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Equivalent fractions Improper fractions and mixed numbersConverting fractions to decimals

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Here we will learn about** ordering fractions**.

There are also ordering fractions* *worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Ordering fractions** is where we rearrange a set of fractions so that the smallest is at the start, followed by the next smallest and so on. This is called **ascending **order.

To do this we rewrite the fractions so that they have the same denominators which we can then compare.

We can order any type of fraction including proper fractions, improper fractions and mixed numbers.

E.g.

Write these fractions in ascending order:

In ascending order:

In order to put fractions in ascending order:

**Write all the fractions so that they have a common denominator****Find the smallest fraction by comparing the numerators and order the fractions****Rewrite the numbers as they appear in the question in size order**

Get your free ordering fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free ordering fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEWrite the following fractions in order of size:

\[\frac{3}{4} \quad \quad \frac{1}{2} \quad \quad \frac{5}{6} \quad \quad \frac{7}{12}\]

**Write all the fractions so that they have a common denominator**

The fractions have different denominators.

The denominators of the fractions are

The lowest common multiple is **12**

\[\frac{3\times3}{4\times3}=\frac{9}{12} \]

\[\frac{1\times6}{2\times6}=\frac{6}{12} \]

\[\frac{5\times2}{6\times2}=\frac{10}{12} \]

2**Find the smallest fraction by comparing the numerators and order the fractions**

Here are the fractions with their common denominator of

\[\frac{9}{12} \quad \quad \frac{6}{12} \quad \quad \frac{10}{12} \quad \quad \frac{7}{12} \]

Writing them in size order would give

\[\frac{6}{12} \quad \quad \frac{7}{12} \quad \quad \frac{9}{12} \quad \quad \frac{10}{12} \]

3**Rewrite the numbers as they appear in the question in size order**

\[\frac{6}{12} \quad \quad \frac{7}{12} \quad \quad \frac{9}{12} \quad \quad \frac{10}{12} \]

\[\frac{1}{2} \quad \quad \;\; \frac{7}{12} \quad \quad \;\frac{3}{4} \quad \quad \; \frac{5}{6}\]

Write the following fractions in order of size:

\[\frac{11}{30} \quad \quad \frac{4}{15} \quad \quad \frac{2}{5} \quad \quad \frac{1}{3} \]

**Write all the fractions so that they have a common denominator**

The fractions have different denominators.

The denominators of the fractions are

The lowest common multiple is **30**

\[\frac{4\times2}{15\times2}=\frac{8}{30} \]

\[\frac{2\times6}{5\times6}=\frac{12}{30} \]

\[\frac{1\times10}{3\times10}=\frac{10}{30} \]

**Find the smallest fraction by comparing the numerators and order the fractions**

Here are the fractions with their common denominator of

\[\frac{11}{30} \quad \quad \frac{8}{30} \quad \quad \frac{12}{30} \quad \quad \frac{10}{30} \]

Writing them in size order would give

\[\frac{8}{30} \quad \quad \frac{10}{30} \quad \quad \frac{11}{30} \quad \quad \frac{12}{30} \]

**Rewrite the numbers as they appear in the question in size order**

\[\frac{8}{30} \quad \quad \frac{10}{30} \quad \quad \frac{11}{30} \quad \quad \frac{12}{30} \]

\[\frac{4}{15} \quad \quad \;\frac{1}{3} \quad \quad \;\frac{11}{30} \quad \quad \;\frac{2}{5}\]

Write the following fractions in order of size:

\[\frac{7}{4} \quad \quad 1\frac{1}{2} \quad \quad 1\frac{2}{3} \quad \quad \frac{29}{24}\]

**Write all the fractions so that they have a common denominator**

We can either write all the fractions as improper fractions or as mixed numbers. It is simpler to write them as mixed numbers and concentrate on the fractional part of the mixed number.

\[\frac{29}{24}=1\frac{5}{24} \quad \quad \quad \frac{7}{4}=1\frac{3}{4}\]

The fractions have different denominators.

The denominators of the fractions are

The lowest common multiple is **24**

\[1\frac{3\times6}{4\times6}=1\frac{18}{24}\]

\[1\frac{1\times12}{2\times12}=1\frac{12}{24} \]

\[1\frac{2\times8}{3\times8}=1\frac{16}{24}\]

**Find the smallest fraction by comparing the numerators and order the fractions**

Here are the fractions with their common denominator of

\[1\frac{18}{24} \quad \quad 1\frac{12}{24} \quad \quad 1\frac{16}{24} \quad \quad 1\frac{5}{24} \]

Writing them in size order would give

\[1\frac{5}{24} \quad \quad 1\frac{12}{24} \quad \quad 1\frac{16}{24} \quad \quad 1\frac{18}{24} \]

**Rewrite the numbers as they appear in the question in size order**

\[1\frac{5}{24} \quad \quad 1\frac{12}{24} \quad \quad 1\frac{16}{24} \quad \quad 1\frac{18}{24} \]

\[\frac{29}{24} \quad \quad \;\;1\frac{1}{2} \quad \quad \;\;\; 1\frac{2}{3} \quad \quad \;\; \frac{7}{4}\]

Write the following fractions in order of size:

\[\frac{12}{5} \quad \quad 2\frac{3}{10} \quad \quad 2\frac{7}{20} \quad \quad \frac{9}{4} \]

**Write all the fractions so that they have a common denominator**

We can either write all the fractions as improper fractions or as mixed numbers. It is simpler to write them as mixed numbers and concentrate on the fractional part of the mixed number.

\[\frac{12}{5}=2\frac{2}{5} \quad \quad \quad \frac{9}{4}=2\frac{1}{4}\]

The fractions have different denominators.

The denominators of the fractions are

The lowest common multiple is **20**

\[2\frac{2\times4}{5\times4}=2\frac{8}{20}\]

\[2\frac{3\times2}{10\times2}=2\frac{6}{20} \]

\[2\frac{1\times5}{4\times5}=2\frac{5}{20}\]

**Find the smallest fraction by comparing the numerators and order the fractions**

Here are the fractions with their common denominator of

\[2\frac{8}{20}\quad \quad 2\frac{6}{20} \quad \quad 2\frac{7}{20} \quad \quad 2\frac{5}{20} \]

Writing them in size order would give

\[2\frac{5}{20} \quad \quad 2\frac{6}{20} \quad \quad 2\frac{7}{20} \quad \quad 2\frac{8}{20} \]

**Rewrite the numbers as they appear in the question in size order**

\[2\frac{5}{20} \quad \quad 2\frac{6}{20} \quad \quad 2\frac{7}{20} \quad \quad 2\frac{8}{20} \]

\[\frac{9}{4} \quad \quad \;\;\;2\frac{3}{10} \quad \quad \;2\frac{7}{20} \quad \quad \;\;\frac{12}{5} \]

Write the following fractions in order of size:

\[\frac{3}{4} \quad \quad 0.55 \quad \quad \frac{1}{2} \quad \quad 0.6 \]

**Write all the fractions so that they have a common denominator**

When there is a mixture of decimals and fractions it is sometimes easier to write them all as decimals. Some fractions and their decimal equivalents may be well known, otherwise we may need to work out a division.

\[\frac{3}{4}=3\div4=0.75\]

\[\frac{1}{2}=1\div2=0.5\]

**Find the smallest fraction by comparing the numerators and order the fractions**

Here are the numbers as decimals. To help with comparing it is a good idea to put in a zero in the hundredths column for

\[0.75 \quad \quad 0.55 \quad \quad 0.50 \quad \quad 0.60 \]

Writing them in size order would give

\[0.50 \quad \quad 0.55 \quad \quad 0.60 \quad \quad 0.75 \]

**Rewrite the numbers as they appear in the question in size order**

\[0.50 \quad \quad 0.55 \quad \quad 0.60 \quad \quad 0.75 \]

\[\frac{1}{2} \quad \quad \;\;\;0.55 \quad \quad \; 0.6 \quad \quad \;\; \frac{3}{4} \]

Write the following numbers in order of size:

\[0.67 \quad \quad \frac{2}{3} \quad \quad 0.603 \quad \quad \frac{5}{8} \]

**Write all the fractions so that they have a common denominator**

When there is a mixture of decimals and fractions it is sometimes easier to write them all as decimal fractions (decimals). Some fractions and their decimal equivalents may be well known, otherwise we may need to work out a division.

\[\frac{2}{3}=2\div3=0.666…\]

\[\frac{5}{8}=5\div8=0.625\]

**Find the smallest fraction by comparing the numerators and order the fractions**

Here are the numbers as decimals. To help with comparing it is a good idea to put in a zero in the thousandths column for

\[0.670 \quad \quad 0.666… \quad \quad 0.603 \quad \quad 0.625 \]

Writing them in size order would give

\[0.603 \quad \quad 0.625 \quad \quad \quad 0.666… \quad \quad 0.670 \]

**Rewrite the numbers as they appear in the question in size order**

\[0.603 \quad \quad 0.625 \quad \quad 0.666… \quad \quad 0.670 \]

\[0.603 \quad \quad \;\;\;\frac{5}{8} \quad \quad \;\; \; \; \;\frac{2}{3} \quad \quad \; \; \;\;\; 0.67 \]

**Changing the numbers into the same type of fractions**

It is much easier to change the fractions so that they have a common denominator and then compare the numerators.

**Use decimals if the common denominator is too tricky to find**

Sometimes finding a common denominator can be very difficult so it can be easier to convert the fractions to decimals and compare them instead.

**Smallest to largest or largest to smallest**?

Usually “in size order” means from smallest to largest. But the question might want you to put the numbers in descending order from largest to smallest.

E.g.

Write these numbers in order of size from largest to smallest:

\[\frac{4}{7} \quad \quad\frac{11}{14}\quad \quad \frac{1}{2}\]

Convert the fractions so they have the same denominator:

\[\frac{8}{14} \quad \quad \frac{11}{14} \quad \quad \frac{7}{14}\]

Write the fractions in order of size from largest to smallest:

\[\frac{11}{14} \quad \quad\frac{8}{14} \quad \quad \frac{7}{14}\]

The final answer is:

\[\frac{11}{14} \quad \quad \frac{4}{7} \quad \quad \frac{1}{2} \]

Ordering fractions 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:

1. Write these numbers in order of size:

\frac{5}{6} \quad \quad \frac{2}{3} \quad \quad \frac{1}{2} \quad \quad \frac{5}{12}

\frac{5}{12} \quad \quad \frac{2}{3} \quad \quad \frac{5}{6} \quad \quad \frac{1}{2}

\frac{5}{12} \quad \quad \frac{1}{2} \quad \quad \frac{2}{3} \quad \quad \frac{5}{6}

\frac{2}{3} \quad \quad \frac{1}{2} \quad \quad \frac{5}{12} \quad \quad \frac{5}{6}

\frac{1}{2} \quad \quad \frac{2}{3} \quad \quad \frac{5}{6} \quad \quad \frac{5}{12}

\frac{5}{12} \quad \quad \frac{1}{2}=\frac{6}{12} \quad \quad \frac{2}{3}=\frac{8}{12} \quad \quad \frac{5}{6}=\frac{10}{12}

2. Write these numbers in order of size:

\frac{5}{8} \quad \quad \frac{3}{4} \quad \quad \frac{13}{24} \quad \quad \frac{7}{12}

\frac{5}{8} \quad \quad \frac{13}{24} \quad \quad \frac{7}{12} \quad \quad \frac{3}{4}

\frac{13}{24} \quad \quad \frac{3}{4} \quad \quad \frac{7}{12} \quad \quad \frac{5}{8}

\frac{13}{24} \quad \quad \frac{7}{12} \quad \quad \frac{5}{8} \quad \quad \frac{3}{4}

\frac{3}{4} \quad \quad \frac{5}{8} \quad \quad \frac{7}{12} \quad \quad \frac{13}{24}

\frac{13}{24} \quad \quad \frac{7}{12}=\frac{14}{24} \quad \quad \frac{5}{8}=\frac{15}{24} \quad \quad \frac{3}{4}=\frac{18}{24}

3. Write these numbers in order of size:

1\frac{2}{5} \quad \quad \frac{19}{15} \quad \quad 1\frac{11}{30} \quad \quad \frac{7}{6}

\frac{7}{6} \quad \quad 1\frac{11}{30} \quad \quad 1\frac{2}{5} \quad \quad \frac{19}{15}

\frac{7}{6} \quad \quad \frac{19}{15} \quad \quad 1\frac{2}{5} \quad \quad 1\frac{11}{30}

\frac{7}{6} \quad \quad \frac{19}{15} \quad \quad 1\frac{11}{30} \quad \quad 1\frac{2}{5}

1\frac{2}{5} \quad \quad \frac{7}{6} \quad \quad \frac{19}{15} \quad \quad 1\frac{11}{30}

\frac{7}{6}=1\frac{5}{30} \quad \quad \frac{19}{15}=1\frac{8}{30} \quad \quad 1\frac{11}{30} \quad \quad 1\frac{2}{5}=1\frac{12}{30}

4. Write these numbers in order of size:

3\frac{7}{10} \quad \quad \frac{17}{5} \quad \quad 3\frac{3}{4} \quad \quad \frac{67}{20}

\frac{67}{20} \quad \quad \frac{17}{5} \quad \quad 3\frac{7}{10} \quad \quad 3\frac{3}{4}

3\frac{3}{4} \quad \quad 3\frac{7}{10} \quad \quad \frac{17}{5} \quad \quad \frac{67}{20}

3\frac{3}{4} \quad \quad \frac{17}{5} \quad \quad 3\frac{7}{10} \quad \quad \frac{67}{20}

\frac{67}{20} \quad \quad 3\frac{7}{10} \quad \quad \frac{17}{5} \quad \quad 3\frac{3}{4}

\frac{67}{20}=3\frac{7}{20} \quad \quad \frac{17}{5}=3\frac{8}{20} \quad \quad 3\frac{7}{10}=3\frac{14}{20} \quad \quad 3\frac{3}{4}=3\frac{15}{20}

5. Write these numbers in order of size:

\frac{1}{4} \quad \quad 0.2 \quad \quad \frac{1}{2} \quad \quad 0.3

0.2 \quad \quad \frac{1}{2} \quad \quad 0.3 \quad \quad \frac{1}{4}

0.2 \quad \quad \frac{1}{4} \quad \quad 0.3 \quad \quad \frac{1}{2}

0.3 \quad \quad \frac{1}{2} \quad \quad 0.2 \quad \quad \frac{1}{4}

\frac{1}{4} \quad \quad 0.3 \quad \quad \frac{1}{2} \quad \quad 0.2

0.2=0.20 \quad \quad \frac{1}{4}=0.25 \quad \quad 0.3=0.30 \quad \quad \frac{1}{2}=0.50

6. Write these numbers in order of size:

0.82 \quad \quad \frac{4}{5} \quad \quad 0.71 \quad \quad \frac{3}{4}

0.71 \quad \quad \frac{3}{4} \quad \quad \frac{4}{5} \quad \quad 0.82

0.71 \quad \quad \frac{3}{4} \quad \quad 0.82 \quad \quad \frac{4}{5}

0.71 \quad \quad \frac{4}{5} \quad \quad 0.82 \quad \quad \frac{3}{4}

\frac{3}{4} \quad \quad 0.71 \quad \quad 0.82 \quad \quad \frac{4}{5}

0.71=0.71 \quad \quad \frac{3}{4}=0.75 \quad \quad \frac{4}{5}=0.80 \quad \quad 0.82=0.82

1. Here are four fractions:

\frac{17}{20} \quad \quad \frac{7}{10} \quad \quad \frac{3}{4} \quad \quad \frac{3}{5}

Write the fractions in order of size.

Starting with the smallest fraction.

**(2 Marks)**

Show answer

\frac{17}{20} \quad \quad \frac{7}{10}=\frac{14} {20} \quad \quad
\frac{3}{5}=\frac{12}{20} \quad \quad \frac{3}{4}=\frac{15}{20}

**(1)**

\frac{3}{5} \quad \quad \frac{7}{10} \quad \quad \frac{3}{4} \quad \quad \frac{17}{20}

**(1)**

2. Here are four fractions:

\frac{2}{5} \quad \quad \frac{1}{4}\quad \quad \frac{4}{13}\quad \quad \frac{3}{10}

Write the fractions in order of size.

Starting with the smallest fraction.

**(2 Marks)**

Show answer

\frac{2}{5}=0.4 \quad \quad \frac{1}{4}=0.25 \quad \quad \frac{4}{13}=0.307… \quad \quad \frac{3}{10}=0.3

**(1)**

\frac{1}{4}\quad \quad \frac{3}{10}\quad \quad \frac{4}{13}\quad \quad \frac{2}{5}

**(1)**

3. Place the following numbers in order of size, smallest first:

2\frac{1}{4} \quad \quad 1.76^2 \quad \quad 2.14 \quad \quad \frac{17}{6}

**(2 Marks)**

Show answer

2\frac{1}{4}=2\frac{3}{12}=2.25 \quad \quad 1.76^2=3.0976 \quad \quad \frac{17}{6}=2\frac{10}{12}=2.833…

**(1)**

2.14 \quad \quad 2\frac{1}{4} \quad \quad \frac{17}{6} \quad \quad 1.76^2

**(1)**

You have now learned how to:

- Write fractions in order of size

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