 # Convert Mixed Numbers into Improper Fractions

In this worksheet, students will practise converting mixed numbers (whole numbers and fractions) into top-heavy (improper) fractions. This is a very useful skill to use when adding or subtracting fractions. 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:   ### QUESTION 1 of 10

When you are working with fractions, you will come across both top-heavy fractions (correctly called improper fractions) and mixed numbers.

Top-heavy fractions have larger numerators than denominators.

Mixed numbers describe expressions which use both whole numbers and fractions together.

You need to be able to convert between these two forms and identify equivalents.

e.g. Convert this mixed number into a top-heavy fraction:

3
 1 5

If we draw this fraction using bars, we have three wholes and one fifth, like this: If we count the shaded sections, we have 16 in total and each one is worth 1/5 so our fraction can now be written as:

 16 5

Doing this the quicker way...

You should have noticed that the denominator is the same in both the question and answer fractions. This is ALWAYS true.

So we just need to find the numerator.

If we have 3 wholes which we are splitting into fifths, we have 3 x 5 = 15 fifths.

We need to remember that we had an extra 1 fifth in the question too, which gives us 16 overall.

To summarise:

In order to find the new numerator, multiply the whole number by the denominator then add the numerator.

The denominator will stay the same in both fractions.

In this activity, you will convert mixed numbers (so whole numbers and fractions) into top-heavy, improper fractions.

This is a very useful skill to use when adding or subtracting fractions.

Convert this mixed number into a top-heavy fraction:

1
 3 7

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

If we convert the mixed number below to a top-heavy fraction, what will the new denominator be?

7
 4 9
9

7

4

How many tenths are in the mixed number below?

2
 9 10

Convert this mixed number into a top-heavy fraction.

8
 1 2

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

Which of the fractions provided is the correct top-heavy fraction representing the mixed number below?

8
 4 15
124/15

120/15

32/15

Convert this mixed number to a top-heavy fraction:

3
 1 10

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

What will the numerator be if we convert the mixed number below into a top-heavy fraction?

12
 1 6
121

1

73

If we convert the mixed number below into a top-heavy fraction, which of the numbers in the table below will be in the answer?

14
 3 4

If you were asked to convert this mixed number into a top-heavy fraction, what would your process be?

13
 2 3

Convert this mixed number to a top-heavy fraction.

8
 7 15

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

• Question 1

Convert this mixed number into a top-heavy fraction:

1
 3 7

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

10/7
EDDIE SAYS
Let's apply our rules for the first time... The denominator stays the same (7). The numerator can be found by multiplying the whole number by the denominator and adding the numerator, so: (1 x 7) + 3 = 10 So our improper fraction is 10/7 How did you find this first question?
• Question 2

If we convert the mixed number below to a top-heavy fraction, what will the new denominator be?

7
 4 9
9
EDDIE SAYS
When we convert mixed numbers into top-heavy fractions, the denominator always stays the same! Hopefully this sneaky question didn't trip you up, and you remembered this all-important, golden rule. It's also essential to know the difference between the denominator and the numerator in each fraction.
• Question 3

How many tenths are in the mixed number below?

2
 9 10
29
EDDIE SAYS
2 wholes are the same as 20 tenths. Then, if we add on the 9 tenths we have from the question, we reach 29 tenths overall. If we were asked to write this as a fraction, the denominator always remains the same, so is 10. So this mixed number written as an improper fraction would be 29/10
• Question 4

Convert this mixed number into a top-heavy fraction.

8
 1 2

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

17/2
EDDIE SAYS
Remember that the denominator stays the same (2). We can find our new numerator using the calculation: (8 x 2) + 1 = 17 So our improper fraction is 17/2
• Question 5

Which of the fractions provided is the correct top-heavy fraction representing the mixed number below?

8
 4 15
124/15
EDDIE SAYS
We know that we get the new numerator by multiplying the denominator by the whole number (8 x 15) and then we add the numerator (4). So our sum would be: (8 x 15) + 4 = 124 Hopefully you didn't forget to add the numerator on at the end!
• Question 6

Convert this mixed number to a top-heavy fraction:

3
 1 10

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

31/10
EDDIE SAYS
The denominator stays the same (10). The numerator can be found using the calculation: (3 x 10) + 1 = 31 So the overall improper fraction is 31/10
• Question 7

What will the numerator be if we convert the mixed number below into a top-heavy fraction?

12
 1 6
73
EDDIE SAYS
We have 12 wholes that are split into sixths. This gives us 72 sixths, but we need to add on the 1 from the question. So our answer is 73/6. The numerator is the top number in the fraction which, in this case, is 73. Hopefully you didn't confuse your numerators and denominators there! Great focus, you're making great progress with each attempt.
• Question 8

If we convert the mixed number below into a top-heavy fraction, which of the numbers in the table below will be in the answer?

14
 3 4
EDDIE SAYS
Choosing 143 is a really common mistake to make - remember that you need to multiply the denominator by the whole then add the numerator. 3 is also a red herring here. We can find our new numerator with the calculation: (14 x 4) + 3 = 59 Did you remember that our denominator always stays the same?
• Question 9

If you were asked to convert this mixed number into a top-heavy fraction, what would your process be?

13
 2 3
EDDIE SAYS
Time to test your vocabulary (and spelling) here champ! Remember our process from the Intro: multiply the whole number by the denominator, then add the numerator. The denominator always stays the same (3). The numerator can be found using the sum: (13 x 3) + 2 = 39
• Question 10

Convert this mixed number to a top-heavy fraction.

8
 7 15

Give your answer in the form a/b, with no spaces and using the / key to indicate the line in your fraction.

127/15
EDDIE SAYS
The denominator stays the same (15). The numerator can be found using the calculation: (8 x 15) + 7 = 127 So our final overall fraction is 127/15 Well done for completing another activity! Why not move on to adding and subtracting fractions now?
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