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Convert Improper Fractions into Mixed Numbers

In this worksheet, students will practise converting improper or top-heavy fractions into mixed numbers (whole numbers with a fraction) by dividing by the denominator and using the remainder as the numerator in the resulting fraction.

'Convert Improper Fractions into Mixed Numbers' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Fractions, Decimals and Percentages

Curriculum subtopic:   Structure and Calculation, Fractions

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

When we are working with fractions, we need to be able to convert between improper fractions and mixed numbers.

 

An improper fraction (also known as a top-heavy fraction) has a top number (or numerator) which is larger than the bottom one (or denominator), such as:

16
5

 

A mixed number is a number written as a whole and a fraction, like:

3
1
5

 

 

So, how do we convert between the two?

 

When we have an improper fraction, we need to think of the line in the middle of the fraction as a division sign.

So the fraction 16/5 can be read as "16 divided by 5" or "how many 5s go into 16?"

 

If we calculated the sum 16 ÷ 5, we get 3 remainder 1.

So how do we write this into a mixed number?

 

Like this:

3
1
5

 

We find the whole number by writing how many 5s go into 16, and the fraction by using the remainder. 

 

 

This rule is ALWAYS true and can be followed in all conversions between improper fractions and mixed numbers. 

 

 

In this activity, you will convert improper or top-heavy fractions into mixed numbers (whole numbers with a fraction) by dividing by the denominator and using the remainder as the numerator in the resulting fraction. 

Consider the sum:

 

95 ÷ 2

 

Then complete the sentence below. 

Work out:

 

95 ÷ 2

 

Give your answer as a decimal rather than with a reminder.

Convert the improper fraction below into a mixed number.

 

31
6
= A
B
C

 

Then match each letter below to its correct number value. 

 

Column A

Column B

A
5
B
6
C
1

If we convert the fraction below into a mixed number, what will be the value of the whole number in the pair?

 

35
4

If we converted the fraction below into a mixed number, what would be the denominator of the new fraction?

 

62
9
9

6

8

Consider the mixed number presented below:

 

81
5
= A
B
C

 

Which of the options in the list would be one of the values of A, B and C?

16

1

4

5

Convert this improper fraction into a mixed number.

 

31
9
= A
B
C

 

Then match each letter below to its correct number value. 

Column A

Column B

A
9
B
4
C
3

Convert this improper fraction into a mixed number.

 

82
3
= A
B
C

 

Then match each letter below to its correct number value. 

 

Column A

Column B

A
27
B
3
C
1

Convert this improper fraction into a mixed number.

 

71
5
= A
B
C

 

Then match each letter below to its correct number value. 

 

Column A

Column B

A
1
B
5
C
14

To summarise what you have learnt, complete the sentence below.

Column A

Column B

A
1
B
5
C
14
  • Question 1

Consider the sum:

 

95 ÷ 2

 

Then complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
How many whole 4s can we fit into 85? You may use a mental method or the bus stop. There's nothing wrong with counting on your fingers or writing out your times tables if that helps. How many 4s in 8? 2 How many 4s in 5? 1, remainder 1 So our answer is: 21, remainder 1
  • Question 2

Work out:

 

95 ÷ 2

 

Give your answer as a decimal rather than with a reminder.

CORRECT ANSWER
47.5
EDDIE SAYS
Did you spot the important point here? You can choose whether to write your answers with remainders or as decimals, but some numbers will work better in each scenario. If you halve a number, you'll get a nice decimal but if you divide by another number, the chances are you won't get a nice decimal, so it's best to use a fraction. If you're struggling on this one, try splitting it up: What's half of 90? What's half of 5? Bang them back together and you'll have your answer! 45 + 2.5 = 47.5
  • Question 3

Convert the improper fraction below into a mixed number.

 

31
6
= A
B
C

 

Then match each letter below to its correct number value. 

 

CORRECT ANSWER

Column A

Column B

A
5
B
1
C
6
EDDIE SAYS
We need to ask ourselves: "How many sixes go into 31?" The closest we can get is: 5 x 6 = 30 So our whole number (A) is 5. We then need to ask ourselves: "What's the remainder?" This will give us B. "What did we divide by?" This will give us C. So our overall answer is 5 1/6
  • Question 4

If we convert the fraction below into a mixed number, what will be the value of the whole number in the pair?

 

35
4
CORRECT ANSWER
8
eight
EDDIE SAYS
To find the whole number, we need to ask ourselves: "How many 4s go into 35?" The closest times table is: 8 x 4 = 32 So our whole number will be 8 and there will be a remainder of 3 to write as a fraction. How are you doing with these challenges so far?
  • Question 5

If we converted the fraction below into a mixed number, what would be the denominator of the new fraction?

 

62
9
CORRECT ANSWER
9
EDDIE SAYS
This was a bit of a trick question! Just remember that the denominator always stays the same when converting between improper fractions and mixed numbers.
  • Question 6

Consider the mixed number presented below:

 

81
5
= A
B
C

 

Which of the options in the list would be one of the values of A, B and C?

CORRECT ANSWER
16
1
5
EDDIE SAYS
We need to ask ourselves: "How many 5s go into 81?" If we count up, we get to 16 x 5 = 80, so our whole number is 16. Then ask: "What's leftover?" This is B. And finally: "What were we dividing by?" This'll be C. So our final mixed number is 16 1/5
  • Question 7

Convert this improper fraction into a mixed number.

 

31
9
= A
B
C

 

Then match each letter below to its correct number value. 

CORRECT ANSWER

Column A

Column B

A
3
B
4
C
9
EDDIE SAYS
We're using the same method again here. We need to ask our three questions: 1) "How many 9s go into 31?" 2) "What do I have as a remainder?" 3) "What was I dividing by?" If you follow these steps, you should reach an answer of 3 4/9
  • Question 8

Convert this improper fraction into a mixed number.

 

82
3
= A
B
C

 

Then match each letter below to its correct number value. 

 

CORRECT ANSWER

Column A

Column B

A
27
B
1
C
3
EDDIE SAYS
Again: 1) "How many 3s go into 82?" 2) "What do I have as a remainder?" 3) "What was I dividing by?" So that's 27 1/3 Great focus, you've almost reached the end of this activity!
  • Question 9

Convert this improper fraction into a mixed number.

 

71
5
= A
B
C

 

Then match each letter below to its correct number value. 

 

CORRECT ANSWER

Column A

Column B

A
14
B
1
C
5
EDDIE SAYS
We're using the same method again here. We need to ask the same three questions: 1) "How many 5s go into 71?" 2) "What do I have as a remainder?" 3) "What was I dividing by?" Did you reach an answer of 14 1/5?
  • Question 10

To summarise what you have learnt, complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
This is a neat,little summary of what we've been looking at throughout this activity. We always divide first to get the whole, the remainder will be our numerator and the denominator will always stay the same. Great work, you've completed another activity! How about attempting another one focused on improper fractions or mixed numbers, so you feel super confident?
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