Compare & Order Fractions

Sometimes we may be given two (2) or more fractions which may have different numerators and denominators to compare using the comparison operators (>, <, =).

We may also be asked to arrange the fractions in ascending order (smallest to the biggest) or descending order (biggest to the smallest).

To compare between 2 or more fractions:

\(*\) Consider their denominators.

1. If their denominators are the same, the fraction with the biggest numerator is greater.

Example:

\(\frac{2}{5} > \frac{1}{5}\)

The two fractions above have the same denominator (5), hence the fraction with the biggest numerator \((\frac{2}{5})\) is greater than the fraction with the smallest numerator \((\frac{1}{5})\).

2. Method 1
If they have different denominators, express the two fractions so they have the same denominators (the LCM of their denominators), then compare the numerators as above.

\(\hspace{0.5cm}\) Method 2
You can also express the two fractions in percentages in order to compare them.

Example

Compare the fractions \(\frac{1}{3}\) and \(\frac{2}{5}\)

Method 1

Fractions given \(\Rightarrow \frac{1}{3}\) and \(\frac{2}{5}\)

\(\frac{1}{3} = \frac{1}{3} \times \frac{5}{5} = \frac{5}{15}\)

\(\frac{2}{5} = \frac{2}{5} \times \frac{3}{3} = \frac{6}{15}\)

Since \(\frac{6}{15} > \frac{5}{15}\)

\(\Rightarrow \frac{2}{5} > \frac{1}{3}\)

Method 2

Fractions given \(\Rightarrow \frac{1}{3}\) and \(\frac{2}{5}\)

Expressing \(\frac{1}{3}\) as a percentage

\(\Rightarrow \frac{1}{3} \times 100\%\)

\(\Rightarrow \frac{100}{3}\%\)

\(\Rightarrow 33\frac{1}{3}\%\)

Expressing \(\frac{2}{5}\) as a percentage

\(\Rightarrow \frac{2}{5} \times 100\%\)

\(\Rightarrow \frac{2 \times 100}{5}\%\)

\(\Rightarrow \frac{2 \times 20 \times 5}{5}\%\)

\(\Rightarrow (2 \times 20)\%\)

\(\Rightarrow 40\%\)

Since \(40\% > 33\frac{1}{3}\%\)

\(\Rightarrow \frac{2}{5} > \frac{1}{3}\)

Practice Questions

Solve the following, showing all workings.

1. Arrange the following fractions in ascending order; \(4\frac{1}{4}, 4\frac{1}{2}, 4\frac{1}{3}\)

2. Arrange the fractions \(\frac{3}{4}, \frac{2}{3}, \frac{4}{5}\) in ascending order of magnitude.

3. Arrange the following in descending order of magnitude: \(0.32, \frac{2}{5}, 27\%, \frac{1}{3}\)

4. Arrange the following fractions in ascending order: \(\frac{7}{12}, \frac{3}{5}, \frac{7}{15}, \frac{3}{4}\).

5. Arrange the following fractions in descending order of magnitude: \(\frac{2}{3}, \frac{5}{7}, \frac{2}{5}, \frac{1}{2}\)

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Quick Test

Test yourself on what you have learnt so far. Click on the link below when your are ready.

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