I'll solve each problem step by step, working through all calculations carefully.
Problem a) Malachi has £208 and spends 3/8 of his money on a toy.
- To find 3/8 of 208: First find 1/8, then multiply by 3
- 208 ÷ 8 = 26
- 26 × 3 = 78
- Malachi spends £78
Problem b) Zach read a book of 270 pages and read 2/9 of it on the first day.
- To find 2/9 of 270: First find 1/9, then multiply by 2
- 270 ÷ 9 = 30
- 30 × 2 = 60
- Zach read 60 pages
Problem c) Leanna's gran lives 120 miles away and she has travelled 5/6 of the distance.
- To find 5/6 of 120: First find 1/6, then multiply by 5
- 120 ÷ 6 = 20
- 20 × 5 = 100
- She has travelled 100 miles
Problem d) Leanna bought 35 litres of paint and used 4/7 of it.
- To find 4/7 of 35: First find 1/7, then multiply by 4
- 35 7 = 5
- 5 × 4 = 20
- She used 20 litres
Problem e) There are 315 rabbits and 2/5 are female. How many are NOT female?
- Method 1: Find females first, then subtract
- 2/5 of 315: 315 ÷ 5 = 63, then 63 × 2 = 126 females
- Not female: 315 - 126 = 189
- Method 2: If 2/5 are female, then 3/5 are not female
- 3/5 of 315: 315 ÷ 5 = 63, then 63 × 3 = 189
- 189 rabbits are not female
Problem f) Tia collects 336 postage stamps and gives 3/7 to her sister. How many does she have left?
- Method 1: Find how many given away, then subtract
- 3/7 of 336: 336 ÷ 7 = 48, then 48 × 3 = 144 given away
- Left: 336 - 144 = 192
- Method 2: If she gives away 3/7, she keeps 4/7
- 4/7 of 336: 336 ÷ 7 = 48, then 48 × 4 = 192
- She has 192 stamps left
Problem g) David scored 42 points total. In the first half he scored 5/7 of all points. How many in the second half?
- Method 1: Find first half score, then subtract
- 5/7 of 42: 42 ÷ 7 = 6, then 6 × 5 = 30 in first half
- Second half: 42 - 30 = 12
- Method 2: If 5/7 in first half, then 2/7 in second half
- 2/7 of 42: 42 ÷ 7 = 6, then 6 × 2 = 12
- David scored 12 points in the second half
Problem h) There are 216 fish total. 7/12 are large fish. How many small fish?
- Method 1: Find large fish first, then subtract
- 7/12 of 216: 216 ÷ 12 = 18, then 18 × 7 = 126 large fish
- Small fish: 216 - 126 = 90
- Method 2: If 7/12 are large, then 5/12 are small
- 5/12 of 216: 216 ÷ 12 = 18, then 18 × 5 = 90
- There are 90 small fish
Let me verify my calculations:
a) 208 ÷ 8 = 26, 26 × 3 = 78 ✓
b) 270 ÷ 9 = 30, 30 × 2 = 60 ✓
c) 120 ÷ 6 = 20, 20 × 5 = 100 ✓
d) 35 ÷ 7 = 5, 5 × 4 = 20 ✓
e) 315 ÷ 5 = 63, 63 × 3 = 189 ✓
f) 336 7 = 48, 48 × 4 = 192 ✓
g) 42 ÷ 7 = 6, 6 × 2 = 12 ✓
h) 216 ÷ 12 = 18, 18 × 5 = 90 ✓
Final Answer:
a) £78
b) 60 pages
c) 100 miles
d) 20 litres
e) 189 rabbits
f) 192 stamps
g) 12 points
h) 90 small fish
Parent Tip: Review the logic above to help your child master the concept of non unit fractions worksheet.
