Welcome to the third quiz in our Difficult section of Eleven Plus maths on fractions. In it you will be tested on your ability to perform multiplication and division with fractions, and more besides!
As in previous quizzes, you will need to know the difference between a numerator and denominator, or between a mixed and an improper fraction. If you have played the previous quizzes then of course you will know. If not, don’t worry – everything is explained in the helpful comments after each question.
Make sure you read each question carefully before you choose your answer. Let’s see if you can get all ten questions right first time. Good luck!















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. 4. Simplify if possible STEP 1: 39 ÷ 9 = 4. STEP 2: Remainder 3. STEP 3: 4^{3}⁄_{9}. Step 4: 4^{1}⁄_{3} 

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 ÷ 6 = 4. STEP 2: Remainder 2. STEP 3: 4^{2}⁄_{6}. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 4^{1}⁄_{3} 
^{25}⁄_{28} of students passed their maths test BUT fractions alone DO NOT tell you the actual number of people or things involved. If you had been told that 28 took the test, then the answer would have been 3 students. Always be on the lookout for the BEST answer


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 × 15 = 30. STEP 2: 30 + 3 = 33. STEP 3: ^{33}⁄_{15}. Divide the numerator and denominator by 3 to reduce the fraction to its simplest form: ^{11}⁄_{5} 
The word OF means multiply: ^{7}⁄_{8} × ^{8}⁄_{12} = ^{56}⁄_{96} = ^{7}⁄_{12}. You multiply the numbers in the denominator together, and you multiply the numbers in the numerator together to form a single fraction. This fraction can then be reduced to its simplest form: sometimes you can reduce the fractions before you multiply them together


^{6}⁄_{10} can be reduced to ^{3}⁄_{5} (divide the numerator and the denominator by 2). Now you can see that ^{3}⁄_{5} is thrice as much as ^{1}⁄_{5}.

The word OF means multiply: ^{1}⁄_{5} × ^{1}⁄_{5} = ^{1}⁄_{25}. You now have to divide 100 by 25 to find how many hundredths equal ^{1}⁄_{25}. 100 ÷ 25 = 4


If Peter has delivered ^{7}⁄_{8} of the letters, all you have to do is find ^{1}⁄_{8} of 560: ^{1}⁄_{8} x 560 = 560 ÷ 8 = 70

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 × 9 = 36. STEP 2: 36 + 6 = 42. STEP 3: ^{42}⁄_{9}. Divide the numerator and denominator by 3 to reduce the fraction to its simplest form: ^{14}⁄_{3} 
First convert all the fraction to the same denominator (in this case twelfths), then add them. If the denominators are the same, you can add/subtract the fractions by simply adding/subtracting their numerators  it really is as easy as that! Finally, write the improper fraction as a mixed fraction