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Mixed Number To Improper Fraction
Here we will learn about converting mixed numbers to improper fractions.
There are also improper fractions and mixed numbers worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
What are mixed numbers and improper fractions?
A proper fraction has a numerator (the top number) that is smaller than the denominator (the bottom number) of the fraction.
An example of a proper fraction is \frac{8}{11} \
An improper fraction has a numerator that is bigger than the denominator of the fraction. Sometimes referred to as ‘top heavy’ fractions.
An example of an improper fraction is \frac{25}{7} \
A mixed number has a whole number part and a fractional part.
An example of a mixed number is 3 \frac{3}{4} \times 2 \frac{5}{8}
What is the process for converting a mixed number to improper fraction?
Converting a mixed number to an improper fraction is an important skill. When calculating with mixed numbers, it can be much easier to perform the arithmetic required if the mixed numbers are converted to improper fractions.
A proper fraction has a numerator (the top number) that is smaller than the denominator (the bottom number) of the fraction.
An improper fraction has a numerator that is bigger than the denominator of the fraction. Sometimes referred to as ‘top heavy’ fractions.
For example,
If we needed to calculate 1 \frac{2}{3} \times 4 \frac{3}{5}, one way would be to use a grid method.
This can be a very long process involving lots of other fraction arithmetic. Converting the mixed numbers to improper fractions before multiplying is a way of simplifying the process.
To convert the mixed numbers to improper fractions we change the whole number to a fraction with the same denominator. We then add the numerators together and get a new numerator over the original denominator.
For example,
To convert a mixed number to an improper fraction quickly we can multiply the whole number by the denominator, add the numerator and then write that over the original denominator.
For example,
This will make the process of adding, subtracting, multiplying and dividing fractions simpler.
What is converting mixed numbers to improper fractions?
How to convert a mixed number to improper fraction
In order to convert a mixed number to an improper fraction:
- Multiply the whole number by the denominator.
- Add on the numerator.
- Write the improper fraction by using the calculated value as the numerator over the original denominator.
Explain how to convert mixed numbers to improper fractions
Converting mixed numbers to improper fractions worksheet
Get your free converting mixed numbers to improper fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREE Converting mixed numbers to improper fractions worksheet
Get your free converting mixed numbers to improper fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREERelated lessons on fractions
Mixed number to improper fraction is part of our series of lessons to support revision on fractions. You may find it helpful to start with the main fractions lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Converting mixed numbers to improper fractions examples
Example 1: change a mixed number to an improper fraction
Write the following mixed number as an improper fraction, 2\frac{4}{5}.
- Multiply the whole number by the denominator.
The whole number part of the mixed number is 2 and the denominator is 5, \ 2 \times 5 = 10.
2Add on the numerator.
The numerator is 4, \ 10 + 4 = 14.
The new numerator for the improper fraction is 14.
3Write the improper fraction by using the calculated value as the numerator over the original denominator.
2\frac{4}{5}=\frac{14}{5}Example 2: change a mixed number to an improper fraction
Write the following mixed number as a improper fraction, 3\frac{1}{6}.
Multiply the whole number by the denominator.
The whole number part of the mixed number is 3 and the denominator is 6, \ 3 \times 6 = 18.
Add on the numerator.
The numerator is 1, \ 18 + 1 = 19.
The new numerator for the improper fraction is 19.
Write the improper fraction by using the calculated value as the numerator over the original denominator.
Example 3: change a mixed number to an improper fraction
Write the following mixed number as a improper fraction, 4\frac{3}{7}.
Multiply the whole number by the denominator.
The whole number part of the mixed number is 4 and the denominator is 7, \ 4 \times 7 = 28.
Add on the numerator.
The numerator is 3, \ 28 + 3 = 31.
The new numerator for the improper fraction is 31.
Write the improper fraction by using the calculated value as the numerator over the original denominator.
Common misconceptions
- Adding the whole number to the denominator instead of multiplying
A common error can occur when adding the whole number to the denominator instead of multiplying.
- Confusing mixed numbers and improper fractions
Mixed numbers are written with a whole number and a fractional part.
For example, 4 \frac{5}{6}.
Improper fractions are not written with a whole number part, but the numerator is always bigger than the denominator.
For example, \frac{29}{6}.
Practice converting mixed numbers to improper fractions questions
1. Write the following mixed number as an improper fraction, 2\frac{3}{5}.
2. Write the following mixed number as an improper fraction, 5\frac{2}{7}.
3. Write the following mixed number as an improper fraction, 8\frac{1}{4}.
4. Write the following mixed number as an improper fraction, 5\frac{3}{11}.
5. Write the following mixed number as an improper fraction, 4\frac{2}{13}.
6. Write the following mixed number as an improper fraction, 2\frac{8}{9}.
Converting mixed numbers to improper fractions GCSE questions
1. Choose the fraction which is the same as 5 \frac{3}{7}?
\frac{22}{7} \hspace{1cm} \frac{38}{7} \hspace{1cm} \frac{15}{7} \hspace{1cm} \frac{35}{7}
(1 mark)
(1)
2. (a) Write 3.2 as an improper fraction in its simplest form.
(b) Work out 3\frac{1}{4}-1\frac{1}{3}.
(5 marks)
(a)
For any correct mixed number. For example, 3\frac{2}{10}.
(1)
\frac{16}{5}(1)
(b)
Converting one of the fractions to an improper fraction. For example, \frac{13}{4} or \frac{4}{3}.
(1)
Write both fractions with a common denominator. For example, \frac{39}{12}, \frac{16}{12}.
(1)
\frac{23}{12} or 1 \frac{11}{12}.
(1)
3. Work out 4 \frac{1}{2} \div 3\frac{2}{3}.
(3 marks)
Converting one of the fractions to an improper fraction. For example, \frac{9}{2} or \frac{11}{3}.
(1)
Correct process to divide used. For example, finding common denominator for multiplying by the reciprocal.
(1)
\frac{27}{22} or 1 \frac{5}{22}.
(1)
Learning checklist
You have now learned how to:
- Convert a mixed number to an improper fraction
The next lessons are
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