In the last Eleven Plus maths quiz we learnt about improper fractions (in which the numerator (top number) is greater than or equal to the denominator (bottom number)) and mixed fractions (in which there is a whole number and a fractional part). In this second easy quiz on fractions, we give you more opportunity to familiarise yourself with these terms.

There will be times in maths when you are asked to convert an improper fraction to a mixed one, and vice versa. Thankfully, there are some simple rules which make this easier: to convert a mixed fraction to an improper fraction, first multiply the whole number part by the denominator, then add your answer to the numerator. E.g. 3 ^{1}⁄_{3} = ((3 x 3) + 1) ÷ 3 = ^{10}⁄_{3}.

To do the reverse, simply divide the numerator by the denominator. Write the answer before the fraction and put any remainders in the numerator place. E.g. ^{10}⁄_{3} = 10 ÷ 3 = 3 remainder 1 = 3 ^{1}⁄_{3}.

1.

What is 6 ^{9}⁄_{12} as an improper fraction?

2.

What is one ninth of 81?

9

90

72

729

3.

What is 3 ^{2}⁄_{3} 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: 3 × 3 = 9. STEP 2: 9 + 2 = 11. STEP 3: ^{11}⁄_{3}

4.

Sophie spent two-thirds of her Christmas money on a book about horses. If she got £24 in total, how much was Sophie’s book?

£20

£18

£16

£14

5.

What is ^{14}⁄_{6} as a mixed fraction?

2 ^{1}⁄_{6}

2 ^{1}⁄_{3}

2 ^{1}⁄_{4}

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: 14 ÷ 6 = 2. STEP 2: Remainder 2. STEP 3: 2 ^{2}⁄_{6}. Of course, this can be simplified further as 2 ^{1}⁄_{3}

6.

What is the quickest way to find ^{2}⁄_{3} of a number?

Divide by two then add three

Divide by three then add two

Multiply by three then divide by two

Divide by three then multiply by two

To find one-third of something, you divide it by three. To find two-thirds, multiply one-third by two

7.

Arnold ate ^{7}⁄_{15} of a cake and Betty ate a third. How much cake is left for their brother Clive?

First, convert all fractions to the same denominator: ^{7}⁄_{15} + ^{1}⁄_{3} = ^{7}⁄_{15} + ^{5}⁄_{15} = ^{12}⁄_{15}. There is ^{3}⁄_{15}, or ^{1}⁄_{3} of the cake left for Clive

8.

John got one-sixth of the questions in his maths test wrong. If there were 120 questions in the test, how many did John get wrong?

100

80

50

20

The word 'of' means multiply; therefore one-sixth OF something means multiply by ^{1}⁄_{6} BUT multiplying by a sixth is the same as dividing by six: 120 ÷ 6 = 20

9.

What is ^{66}⁄_{24} as a mixed fraction?

2 ^{17}⁄_{24}

2 ^{3}⁄_{4}

2 ^{19}⁄_{24}

2 ^{2}⁄_{3}

REDUCE the fraction to its simplest form: divide the denominator by 24 to get 2 remainder 18. So, the fraction is 2 ^{18}⁄_{24}. This can be simplified further by dividing the numerator and denominator by 6: 2 ^{18}⁄_{24} = 2 ^{3}⁄_{4}

10.

What is ^{1}⁄_{3} of ^{1}⁄_{3}?

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 1 = 1 and 3 x 3 = 9 so ^{1}⁄_{3} x ^{1}⁄_{3} = ^{1}⁄_{9}

STEP 1: 6 × 12 = 72. STEP 2: 72 + 9 = 81. STEP 3:

^{81}⁄_{12}BUT you must now REDUCE the fraction to its simplest form: divide the numerator and the denominator by 3 to get^{27}⁄_{4}