Learn | Grasp Maths

Lesson overview

Number — fractions, decimals and percentages

Fluency with fractions, decimals and percentages requires understanding their equivalence and being able to switch between forms. When multiplying fractions: $\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$ . When dividing fractions: $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$ . Percentages are proportional: a 20% increase means multiply by 1.2; a 20% decrease means multiply by 0.8. Multi-stage problems require identifying the operation sequence and maintaining accuracy throughout.

Multiplying fractions

Calculate $\frac{3}{4} \times \frac{2}{5}$ .

Multiply numerators together and denominators together. Cancel common factors to simplify.

Dividing fractions

Calculate $\frac{5}{6} \div \frac{2}{3}$ .

Keep the first fraction, flip the second, then multiply. 'Flip and multiply' is the key rule.

Percentage increase and decrease

A product costs £80. The price increases by 15%. What is the new price?

For a 15% increase, multiply by 1.15 (which is 100% + 15%). For a 15% decrease, multiply by 0.85 (100% − 15%).

Converting between forms

Express $\frac{3}{8}$ , $0.375$ and $37.5\%$ and show they are equivalent.

Divide numerator by denominator to get decimal. Multiply decimal by 100 to get percentage.

Worked example — multi-stage percentage problem

A shop buys a jacket for £40. It adds 60% markup for profit. Then there is a sale with 25% off the selling price. What is the final sale price?

Find the selling price after the 60% markup: multiply by 1.60.
£40 × 1.60 = £64.
Apply the 25% discount by multiplying by 0.75 (which is 100% − 25%).
£64 × 0.75 = £48.
The final sale price is £48.

Try it

Work through each question. Show your working clearly. Use multipliers for percentage changes rather than finding the percentage amount first.

Question 1

Calculate $\frac{2}{3} \times \frac{3}{4}$ .

💡 Multiply numerators and denominators. Then cancel common factors.

Question 2

Calculate $\frac{7}{8} \div \frac{1}{4}$ .

💡 Flip the second fraction to $\frac{4}{1}$ and multiply.

Question 3

A price of £60 increases by 20%. What is the new price?

💡 Multiply by 1.20 (100% + 20%).

Question 4

Express $\frac{5}{8}$ as a decimal.

💡 Divide 5 by 8.

Question 5

A coat costs £50 and is reduced by 30% in a sale. What is the sale price?

💡 Multiply by 0.70 (100% − 30%).

Common mistakes

Watch for these when working through the lesson.

When dividing fractions, forgetting to flip the second fraction before multiplying.
Using the wrong multiplier for percentage changes. Remember: 20% increase means multiply by 1.20, not 0.20.
Not cancelling common factors before multiplying fractions, leading to unnecessary large fractions.
Confusing percentage of the original with percentage change in multi-stage problems.

Fractions, decimals and percentages: all operations

Lesson overview

Worked example — multi-stage percentage problem

Try it

Common mistakes

Related topics

Independent practice will plug in here