In this Eleven Plus maths quiz on fractions, you will be asked to convert mixed fractions to improper ones, and vice versa. You’ll also need to be able to compare fractions and find which has the greater or lower value.

Here’s a little reminder:

- Mixed fractions have a whole number and a fraction, e.g. 2
^{1}⁄_{3}is a mixed fraction - Improper fractions have a larger numerator than denominator, e.g.
^{4}⁄_{3}is an improper fraction

So, now we’ve remembered the two types of fraction, can you recall how to convert one to the other? If not then I suggest you go back and play some of our previous quizzes where it’s explained in detail.

Now on with the quiz. Good luck!

1.

What is 2^{7}⁄_{8} as an improper fraction?

2.

What is ^{3}⁄_{12} + ^{3}⁄_{6} + ^{3}⁄_{4}?

1^{1}⁄_{4}

1^{1}⁄_{2}

1^{1}⁄_{3}

1^{1}⁄_{6}

First, convert all the fractions to the same numerator: ^{3}⁄_{12} + ^{3}⁄_{6} + ^{3}⁄_{4} = ^{3}⁄_{12} + ^{6}⁄_{12} + ^{9}⁄_{12} = ^{18}⁄_{12}. We then convert this into a mixed fraction: 1^{6}⁄_{12} which can be simplified to 1^{1}⁄_{2}

3.

What is 6^{3}⁄_{4} 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: 6 × 4 = 24. STEP 2: 24 + 3 = 27. STEP 3:^{27}⁄_{4}

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: 6 × 4 = 24. STEP 2: 24 + 3 = 27. STEP 3:

4.

How many thirteenths are there in 6?

72

74

76

78

There are thirteen thirteenths in 1, so there are 13 × 6 = 78 thirteenths in 6. In general, the number in the denominator tells you how many fractions of that type are needed to make 1. For example, you need three thirds to make 1, but you need ten tenths to make 1 and so on.

REMEMBER this stuff, and you won't get confused with fractions

REMEMBER this stuff, and you won't get confused with fractions

5.

What is ^{13}⁄_{16} - ^{1}⁄_{2} + ^{3}⁄_{4}?

1

1^{1}⁄_{16}

1^{1}⁄_{8}

Convert all the fractions to the same numerator, then do your calculations. If the denominators are the same, you can add the fractions by simply adding their numerators - it really is as easy as that!

6.

What is ^{43}⁄_{5} as a mixed fraction?

8^{1}⁄_{5}

7^{3}⁄_{5}

8^{3}⁄_{5}

9^{1}⁄_{5}

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: 43 ÷ 5 = 8. STEP 2: Remainder 3. STEP 3: 8^{3}⁄_{5}

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: 43 ÷ 5 = 8. STEP 2: Remainder 3. STEP 3: 8

7.

Which is greater: ^{1}⁄_{2} x ^{1}⁄_{13}, or ^{1}⁄_{3} x ^{1}⁄_{9}?

They are both the same

There is not enough information to answer the question

To multiply fractions, times the numerators by each other, and the denominators by each other: ^{1}⁄_{2} x ^{1}⁄_{13} = ^{1}⁄_{26}

^{1}⁄_{3} x ^{1}⁄_{9} = ^{1}⁄_{27}

8.

What is ^{19}⁄_{4} as a mixed fraction?

5^{1}⁄_{4}

5

4^{3}⁄_{4}

4^{1}⁄_{2}

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: 19 ÷ 4 = 4. STEP 2: Remainder 3. STEP 3: 4^{3}⁄_{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: 19 ÷ 4 = 4. STEP 2: Remainder 3. STEP 3: 4

9.

What is ^{6}⁄_{7} of 84?

82

78

72

66

Of means multiply in this case: ^{6}⁄_{7} × 84 = (6 × 84) ÷ 7 = 504 ÷ 7 = 72. Do the brackets first

10.

What is ^{13}⁄_{9} of 63?

91

84

77

70

Of means multiply in this case: ^{13}⁄_{9} × 63 = (13 × 63) ÷ 9 = 819 ÷ 9 = 91. ^{13}⁄_{9} is greater than 1, so the answer will be more than 63

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: 2 × 8 = 16. STEP 2: 16 + 7 = 23. STEP 3:

^{23}⁄_{8}