Understand the rule first
The denominator names the size of each part. Use equivalent fractions when denominators differ, and divide by the denominator before multiplying by the numerator when finding a fraction of a quantity.
Fractions 11+ practice
Compare, combine and find fractions by making the parts comparable.
Calculate 3/4 + 1/8.
- Use eighths: 3/4 = 6/8.
- Add the numerators: 6/8 + 1/8 = 7/8.
- Seven eighths cannot be simplified.
A common misconception
Adding denominators as well as numerators, such as writing 1/4 + 1/4 = 2/8.
Reusable method: Draw a quick bar when the relationship is hard to see.Question 1 of 10 MathscoreWhich fraction is equivalent to 3/5?
- A6/8
- B6/10
- C9/20
- D12/25
Need a hint?
Multiply numerator and denominator by the same number.
Show worked answer
Answer B: 6/10
3/5 × 2/2 = 6/10.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 2 of 10 MathscoreCalculate 2/3 + 1/6.
- A3/9
- B1/2
- C3/6
- D5/6
Need a hint?
Rewrite two thirds in sixths.
Show worked answer
Answer D: 5/6
2/3 = 4/6, so 4/6 + 1/6 = 5/6.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 3 of 10 MathscoreWhat is 3/8 of 64?
- A8
- B16
- C32
- D24
Need a hint?
First find one eighth of 64.
Show worked answer
Answer D: 24
64 ÷ 8 = 8, and 3 × 8 = 24.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 4 of 10 Mathsexam-styleCalculate 5/6 − 1/4.
- A4/2
- B7/12
- C2/3
- D4/12
Need a hint?
Use a common denominator of 12.
Show worked answer
Answer B: 7/12
5/6 = 10/12 and 1/4 = 3/12, so the difference is 7/12.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 5 of 10 Mathsexam-styleA tank is 7/10 full. One fifth of the whole tank is used. What fraction remains?
- A1/2
- B2/5
- C3/10
- D6/10
Need a hint?
Express one fifth in tenths before subtracting.
Show worked answer
Answer A: 1/2
1/5 = 2/10. Then 7/10 − 2/10 = 5/10 = 1/2.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 6 of 10 MathscoreWhat is 3/5 of 45?
- A18
- B27
- C30
- D36
Need a hint?
Find one fifth first.
Show worked answer
Answer B: 27
45 ÷ 5 = 9, and 3 × 9 = 27.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 7 of 10 MathscoreCalculate 7/12 + 1/6. Give the answer in its simplest form.
- A2/3
- B8/18
- C3/4
- D5/6
Need a hint?
Rewrite one sixth in twelfths.
Show worked answer
Answer C: 3/4
1/6 = 2/12, so 7/12 + 2/12 = 9/12 = 3/4.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 8 of 10 MathscoreWhich fraction is greatest?
- A5/8
- B2/3
- C3/5
- D7/10
Need a hint?
Compare using decimals or a common denominator.
Show worked answer
Answer D: 7/10
5/8 = 0.625, 2/3 ≈ 0.667, 3/5 = 0.6 and 7/10 = 0.7, so 7/10 is greatest.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 9 of 10 MathsexamA roll contains 3.6 m of ribbon. Priya uses 5/12 of it. How much ribbon does she use?
- A1.5 m
- B1.2 m
- C1.8 m
- D2.1 m
Need a hint?
Divide 3.6 by 12, then multiply by 5.
Show worked answer
Answer A: 1.5 m
One twelfth of 3.6 m is 0.3 m; five twelfths is 5 × 0.3 = 1.5 m.
Quick method: Draw a quick bar when the relationship is hard to see.
Question 10 of 10 MathsstretchA tank is 2/7 emptied in the morning. In the afternoon, 1/3 of what remains is emptied. What fraction of the original tank remains?
- A5/21
- B10/21
- C4/7
- D2/3
Need a hint?
After the morning, find two thirds of the amount left.
Show worked answer
Answer B: 10/21
After the morning, 5/7 remains. Two thirds of that remains after the afternoon: 2/3 × 5/7 = 10/21.
Quick method: Draw a quick bar when the relationship is hard to see.