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!

1.

What is ^{39}⁄_{9} as a mixed fraction in its simplest form?

4^{3}⁄_{9}

4^{1}⁄_{3}

4^{1}⁄_{4}

4^{2}⁄_{3}

2.

If ^{25}⁄_{28} of students passed their maths test, how many students failed their maths test?

3 students

5 students

3.

Peter the Postman had 560 letters to deliver. So far he has delivered ^{7}⁄_{8} of them. How many letters has Peter still to deliver?

490

70

120

60

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

4.

What is 4^{6}⁄_{9} as an improper fraction in its simplest form?

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}

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:

5.

What is ^{2}⁄_{4} + ^{3}⁄_{2} + ^{4}⁄_{6} expressed as a mixed fraction?

2^{2}⁄_{3}

2^{4}⁄_{6}

1^{2}⁄_{3}

1^{5}⁄_{6}

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

6.

A fifth of a fifth is the same as how many hundredths?

20

10

5

4

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

7.

How many ^{1}⁄_{5} are there in ^{6}⁄_{10}?

12

8

3

6

8.

What is ^{26}⁄_{6} as a mixed fraction in its simplest form?

4^{2}⁄_{6}

4^{1}⁄_{6}

4^{1}⁄_{3}

4^{2}⁄_{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}

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

9.

What is seven-eighths of eight-twelfths in its simplest form?

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

10.

What is 2^{3}⁄_{15} as an improper fraction in its simplest form?

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}

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:

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}