Welcome to the third quiz in our Easy series of Eleven Plus maths quizzes on fractions. If you have played the first two, then you’ll know all about denominators and numerators, but how are you when it comes to multiplying or dividing fractions? Now’s your chance to find out!

Here’s a quick recap which will help prepare you for some of the questions:

To convert an improper fraction to a mixed fraction, follow these steps:- Divide the numerator by the denominator.
- Note the whole number remainder.
- 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.

Can you remember how to do the opposite and convert a mixed fraction into an improper one? If not, don’t worry. The helpful comments after the questions will make things clear. Good luck!

1.

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

2.

What is ^{1}⁄_{5} of ^{3}⁄_{4}?

3^{3}⁄_{4}

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}

3.

What is one twelfth of 132?

11

13

9

7

4.

What is 4^{9}⁄_{27} as an improper fraction?

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

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:

5.

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

6.

What is ^{36}⁄_{16} as a mixed fraction?

2^{1}⁄_{4}

2^{1}⁄_{3}

2^{1}⁄_{2}

2

36 ÷ 16 = 2.25

7.

What is the improper fraction ^{26}⁄_{8} as a mixed fraction?

3^{3}⁄_{8}

3^{1}⁄_{2}

3^{1}⁄_{4}

3^{1}⁄_{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: 3^{2}⁄_{8} which can be simplified to 3^{1}⁄_{4}

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: 3

8.

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?

First, convert all fractions to the same denominator: ^{1}⁄_{4} + ^{6}⁄_{10} = ^{5}⁄_{20} + ^{12}⁄_{20} = ^{17}⁄_{20}.

^{20}⁄_{20} - ^{17}⁄_{20} = ^{3}⁄_{20}

9.

What is 7^{3}⁄_{5} as an improper fraction?

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}

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:

10.

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?

14

69

76

84

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

If Susan got 14 questions wrong then she got 98 - 14 = 84 questions right

^{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