Fractions, decimals and percentages
Equivalent fractions, calculating with fractions, and changing between fractions, decimals and percentages.
📌 Key points
- Equivalent fractions have the same value. Multiply or divide the top and bottom by the same number: 23 = 812.
- To simplify a fraction, divide the numerator and denominator by a common factor: 1218 = 23.
- An improper fraction can be written as a mixed number: 114 = 234.
- To add or subtract fractions, make the denominators the same first: 12 + 13 = 36 + 26 = 56.
- To multiply a fraction by a whole number, multiply the numerator: 27 × 3 = 67.
- To find a fraction of an amount, divide by the denominator, then multiply by the numerator: 35 of 40 = 40 ÷ 5 × 3 = 24.
- Per cent means "out of 100": 35% = 35100 = 0.35.
- Learn these: 12 = 0.5 = 50%, 14 = 0.25 = 25%, 34 = 0.75 = 75%, 15 = 0.2 = 20%, 110 = 0.1 = 10%.
- To find a percentage of an amount, start with 10%: 10% of 60 is 6, so 30% of 60 is 18 and 5% of 60 is 3.
📖 Key words
- Numerator
- The top number of a fraction: how many parts you have.
- Denominator
- The bottom number of a fraction: how many equal parts the whole is split into.
- Equivalent fractions
- Fractions that have the same value, such as 12 and 48.
- Simplest form
- A fraction where the numerator and denominator have no common factor except 1.
- Mixed number
- A whole number and a fraction together, such as 312.
- Improper fraction
- A fraction whose numerator is bigger than its denominator, such as 74.
- Percentage
- A number of parts out of 100, written with the % sign.
✏️ Worked example
A jacket costs $80. In a sale the price is reduced by 15%. What is the sale price?
- 10% of $80 = $80 ÷ 10 = $8.
- 5% is half of 10%, so 5% of $80 = $4.
- 15% = 10% + 5%, so 15% of $80 = $8 + $4 = $12.
- Sale price = $80 − $12 = $68.
- Answer: $68.
To compare fractions, decimals and percentages, change them all into the same form first (for example, all decimals).
Test yourself8 questions from a bank of 23. A new mix every time.
Start the quiz →