Step-by-step Maths Level 3: Multiplication, fractions and measures
Part of the Step-by-step Maths Level 3 level 3 check chapter. Chapter overview · whole chapter on one page
Multiplication, fractions and measures
Equal groups are repeated addition. The 2, 5 and 10 facts help with the total and with division.
A quarter is one of four equal parts. Change length and mass to the same unit before you compare them.
Key ideas
- Equal groups: add the group size once for each group.
- The 2, 5 and 10 facts help with division.
- Quarters are four equal parts; 3/4 is three of them.
- 100 cm = 1 m and 1000 g = 1 kg.
Method. Repeated addition: add the same number once for each group.
- Write one 4 for each group. There are 3 groups, so there are 3 lots of 4.4 + 4 + 4
- Add them up. Add the groups one after another, or count in steps of the group size.4 + 4 + 4 = 12
- Write the answer. This is the total altogether.12
Check. Count in 4s 3 times and you reach 12.
Watch out. Add 4 3 times. Do not add 3 4 times.
Method. Use the 2, 5 or 10 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 10 × ? = 60. Division asks how many groups.10 × ? = 60
- Count in 10s until you reach 60. Count the steps as you go.10, 20, 30, 40, 50, 60
- Write the answer. This is the number of groups.6
Check. Check: 10 × 6 = 60, so 60 ÷ 10 = 6.
Watch out. The times table of 10 is the key. Division is the opposite of multiplication.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 20 into 4 equal groups. Each group is one part of the whole.20 ÷ 4 = 5
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 5 = 5
- Write the answer. This is the amount for the fraction.5
Check. Check: 5 is 1 of the 4 equal groups of 5.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Watch out
Watch out. 1/4 of 20 is 5, not 10. Divide by 4 for quarters.
Exam tip
Grown-up tip. Make a quick list: the times tables, the halves and quarters, the units. Practise one list each day.
Exercise 10C Mixed practice: multiplication, fractions and measures
Non-calculatorMethod. Count in 10s to find 10 groups of 9. The order of the two numbers does not matter.
- Count in 10s, 9 times. Each count adds one more group of 10.10, 20, 30, 40, 50, 60, 70, 80, 90
- The last number we said is the answer. We counted in equal groups.10 × 9 = 90
- Write the answer. The order of the numbers does not change the answer.90
Check. Check: 9 × 10 is also 90.
Watch out. Say the 10 times table in order until you reach the fact you need.
Method. Change to cm, work it out, then change back.
- Change both to the smaller unit. 100 cm make one bigger unit.2 m 45 cm = 245 cm, 1 m 25 cm = 125 cm
- Add the cm. Work with the numbers in cm.245 + 125 = 370
- Change back to the bigger units. 370 cm is written with 100 cm as one bigger unit.370 cm = 3 m 70 cm
- Write the answer. This is the answer.3 m 70 cm
Check. Check: 3 m 70 cm - 1 m 25 cm = 2 m 45 cm.
Watch out. Work in cm to avoid mistakes. Change back at the end.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 6 groups, so there are 6 lots of 3.3 + 3 + 3 + 3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 + 3 + 3 + 3 = 18
- Write the answer. This is the total altogether.18
Check. Count in 3s 6 times and you reach 18.
Watch out. Add 3 6 times. Do not add 6 3 times.
Method. Count the rows and the dots in each row, then multiply.
- Count the rows. There are the number of rows given.2 rows
- Count the dots in each row. Each row has the same number of dots.3 dots
- Multiply. Rows times dots in a row.2 × 3 = 6
- Write the answer. This is the total number of dots.6
Check. Count the dots one by one to check: 6.
Watch out. Multiply the number of rows by the number in each row.
Method. Turning it round changes the rows and the columns. The total does not change.
- Now there are 3 rows. Each row now has the same dots as before, but turned.3 rows
- Multiply 3 by 2. Rows times dots in each row.3 × 2 = 6
- Write the answer. The total is the same as before.6
Check. 2 × 3 and 3 × 2 both give 6.
Watch out. Turning a number sentence round does not change the answer when you multiply.
Method. Count in 5s to find 5 groups of 11. The order of the two numbers does not matter.
- Count in 5s, 11 times. Each count adds one more group of 5.5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55
- The last number we said is the answer. We counted in equal groups.5 × 11 = 55
- Write the answer. The order of the numbers does not change the answer.55
Check. Check: 11 × 5 is also 55.
Watch out. Say the 5 times table in order until you reach the fact you need.
Method. Choose the unit that fits the size of the object.
- Think about how big or heavy it is. A strawberry is about the size of a thing we can check easily.a strawberry
- Choose the unit that fits. Heavy things are weighed in kilograms. Light things are weighed in grams.g
- Write the answer. This is the unit to use.g
Check. Think of a thing that is about the same size, so you can picture the unit.
Watch out. Metres and kilograms are large. Centimetres and grams are small.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.9 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 9
- Write the fraction. The top number is 1 for one part.1/9
Check. Check: 9 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. Use the 2, 5 or 10 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 10 × ? = 60. Division asks how many groups.10 × ? = 60
- Count in 10s until you reach 60. Count the steps as you go.10, 20, 30, 40, 50, 60
- Write the answer. This is the number of groups.6
Check. Check: 10 × 6 = 60, so 60 ÷ 10 = 6.
Watch out. The times table of 10 is the key. Division is the opposite of multiplication.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 4 equal parts.4 equal parts
- Count the shaded parts. 2 of the 4 parts are shaded.2 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.2/4
Check. Check: 2 shaded parts out of 4 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. Repeated addition: add the same number once for each group.
- Write one 3 for each group. There are 3 groups, so there are 3 lots of 3.3 + 3 + 3
- Add them up. Add the groups one after another, or count in steps of the group size.3 + 3 + 3 = 9
- Write the answer. This is the total altogether.9
Check. Count in 3s 3 times and you reach 9.
Watch out. Add 3 3 times. Do not add 3 3 times.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Find where the line starts. The line starts at this mark.start = 6 cm
- Find where the line ends. The line ends at this mark.end = 15 cm
- Subtract the start from the end. The length is the distance between the two marks.15 - 6 = 9
- Write the length. This is how long the line is.9 cm
Check. Add the length to the start: 6 + 9 = 15 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.
Method. Use the 2, 5 or 10 facts. Count in steps of the number to find the missing number.
- Think of the multiplication: 10 × ? = 20. Division asks how many groups.10 × ? = 20
- Count in 10s until you reach 20. Count the steps as you go.10, 20
- Write the answer. This is the number of groups.2
Check. Check: 10 × 2 = 20, so 20 ÷ 10 = 2.
Watch out. The times table of 10 is the key. Division is the opposite of multiplication.
Method. Use repeated addition, or count in steps of the group size.
- Write 5 groups of 2 as repeated addition. Each pack or group has the same number.2 + 2 + 2 + 2 + 2
- Add them up, or count in steps. Count in 2s, 5 times.2, 4, 6, 8, 10
- Write the answer. This is the total altogether.10
Check. Count in 2s 5 times and you reach 10.
Watch out. Multiply 5 by 2: each group is 2.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/5. We want a fraction with the same value.1/5
- Compare each option with the target. 2/10 covers the same part of a shape as 1/5.2/10
- Write the answer. This fraction is the same as the target.2/10
Check. Shade 1/5 and 2/10 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Count in 5s to find 5 groups of 12. The order of the two numbers does not matter.
- Count in 5s, 12 times. Each count adds one more group of 5.5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
- The last number we said is the answer. We counted in equal groups.5 × 12 = 60
- Write the answer. The order of the numbers does not change the answer.60
Check. Check: 12 × 5 is also 60.
Watch out. Say the 5 times table in order until you reach the fact you need.
Method. Use the ruler: find the start and the end of the line, then the difference.
- Put the 0 at the start of the line. Line up the ruler so the line begins at 0.0 cm
- Read where the line ends. The end of the line is on this number.The end is at 6
- Write the length. The length is the end number, because we started at 0.6 cm
Check. Count the centimetres from 0 to 6: 6 cm.
Watch out. Put the 0 of the ruler at the start of the line, then read the end.