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Change Improper Fractions into Mixed Numbers

In this worksheet, students will practise converting improper fractions into mixed numbers.

'Change Improper Fractions into Mixed Numbers' worksheet

Key stage:  KS 4

Curriculum topic:  

Curriculum subtopic:  

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

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

An improper fraction (also called a top-heavy fraction) is just a fraction where the top number is bigger than the bottom one, such as...

16
5

A mixed number is just a number that is 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 that the line in the middle of a fraction means to divide.

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

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

So how do we put this into the mixed number?

Like this;

3
1
5

The 3 comes from how many whole 5 go into 16, the 1 comes from the remainder and the 5 comes from how much we divide by.

And it always will be.

Work out 95 ÷ 2

 

Giving your answer as a decimal.

Work out 95 ÷ 2

 

Give your answer as a decimal.

Convert this improper fraction into a mixed number.

 

31
6
= A
B
C

 

Column A

Column B

A
5
B
6
C
1
35
4

If I convert this fraction to a mixed number, what will be the value of the whole number?

62
9

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

9

6

8

81
5
= A
B
C

 

 

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

16

1

4

5

Convert this improper fraction into a mixed number.

 

31
9
= A
B
C

 

Column A

Column B

A
3
B
4
C
9

Convert this improper fraction into a mixed number.

 

82
3
= A
B
C

 

Column A

Column B

A
1
B
3
C
27

Convert this improper fraction into a mixed number.

 

71
5
= A
B
C

 

Column A

Column B

A
1
B
5
C
14

Compete the following sentence;

Column A

Column B

A
1
B
5
C
14
  • Question 1

Work out 95 ÷ 2

 

Giving your answer as a decimal.

CORRECT ANSWER
EDDIE SAYS
How many whole 4s can we fit into 85? (There's nothing wrong with counting on your fingers or writing out your times tables.) What's left over?
  • Question 2

Work out 95 ÷ 2

 

Give your answer as a decimal.

CORRECT ANSWER
47.5
EDDIE SAYS
I'm illustrating a point here. If you half something, you'll get a nice decimal but if you divide by something else, the chances are you won't 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)!
  • Question 3

Convert this improper fraction into a mixed number.

 

31
6
= A
B
C

 

CORRECT ANSWER

Column A

Column B

A
5
B
1
C
6
EDDIE SAYS
If we ask how many sixes go into 31, we get 5. We then need to ask... "What's the remainder?" This will give us B. "What did we divide by?" This will give us C.
  • Question 4
35
4

If I convert this fraction to a mixed number, what will be the value of the whole number?

CORRECT ANSWER
8
eight
EDDIE SAYS
We just need to ask here 'How many 4s go into 35?'
  • Question 5
62
9

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

CORRECT ANSWER
9
EDDIE SAYS
Just remember, the denominator stays the same.
  • Question 6
81
5
= A
B
C

 

 

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

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

Convert this improper fraction into a mixed number.

 

31
9
= A
B
C

 

CORRECT ANSWER

Column A

Column B

A
3
B
4
C
9
EDDIE SAYS
We're using the same method again here. You need to ask the three questions. 1) "How many 9s go into 31?" 2) "What do I have as a remainder?" 3) "What was I dividing by?"
  • Question 8

Convert this improper fraction into a mixed number.

 

82
3
= A
B
C

 

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?" 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

 

CORRECT ANSWER

Column A

Column B

A
14
B
1
C
5
EDDIE SAYS
We're using the same method again here. You 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?"
  • Question 10

Compete the following sentence;

CORRECT ANSWER
EDDIE SAYS
This question was a nice little summary of what we've been looking at throughout this worksheet. 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 so you feel super confident?
---- OR ----

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