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pairs of shoes hanging on a washing line

James spent two-thirds of a quarter of his wages on some new shoes.

Fractions 3 (Easy)

Fractions are everywhere in life, from sharing cake to measuring land. This 11 Plus Maths quiz helps you explore how parts combine to make a whole.

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Fascinating Fact:

One third of the world’s land is used for farming, meaning humans really do take a large slice of the planet’s pie.

In 11 Plus Maths, pupils learn to understand fractions as equal parts of a whole. This includes comparing, simplifying, and linking them to decimals and percentages.

Key Terms

Fraction: A way of showing part of a whole using a numerator and a denominator.
Equivalent Fractions: Fractions that represent the same value, such as ½ and 2?4.
Simplify: To reduce a fraction to its lowest form without changing its value.

For help finding trusted learning resources, read our Guide to 11 Plus Courses and Materials for Parents .

Frequently Asked Questions (Click to see answers)

What is an equivalent fraction?

An equivalent fraction has the same value as another fraction, even if the numbers look different. For example, ½ equals 2?4.

How do I simplify a fraction?

Divide both the numerator and the denominator by their highest common factor until you cannot simplify further.

Why are fractions important in maths?

Fractions help us measure, divide, and understand relationships between quantities in real-life situations such as cooking or building.

Try These Related Quizzes

1 .

What is ³⁶⁄₁₆ as a mixed fraction?

2¹⁄₄

2¹⁄₃

2¹⁄₂

36 ÷ 16 = 2.25

2 .

If, in an election, ¹⁄₄ of people voted for the Red Party, ⁶⁄₁₀ voted for the Yellow Party and the rest voted for the Blue Party, what fraction of voters voted for the Blue Party?

³⁄₁₀

³⁄₂₀

¹⁄₄

¹⁷⁄₂₀

First, convert all fractions to the same denominator: ¹?₄ + ⁶?₁₀ = ⁵?₂₀ + ¹²?₂₀ = ¹⁷?₂₀.
²⁰?₂₀ - ¹⁷?₂₀ = ³?₂₀

3 .

What is the improper fraction ²⁶⁄₈ as a mixed fraction?

3³⁄₈

3¹⁄₂

3¹⁄₄

3¹⁄₆

To convert an improper fraction to a mixed fraction, follow these steps:
1. Divide the numerator by the denominator.
2. Note the whole number remainder.
3. Write the number from step 1 as the whole number in front of the fractional part AND write the fractional part with the remainder in the numerator and keep the original denominator.
STEP 1: 26 ÷ 8 = 3. STEP 2: Remainder 2. STEP 3: 3²?₈ which can be simplified to 3¹?₄

4 .

James spent two-thirds of a quarter of his wages on some new shoes. If his wages were £312, how much did James’ new shoes cost?

£208

£26

£78

£52

¹?₄ × £312 = (312 ÷ 4) = £78. That’s a quarter of James’ wages.
78 ÷ 3 = £26. That’s a third of a quarter of James’ wages.
26 x 2 = £52. That’s two-thirds of a quarter of James’ wages

5 .

What is one twelfth of 132?

¹?₁₂ × 132 = 132 ÷ 12 = 11

6 .

What is 7³⁄₅ as an improper fraction?

³⁸⁄₁₀

³⁸⁄₅

³⁶⁄₅

³⁴⁄₅

To convert a mixed fraction to an improper fraction, follow these steps:
1. Multiply the whole number part by the denominator.
2. Add this result to the numerator.
3. Write the fraction with step 2 in the numerator and keep the original denominator.
STEP 1: 5 × 7 = 35. STEP 2: 35 + 3 = 38. STEP 3: ³⁸?₅

7 .

What is 4⁹⁄₂₇ as an improper fraction?

¹³⁄₉

¹³⁄₆

¹³⁄₃

¹³⁄₂

To convert a mixed fraction to an improper fraction, follow these steps:
1. Multiply the whole number part by the denominator.
2. Add this result to the numerator.
3. Write the fraction with step 2 in the numerator and keep the original denominator.
STEP 1: 4 × 27 = 108. STEP 2: 108 + 9 = 117. STEP 3: ¹¹⁷?₂₇. This can be simplified to ¹³?₃ by dividing the numerator and denominator by 9

8 .

If you are asked to find ⁴⁄₅ of something, what is the best method of doing it?

Multiply by 4 then divide by 5

Divide by 4 then multiply by 5

Multiply by 5 then divide by 4

Divide by 5 then multiply by 4

To find one-fifth of something, you divide it by five. To find four-fifths, multiply one-fifth by four

9 .

Susan got one-seventh of the questions in her maths test wrong. If there were 98 questions in the test, how many did Susan get right?

The word 'of' means multiply; therefore one-seventh OF something means multiply by ¹?₇ BUT multiplying by a seventh is the same as dividing by seven: 98 ÷ 7 = 14.
If Susan got 14 questions wrong then she got 98 - 14 = 84 questions right

10 .

What is ¹⁄₅ of ³⁄₄?

3³⁄₄

¹⁄₂₀

³⁄₉

³⁄₂₀

Of, in this case, means multiply. You multiply the numbers in the denominator together, and you multiply the numbers in the numerator together to form a single fraction: 1 x 3 = 3 and 5 x 4 = 20 so ¹?₅ x ³?₄ = ³?₂₀

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)