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Writing Mixed Numbers As Improper Fractions

Fractions

Fractions represent part of a whole number. Fractions, decimals and percentages can all have the same values and you may find it useful to know how to convert between them.

Mixed numbers and improper fractions

Diagram showing 4 full circles (1, 2/2, 3/3, 4/4) explaining fractions

A whole number can be written as \(\frac{2}{2}\) , \(\frac{3}{3}\) , \(\frac{4}{4}\) , etc.

So \(1 \frac{2}{3}\) can be written as:

\[\frac{3}{3} + \frac{2}{3} = \frac{5}{3}\]

Mixed numbers

\(1\frac{2}{3}\) is known as a mixed number , because it is made up of a whole number and a fraction.

Improper fractions

\(\frac{5}{3}\) is called an improper fraction , because the top number is bigger than the bottom number.

Converting from a mixed number to an improper fraction

You can write the whole number part as a fraction, with the same denominator as the other fraction, and then add the fractions together.

Example

\[1 \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}\]

Here is another example:

\[2 \frac{1}{4} = 1 + 1 + \frac{1}{4} = \frac{4}{4} + \frac{4}{4} + \frac{1}{4} = \frac{9}{4}\]

Converting from improper fractions to mixed numbers

You can separate the fraction into as many whole numbers as possible, with a smaller remaining fraction.

Example

\[\frac{17}{5}= \frac{5}{5} + \frac{5}{5} + \frac{5}{5} + \frac{2}{5} = 3 \frac{2}{5}\]

Another way to convert an improper fraction is to find how many whole numbers you get, by using a division.

For example let's convert \(\frac{17}{5}\) to a mixed number again.

We start by dividing the top number by the bottom number.

\({17}\) divided by \({5}\) is \({3}\) remainder \({2}\) .

So the whole number part is \({3}\) , and the remainder \({2}\) means there are \(\frac{2}{5}\) left over.

So the answer is \(\frac{17}{5} = 3 \frac{2}{5}\)

Question

Write \(\frac{20}{7}\) as a mixed number.

Method 1:

\[\frac{20}{7} = \frac{7}{7} + \frac{7}{7} + \frac{6}{7} = {2}\frac{6}{7}\]

Method 2:

\(\frac{20}{7} = 20 \div 7 = 2\) remainder \({6}\) , so:

\[\frac{20}{7} = 2 \frac{6}{7}\]

Using a calculator

Example of a fraction button on a calculator

If your calculator has a fraction button you can use this to convert from improper fractions to mixed numbers. Type in the improper fraction, press ' \({=}\) ', and the calculator will convert it to a mixed number.

Writing Mixed Numbers As Improper Fractions

Source: https://www.bbc.co.uk/bitesize/guides/zt6p34j/revision/5

Posted by: lawsontheast.blogspot.com

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