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:
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!














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

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} 

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

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 

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} 
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: 2 × 8 = 16. STEP 2: 16 + 7 = 23. STEP 3: ^{23}⁄_{8} 

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} 
^{13}⁄_{16}  ^{1}⁄_{2} + ^{3}⁄_{4} = ^{13}⁄_{16}  ^{8}⁄_{16} + ^{12}⁄_{16} = ^{17}⁄_{16} which is the same as 1^{1}⁄_{16}
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! 

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}

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} 