National 5MathsSQAApplications of MathematicsRevision NotesNumeracy SkillsFractions & PercentagesComparing Fractions & Percentages

Comparing Fractions & Percentages (SQA National 5 Applications of Mathematics): Revision Note

Exam code: X844 75

Written by: Dan Finlay

Reviewed by: Roger B

Updated on 1 December 2025

Comparing fractions & percentages

How do I compare a fraction and a percentage?

You need to write both as either percentages or fractions

Convert the fraction to a percentage

You can easily compare a fraction and a percentage if they are both written as a percentage
- With a calculator:
  - multiply the fraction by 100
- Without a calculator:
  - divide 100% by the denominator
  - then multiply by the numerator
This method is quicker using a calculator
It can be tricky without a calculator if 100% doesn't divide nicely by the denominator

Convert the percentage to a fraction with the same denominator

You need to write the percentage as a fraction using the same denominator as the other fraction
Find the percentage of the denominator of the fraction
- Consider $\frac{13}{90}$ and 14%
  - $14 % of 90 = 0.14 \times 90 = 12.6$
This then becomes the numerator
- $14 % = \frac{12.6}{90}$
You can then just compare the numerators
- $13 > 12.6$
- Therefore, $\frac{13}{90} > 14 %$

Worked Example

Greg had two tests at school.

Greg scored 28 out of 40 in his Physics test.

Greg scored 72% in his Chemistry test.

Determine which subject Greg performed better in.

Answer:

Method 1

Write the Physics score as a fraction

$\frac{28}{40} = \frac{7}{10}$

Divide 100% by the denominator and then multiply by the numerator

$\begin{array}{rcl} 100 % \div 10 & = & 10 % \\ 7 \times 10 % & = & 70 % \end{array}$

Compare the percentages

Greg performed better at Chemistry since 72% > 70%

Method 2

Write 72% as a decimal

$72 \div 100 = 0.72$

Find 72% of 40 and write 72% as a fraction out of 40

$\begin{array}{rcl} 0.72 \times 40 & = & 28.8 \end{array}$

$72 % = \frac{28.8}{40}$

Compare the numerators

Greg performed better at Chemistry since 28.8 > 28

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