Fractions, Decimals and Percentages

Converting Fractions to Decimals

Divide the numerator by the denominator.

$\frac{3}{8} = 3 \div 8 = 0.375$

Some fractions produce recurring decimals:

$\frac{1}{3} = 0.333... = 0.\dot{3}$

Converting Decimals to Fractions

Write the decimal as a fraction over a power of 10, then simplify.

$0.45 = \frac{45}{100} = \frac{9}{20}$

Converting Fractions to Percentages

Multiply the fraction by 100:

$\frac{3}{5} = \frac{3}{5} \times 100 = 60\%$

Alternatively, convert to a decimal first, then multiply by 100.

Converting Percentages to Fractions

Write the percentage over 100 and simplify:

$35\% = \frac{35}{100} = \frac{7}{20}$

Converting Percentages to Decimals

Divide by 100 (move the decimal point two places to the left):

$45\% = 0.45$

Converting Decimals to Percentages

Multiply by 100 (move the decimal point two places to the right):

$0.72 = 72\%$

Key Equivalences to Memorise

Fraction	Decimal	Percentage
$\frac{1}{2}$	$0.5$	$50\%$
$\frac{1}{4}$	$0.25$	$25\%$
$\frac{3}{4}$	$0.75$	$75\%$
$\frac{1}{5}$	$0.2$	$20\%$
$\frac{1}{3}$	$0.\dot{3}$	$33.\dot{3}\%$
$\frac{1}{10}$	$0.1$	$10\%$
$\frac{1}{8}$	$0.125$	$12.5\%$

Adding and Subtracting Fractions

To add or subtract fractions, they must have a common denominator.

$\frac{2}{5} + \frac{1}{3} = \frac{6}{15} + \frac{5}{15} = \frac{11}{15}$

Multiplying Fractions

Multiply numerators together and denominators together:

$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Dividing Fractions

Flip the second fraction (find its reciprocal) and multiply:

$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}$

Percentage of an Amount

To find a percentage of an amount, convert the percentage to a decimal and multiply:

$15\% \text{ of } 240 = 0.15 \times 240 = 36$

Or use the "1% method": find 1% by dividing by 100, then multiply.

Percentage Increase and Decrease

To increase by a percentage, use a multiplier greater than 1.

Increase £200 by 15%: multiplier $= 1.15$

$200 \times 1.15 = £230$

To decrease by a percentage, use a multiplier less than 1.

Decrease £200 by 15%: multiplier $= 0.85$

$200 \times 0.85 = £170$

Percentage Change

To calculate the percentage change:

$\text{Percentage change} = \frac{\text{change}}{\text{original}} \times 100$

Tip 1: Memorise Key Equivalences

Knowing the common FDP conversions by heart saves valuable time in exams. Practise until instant recall.

Tip 2: Use Multipliers for Percentage Problems

Multipliers are faster and less error-prone than working out the percentage and adding or subtracting. For a 12% increase, multiply by 1.12. For a 12% decrease, multiply by 0.88.

Tip 3: Always Simplify Fractions

After any calculation with fractions, check whether your answer can be simplified. Divide the numerator and denominator by their highest common factor (HCF).

Tip 4: Convert to the Same Form for Comparison

To compare or order fractions, decimals and percentages, convert them all to the same form. Decimals are usually the easiest to compare.

Tip 5: Use Estimation to Check

Before calculating, estimate. For example, 18% of 400 should be close to 20% of 400 = 80. If your answer is nowhere near 80, check again.