Welcome to this, the second of our medium level quizzes on fractions. In it we shall recap what we have learnt about denominators, numerators, mixed and improper fractions. These are all important parts of Eleven Plus maths, so you need to understand them before you take your exams.

Fractions, as you know, are a way of representing parts of numbers. They do exactly the same job as decimal numbers, but in a very different way! For example, one-half as a decimal is 0.5, but as a fraction it’s written ^{1}⁄_{2}. That simply means the top number (1) ÷ the bottom number (2).

Just to make sure you know, the top number in a fraction is the NUMERATOR and the bottom number is the DENOMINATOR. Denominators (the 2 in ^{1}⁄_{2}) tell us how many pieces to cut a whole into, while numerators tell us how many of these pieces we get.

I’m sure by now that you are a whizz with fractions. So, have a go at this quiz and see if you can get ^{10}⁄_{10} of the questions right!

1.

What is ^{4}⁄_{5} of 45?

42

40

36

32

2.

What is ^{9}⁄_{7} of 49?

56

63

70

77

Of means multiply in this case: ^{9}⁄_{7} × 49 = (9 × 49) ÷ 7 = 441 ÷ 7 = 63. ^{9}⁄_{7} is greater than 1, so the answer will be more than 49

3.

Which is greater: ^{1}⁄_{7} x ^{1}⁄_{4}, or ^{1}⁄_{9} x ^{1}⁄_{3}?

They are equal in value

Not enough information to answer

To multiply fractions, times the numerators by each other, and the denominators by each other: ^{1}⁄_{7} x ^{1}⁄_{4} = ^{1}⁄_{28}

^{1}⁄_{9} x ^{1}⁄_{3} = ^{1}⁄_{27}

4.

What is 4 ^{7}⁄_{8} 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 × 8 = 32. STEP 2: 32 + 7 = 39. STEP 3: ^{39}⁄_{8}

5.

What is ^{2}⁄_{3} + ^{4}⁄_{6} + ^{8}⁄_{9}?

2 ^{2}⁄_{3}

2 ^{7}⁄_{9}

3

2 ^{2}⁄_{9}

First, convert all the fractions to the same numerator: ^{2}⁄_{3} + ^{4}⁄_{6} + ^{8}⁄_{9} = ^{6}⁄_{9} + ^{6}⁄_{9} + ^{8}⁄_{9} = ^{20}⁄_{9}. We then convert this into a mixed fraction: 2 ^{2}⁄_{9}

6.

How many nineteenths are there in 3?

60

57

54

22

There are 19 nineteenths in 1, so there are 19 × 3 = 57 nineteenths in 3. 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, 1⁄3, to make 1, but you need ten tenths, 1⁄10, to make 1 and so on. REMEMBER this stuff, and you won't get confused with fractions

7.

What is ^{9}⁄_{10} - ^{2}⁄_{5} + ^{3}⁄_{2}?

2 ^{1}⁄_{15}

1 ^{4}⁄_{5}

2 ^{1}⁄_{10}

2

8.

What is ^{52}⁄_{13} as a mixed fraction?

4

3 ^{12}⁄_{13}

4 ^{1}⁄_{13}

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: 52 ÷ 13 = 4. STEP 2: Remainder 0. STEP 3: 4. If there is no remainder then the answer will be a whole number

9.

What is ^{18}⁄_{4} as a mixed fraction?

4

4 ^{1}⁄_{4}

4 ^{1}⁄_{2}

4 ^{3}⁄_{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: 18 ÷ 4 = 4. STEP 2: Remainder 2. STEP 3: 4 ^{2}⁄_{4}. 4 ^{2}⁄_{4} can be simplified by dividing the denominator and numerator by the same number, in this case 2, to give 4 ^{1}⁄_{2}

10.

What is 7 ^{14}⁄_{21} 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: 7 × 21 = 147. STEP 2: 147 + 14 = 161. STEP 3: ^{161}⁄_{21}. This can then be simplified by dividing denominator and numerator by the same number, in this case 7, to give ^{23}⁄_{3}

^{4}⁄_{5}× 45 = (4 × 45) ÷ 5 = 180 ÷ 5 = 36. Do the brackets first.