 52,380?
4
FRound 6,285 to the nearest 100.
5
FWhat is 48 ÷ 6?
4.1

Two-digit by one-digit numbers, no carrying

Level 5
Multiply a two-digit number by a one-digit number, column by column
Video lesson: Two-digit by one-digit numbers, no carryingComing soon

Write the two-digit number in columns, with the tens under the tens and the ones under the ones. Multiply the ones first, then the tens.

If every product fits in its column, you do not need to carry. Write each product under its column.

Key ideas

  • Multiply the ones first, then the tens.
  • Write each product in its column.
  • If a product is ten or more, carry the tens to the next column.
Worked example 4.1.1
Work out 23 × 3.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 3. Write 9 in the ones column.
    3 × 3 = 9
  2. Multiply the tens digit by 3. Write 6 in the tens column.
    2 × 3 = 6
  3. Write the answer. Read the digits from the bottom of each column, from the left.
    69

Check. Check: 69 ÷ 3 = 23.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Worked example 4.1.2
Work out 41 × 7.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 7. Write 7 in the ones column.
    1 × 7 = 7
  2. Multiply the tens digit by 7. Write 8 in the tens column and carry 2 to the hundreds column.
    4 × 7 = 28
  3. Write the carried number in front. The carried number is the next digit on the left.
    2 in the hundreds column
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    287

Check. Check: 287 ÷ 7 = 41.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Worked example 4.1.3
Work out 62 × 4.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 4. Write 8 in the ones column.
    2 × 4 = 8
  2. Multiply the tens digit by 4. Write 4 in the tens column and carry 2 to the hundreds column.
    6 × 4 = 24
  3. Write the carried number in front. The carried number is the next digit on the left.
    2 in the hundreds column
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    248

Check. Check: 248 ÷ 4 = 62.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Watch out

Watch out. Multiply the tens digit by the number, not the whole number. 20 × 3 is 60, not 23.

Exam tip

Grown-up tip. Ask the child to say the answer to each column before they write it: “Three times three is nine; three times two is six.”

Exercise 4A  Practice: two-digit by one-digit, no carrying

Non-calculator
1
FWork out 13 × 2.
2
FWork out 21 × 4.
3
FWork out 10 × 6.
4
FWork out 10 × 8.
5
FWork out 10 × 2.
6
FWork out 10 × 9.
7
FWork out 20 × 2.
8
FWork out 10 × 5.
9
FWork out 23 × 3.
10
FWork out 24 × 2.
11
FWork out 10 × 3.
12
FWork out 14 × 2.
13
FWork out 20 × 4.
14
FWork out 32 × 2.
15
FWork out 31 × 2.
16
FWork out 22 × 4.
4.2

Carrying tens from the ones column

Level 5
Multiply a two-digit number by a one-digit number, carrying the tens
Video lesson: Carrying tens from the ones columnComing soon

When the ones product is ten or more, write the ones digit and carry the tens to the tens column.

Then multiply the tens digit and add the carried number before you write the tens digit.

Key ideas

  • Write the ones digit; carry the tens.
  • Multiply the tens, then add the carried number.
  • Estimate first to check the answer is the right size.
Worked example 4.2.1
Work out 38 × 6.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 6. Write 8 in the ones column and carry 4 to the tens column.
    8 × 6 = 48
  2. Multiply the tens digit by 6. Write 2 in the tens column and carry 2 to the hundreds column.
    3 × 6 = 18, plus 4 carried = 22
  3. Write the carried number in front. The carried number is the next digit on the left.
    2 in the hundreds column
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    228

Check. Check: 228 ÷ 6 = 38.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Worked example 4.2.2
Work out 57 × 4.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 4. Write 8 in the ones column and carry 2 to the tens column.
    7 × 4 = 28
  2. Multiply the tens digit by 4. Write 2 in the tens column and carry 2 to the hundreds column.
    5 × 4 = 20, plus 2 carried = 22
  3. Write the carried number in front. The carried number is the next digit on the left.
    2 in the hundreds column
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    228

Check. Check: 228 ÷ 4 = 57.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Worked example 4.2.3
Estimate 38 × 6 by rounding 38 to the nearest 10.

Method. Round to a number that is easy to multiply, then calculate.

  1. Round 38 to the nearest 10. Look at the ones digit: 5 or more rounds up.
    38 is about 40
  2. Multiply the rounded number. Use a fact we know from the tables.
    40 × 6 = 240
  3. Write the estimate. The exact answer should be close to this.
    240

Check. The exact answer is 228, which is close to 240.

Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.

Watch out

Watch out. Do not forget to add the carried number to the tens product. 38 × 6: 3 tens × 6 = 18, plus 4 carried = 22 tens.

Exam tip

Grown-up tip. Ask: “Did you add the carried number? Is the answer about the estimate?”

Exercise 4B  Practice: carrying from the ones

Non-calculator
1
FWork out 82 × 2.
2
FWork out 68 × 8.
3
FWork out 29 × 5.
4
FWork out 71 × 7.
5
FWork out 62 × 2.
6
FWork out 68 × 5.
7
FWork out 14 × 6.
8
FWork out 26 × 6.
9
FWork out 46 × 6.
10
FWork out 34 × 6.
11
FWork out 69 × 5.
12
FWork out 58 × 5.
13
FWork out 57 × 5.
14
FWork out 74 × 3.
15
FWork out 65 × 4.
16
FWork out 45 × 5.
4.3

Three-digit by one-digit numbers

Level 5
Multiply a three-digit number by a one-digit number, carrying where needed
Video lesson: Three-digit by one-digit numbersComing soon

The same method works for three columns. Start at the ones, then the tens, then the hundreds.

Carry from each column to the next, and write any carried number that is left over at the front.

Key ideas

  • Work from the right, one column at a time.
  • Carry from each column into the next one on the left.
  • Write a carried number left over at the end in front of the answer.
Worked example 4.3.1
Work out 246 × 3.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 3. Write 8 in the ones column and carry 1 to the tens column.
    6 × 3 = 18
  2. Multiply the tens digit by 3. Write 3 in the tens column and carry 1 to the hundreds column.
    4 × 3 = 12, plus 1 carried = 13
  3. Multiply the hundreds digit by 3. Write 7 in the hundreds column.
    2 × 3 = 6, plus 1 carried = 7
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    738

Check. Check: 738 ÷ 3 = 246.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Worked example 4.3.2
Work out 537 × 6.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 6. Write 2 in the ones column and carry 4 to the tens column.
    7 × 6 = 42
  2. Multiply the tens digit by 6. Write 2 in the tens column and carry 2 to the hundreds column.
    3 × 6 = 18, plus 4 carried = 22
  3. Multiply the hundreds digit by 6. Write 2 in the hundreds column and carry 3 to the thousands column.
    5 × 6 = 30, plus 2 carried = 32
  4. Write the carried number in front. The carried number is the next digit on the left.
    3 in the thousands column
  5. Write the answer. Read the digits from the bottom of each column, from the left.
    3,222

Check. Check: 3,222 ÷ 6 = 537.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Worked example 4.3.3
Work out 57 × 4.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 4. Write 8 in the ones column and carry 2 to the tens column.
    7 × 4 = 28
  2. Multiply the tens digit by 4. Write 2 in the tens column and carry 2 to the hundreds column.
    5 × 4 = 20, plus 2 carried = 22
  3. Write the carried number in front. The carried number is the next digit on the left.
    2 in the hundreds column
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    228

Check. Check: 228 ÷ 4 = 57.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Watch out

Watch out. Keep the zero column. In 204 × 3, the tens give 0 × 3 = 0, so write 0 in the tens column.

Exam tip

Grown-up tip. Ask the child to count the columns before they start, so that no column is missed.

Exercise 4C  Practice: three-digit by one-digit numbers

Non-calculator
1
FWork out 429 × 4.
2
FWork out 796 × 2.
3
FWork out 827 × 3.
4
FWork out 765 × 2.
5
FWork out 186 × 4.
6
FWork out 600 × 9.
7
FWork out 183 × 9.
8
FWork out 260 × 6.
9
FWork out 792 × 5.
10
FWork out 651 × 9.
11
FWork out 482 × 8.
12
FWork out 791 × 6.
13
FWork out 461 × 4.
14
FWork out 947 × 5.
15
FWork out 896 × 2.
16
FWork out 606 × 3.
4.4

Estimating and checking

Level 5
Estimate a product by rounding, and check a product by division
Video lesson: Estimating and checkingComing soon

An estimate uses numbers that are easy to multiply, such as a multiple of 10. 38 × 6 is about 40 × 6 = 240.

Check a product by dividing the answer by one of the numbers. You should get the other number back.

Key ideas

  • Round to a number that is easy to multiply.
  • The exact answer should be close to the estimate.
  • Check a product by division.
Worked example 4.4.1
Estimate 38 × 6 by rounding 38 to the nearest 10.

Method. Round to a number that is easy to multiply, then calculate.

  1. Round 38 to the nearest 10. Look at the ones digit: 5 or more rounds up.
    38 is about 40
  2. Multiply the rounded number. Use a fact we know from the tables.
    40 × 6 = 240
  3. Write the estimate. The exact answer should be close to this.
    240

Check. The exact answer is 228, which is close to 240.

Watch out. An estimate is not the exact answer. It tells you whether the exact answer is about the right size.

Worked example 4.4.2
Is 168 the correct answer to 24 × 7? Check it and write Yes or No.

Method. Check a multiplication by division: the answer divided by one factor gives the other factor.

  1. Divide the answer by 7. If the multiplication is right, dividing by the same number gives back the first number.
    168 ÷ 7 = 24
  2. Compare with 24. Is the answer 24?
    Same
  3. Write Yes or No. Yes if the check works; No if it does not.
    Yes

Check. The correct answer is 168.

Watch out. Find the mistake in the columns if the check does not work.

Worked example 4.4.3
Work out 57 × 4.

Method. Multiply each digit by the number, starting with the ones. Carry the tens to the next column.

  1. Multiply the ones digit by 4. Write 8 in the ones column and carry 2 to the tens column.
    7 × 4 = 28
  2. Multiply the tens digit by 4. Write 2 in the tens column and carry 2 to the hundreds column.
    5 × 4 = 20, plus 2 carried = 22
  3. Write the carried number in front. The carried number is the next digit on the left.
    2 in the hundreds column
  4. Write the answer. Read the digits from the bottom of each column, from the left.
    228

Check. Check: 228 ÷ 4 = 57.

Watch out. Add any carried number before you write the digit of that column. Carry the tens; do not write them as a digit.

Watch out

Watch out. An estimate tells you whether the answer is about right, not whether it is exact.

Exam tip

Grown-up tip. Ask: “Is the answer close to the estimate?” before the child checks the exact answer.

Exercise 4D  Practice: estimating and checking

Non-calculator
1
FEstimate 91 × 2 by rounding 91 to the nearest 10.
2
FEstimate 66 × 8 by rounding 66 to the nearest 10.
3
FEstimate 56 × 6 by rounding 56 to the nearest 10.
4
RIs 520 the correct answer to 64 × 5? Check it and write Yes or No.
5
RIs 582 the correct answer to 97 × 6? Check it and write Yes or No.
6
RIs 69 the correct answer to 17 × 4? Check it and write Yes or No.
7
RIs 447 the correct answer to 89 × 5? Check it and write Yes or No.
8
FEstimate 52 × 7 by rounding 52 to the nearest 10.
9
FEstimate 71 × 9 by rounding 71 to the nearest 10.
10
FEstimate 55 × 6 by rounding 55 to the nearest 10.
11
RIs 273 the correct answer to 39 × 7? Check it and write Yes or No.
12
FEstimate 13 × 9 by rounding 13 to the nearest 10.
13
FEstimate 44 × 9 by rounding 44 to the nearest 10.
14
RIs 480 the correct answer to 60 × 8? Check it and write Yes or No.
15
FEstimate 90 × 8 by rounding 90 to the nearest 10.
16
RIs 48 the correct answer to 16 × 3? Check it and write Yes or No.
4.5

Multiplication word problems

Level 5
Solve problems with equal groups, scaling and pence, Choose multiplication and check the units
Video lesson: Multiplication word problemsComing soon

Equal groups: multiply the number in each group by the number of groups.

Scaling: multiply by the number of times, for example 3 times as many as 14 is 3 × 14.

Key ideas

  • Equal groups: number in each group × number of groups.
  • Scaling: amount × number of times.
  • Give the answer in the same unit as the question.
Worked example 4.5.1
A box holds 24 pencils. How many pencils are in 7 boxes?

Method. Multiply the number in each group by the number of groups, or the amount by the number of times.

  1. Find the number in each group and the number of groups. Each box is one group.
    24 pencils in each of 7 boxes
  2. Multiply to find the total. Equal groups: multiply the number in each group by the number of groups.
    24 × 7 = 168
  3. Write the answer. This is the total number of pencils.
    168 pencils

Check. Check: 168 is more than the first number, because we multiplied by 7.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Worked example 4.5.2
Sam has 14 stamps. Lee has 3 times as many stamps as Sam. How many stamps does Lee have?

Method. Multiply the number in each group by the number of groups, or the amount by the number of times.

  1. Find the scaling number. Lee has the number of times as many as Sam.
    3 times 14
  2. Multiply. Scaling is multiplying by the number of times.
    14 × 3 = 42
  3. Write the answer. This is the number of stamps Lee has.
    42 stamps

Check. Check: 42 is more than the first number, because we multiplied by 3.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Worked example 4.5.3
One pen costs 32p. How much do 5 pens cost? Give the answer in pence.

Method. Multiply the number in each group by the number of groups, or the amount by the number of times.

  1. Find the cost of one pen and the number of pens. Each pen costs the same amount.
    32p for each of 5 pens
  2. Multiply the cost of one pen by the number of pens. The total cost is the cost of each times the number.
    32p × 5 = 160p
  3. Write the answer. Give the cost in pence, as the question asks.
    160p

Check. Check: 160p is more than the first number, because we multiplied by 5.

Watch out. Check the units: the answer should be in the same unit as the question (pencils, pence, stamps).

Watch out

Watch out. Times as many means multiply, not add. 3 times as many as 14 is 42, not 17.

Exam tip

Grown-up tip. Ask the child to say the unit in the answer: pencils, pence or stamps.

Exercise 4E  Practice: multiplication word problems

Non-calculator
1
PSOne pen costs 13p. How much do 8 pens cost? Give the answer in pence.
2
PSA box holds 20 pencils. How many pencils are in 4 boxes?
3
PSOne pen costs 29p. How much do 8 pens cost? Give the answer in pence.
4
PSSam has 35 stamps. Lee has 2 times as many stamps as Sam. How many stamps does Lee have?
5
PSA box holds 12 pencils. How many pencils are in 4 boxes?
6
PSA box holds 46 pencils. How many pencils are in 7 boxes?
7
PSA box holds 28 pencils. How many pencils are in 5 boxes?
8
PSOne pen costs 41p. How much do 8 pens cost? Give the answer in pence.
9
PSOne pen costs 28p. How much do 3 pens cost? Give the answer in pence.
10
PSA box holds 24 pencils. How many pencils are in 8 boxes?
11
PSSam has 58 stamps. Lee has 2 times as many stamps as Sam. How many stamps does Lee have?
12
PSA box holds 30 pencils. How many pencils are in 6 boxes?
13
PSOne pen costs 76p. How much do 9 pens cost? Give the answer in pence.
14
PSOne pen costs 54p. How much do 3 pens cost? Give the answer in pence.
15
PSSam has 14 stamps. Lee has 5 times as many stamps as Sam. How many stamps does Lee have?
16
PSSam has 24 stamps. Lee has 9 times as many stamps as Sam. How many stamps does Lee have?

Chapter summary

SkillMethod
Two-digit by one-digitMultiply the ones, then the tens; write each in its column
CarryingWrite the ones digit; carry the tens; add the carry to the next product
Three-digit by one-digitWork from the right; carry from each column into the next
Estimating and checkingRound to an easy number; check by dividing
Word problemsEqual groups and scaling are multiplication; keep the unit

Can you…?

  • I can multiply a two-digit number by a one-digit number, column by column
  • I can carry tens into the next column when multiplying
  • I can multiply a three-digit number by a one-digit number
  • I can estimate a product by rounding, and check it by division
  • I can solve multiplication word problems with equal groups and scaling

Key terms

product
the answer to a multiplication
carry
move the tens from one column to the column on its left
estimate
a sensible guess, found by rounding first
scaling
making an amount a number of times as big

Exercise 4Z  Check-up

Non-calculator
1
Work out 576 × 2.
2
Work out 17 × 8.
3
Work out 931 × 6.
4
One pen costs 63p. How much do 4 pens cost? Give the answer in pence.
5
Sam has 28 stamps. Lee has 4 times as many stamps as Sam. How many stamps does Lee have?
6
Work out 47 × 9.
7
Sam has 36 stamps. Lee has 8 times as many stamps as Sam. How many stamps does Lee have?
8
Work out 722 × 6.
9
Is 776 the correct answer to 97 × 8? Check it and write Yes or No.
10
Work out 257 × 2.

Total 19 marks. Allow about 19 minutes.

Exercise 4X  Practice test questions

Non-calculator
1
FWork out 204 × 6.[1 mark]
2
FWork out 33 × 3.[1 mark]
3
FEstimate 67 × 4 by rounding 67 to the nearest 10.[1 mark]
4
FEstimate 58 × 2 by rounding 58 to the nearest 10.[1 mark]
5
FWork out 12 × 3.[2 marks]
6
FWork out 77 × 7.[2 marks]
7
FWork out 22 × 9.[2 marks]
8
FWork out 43 × 4.[3 marks]
9
PSA box holds 35 pencils. How many pencils are in 9 boxes?[3 marks]
10
RIs 85 the correct answer to 17 × 5? Check it and write Yes or No.[3 marks]
← Chapter 3: Times tables 6 to 12Chapter 5: Short division with remainders →

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