Step-by-step Maths Level 4: Fractions of amounts in problems
Part of the Step-by-step Maths Level 4 solving problems with the four operations chapter. Chapter overview · whole chapter on one page
Fractions of amounts in problems
To find a fraction of an amount in a story, divide by the bottom number to find one equal part. Then multiply by the top number.
If the question asks what is left, take the part away from the total.
Key ideas
- Divide by the bottom number for one equal part.
- Multiply by the top number for the fraction.
- Read the question: “how many are left” needs one more step.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 60 ÷ 5. The bottom number tells how many equal parts.60 ÷ 5 = 12
- Take 3 parts. The top number tells how many parts are green.3 × 12 = 36
- Write the answer. This is the number of green marbles.36
Check. Check: 36 green and 24 not green make 60.
Watch out. A fraction of an amount needs the division first.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 48 ÷ 8. Divide by the bottom number.48 ÷ 8 = 6
- Find the cards given away: 3 × 6. Multiply by the top number.3 × 6 = 18
- Take it away from the total. The question asks what is left.48 - 18 = 30
- Write the answer. This is how many are left.30
Check. Check: 18 given and 30 left make 48.
Watch out. Find the amount given away, then take it from the total.
Method. Find one equal part by dividing by the bottom number. Then find the part that is not red.
- Find the red cards: 36 ÷ 4. A quarter of 36 is one part of four equal parts.36 ÷ 4 = 9
- Find the cards that are not red. Take the red cards away from the total.36 - 9 = 27
- Write the answer. This is the number of cards that are not red.27
Check. Check: 9 red and 27 not red make 36.
Watch out. The part that is not red is the total minus the red part.
Watch out
Watch out. 3/8 of 48 is 18, not 3/8 of 8. Divide the total by the bottom number, not by the top.
Exam tip
Grown-up tip. Ask: “How many equal parts are there? What is one part? How many parts do we need?”
Exercise 9D Practice: fractions of amounts in problems
Non-calculatorMethod. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 16 ÷ 2. The bottom number tells how many equal parts.16 ÷ 2 = 8
- Take 1 parts. The top number tells how many parts are blue.1 × 8 = 8
- Write the answer. This is the number of blue ones.8
Check. Check: the parts given and the parts left make 16.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 155 ÷ 5. Divide by the bottom number.155 ÷ 5 = 31
- Find the amount given away: 1 × 31. Multiply by the top number.1 × 31 = 31
- Take it away from the total. The question asks what is left.155 - 31 = 124
- Write the answer. This is how many are left.124
Check. Check: the parts given and the parts left make 155.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 78 ÷ 2. The bottom number tells how many equal parts.78 ÷ 2 = 39
- Take 1 parts. The top number tells how many parts are blue.1 × 39 = 39
- Write the answer. This is the number of blue ones.39
Check. Check: the parts given and the parts left make 78.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 57 ÷ 3. The bottom number tells how many equal parts.57 ÷ 3 = 19
- Take 1 parts. The top number tells how many parts are blue.1 × 19 = 19
- Write the answer. This is the number of blue ones.19
Check. Check: the parts given and the parts left make 57.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 69 ÷ 3. Divide by the bottom number.69 ÷ 3 = 23
- Find the amount given away: 1 × 23. Multiply by the top number.1 × 23 = 23
- Take it away from the total. The question asks what is left.69 - 23 = 46
- Write the answer. This is how many are left.46
Check. Check: the parts given and the parts left make 69.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 132 ÷ 4. Divide by the bottom number.132 ÷ 4 = 33
- Find the amount given away: 3 × 33. Multiply by the top number.3 × 33 = 99
- Take it away from the total. The question asks what is left.132 - 99 = 33
- Write the answer. This is how many are left.33
Check. Check: the parts given and the parts left make 132.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 184 ÷ 8. Divide by the bottom number.184 ÷ 8 = 23
- Find the amount given away: 7 × 23. Multiply by the top number.7 × 23 = 161
- Take it away from the total. The question asks what is left.184 - 161 = 23
- Write the answer. This is how many are left.23
Check. Check: the parts given and the parts left make 184.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 200 ÷ 5. The bottom number tells how many equal parts.200 ÷ 5 = 40
- Take 1 parts. The top number tells how many parts are blue.1 × 40 = 40
- Write the answer. This is the number of blue ones.40
Check. Check: the parts given and the parts left make 200.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 28 ÷ 2. The bottom number tells how many equal parts.28 ÷ 2 = 14
- Take 1 parts. The top number tells how many parts are blue.1 × 14 = 14
- Write the answer. This is the number of blue ones.14
Check. Check: the parts given and the parts left make 28.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 20 ÷ 5. The bottom number tells how many equal parts.20 ÷ 5 = 4
- Take 4 parts. The top number tells how many parts are blue.4 × 4 = 16
- Write the answer. This is the number of blue ones.16
Check. Check: the parts given and the parts left make 20.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 46 ÷ 2. The bottom number tells how many equal parts.46 ÷ 2 = 23
- Take 1 parts. The top number tells how many parts are blue.1 × 23 = 23
- Write the answer. This is the number of blue ones.23
Check. Check: the parts given and the parts left make 46.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 120 ÷ 3. The bottom number tells how many equal parts.120 ÷ 3 = 40
- Take 2 parts. The top number tells how many parts are blue.2 × 40 = 80
- Write the answer. This is the number of blue ones.80
Check. Check: the parts given and the parts left make 120.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 32 ÷ 2. Divide by the bottom number.32 ÷ 2 = 16
- Find the amount given away: 1 × 16. Multiply by the top number.1 × 16 = 16
- Take it away from the total. The question asks what is left.32 - 16 = 16
- Write the answer. This is how many are left.16
Check. Check: the parts given and the parts left make 32.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 93 ÷ 3. Divide by the bottom number.93 ÷ 3 = 31
- Find the amount given away: 2 × 31. Multiply by the top number.2 × 31 = 62
- Take it away from the total. The question asks what is left.93 - 62 = 31
- Write the answer. This is how many are left.31
Check. Check: the parts given and the parts left make 93.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 48 ÷ 4. Divide by the bottom number.48 ÷ 4 = 12
- Find the amount given away: 1 × 12. Multiply by the top number.1 × 12 = 12
- Take it away from the total. The question asks what is left.48 - 12 = 36
- Write the answer. This is how many are left.36
Check. Check: the parts given and the parts left make 48.
Watch out. A fraction of an amount needs the division first, then the multiplication.
Method. Find one equal part by dividing by the bottom number, then multiply by the top number.
- Find one equal part: 280 ÷ 8. The bottom number tells how many equal parts.280 ÷ 8 = 35
- Take 2 parts. The top number tells how many parts are blue.2 × 35 = 70
- Write the answer. This is the number of blue ones.70
Check. Check: the parts given and the parts left make 280.
Watch out. A fraction of an amount needs the division first, then the multiplication.