Fractions, Decimals & Percentages — Year 7 Revision Notes
These notes cover equivalent and simplest-form fractions, converting between fractions, decimals and percentages, and adding, subtracting, multiplying and dividing fractions at Year 7 level.
Equivalent fractions and simplest form
Equivalent fractions have the same value: multiply or divide the numerator and denominator by the same number. To simplify, divide both by their highest common factor. For example, 6/8 simplifies to 3/4.
Key Facts & Formulas
- a/b = (a×k)/(b×k)
- simplest form: divide top and bottom by the HCF
Tips
- Always give a final fraction in its simplest form unless told otherwise.
- To compare fractions, write them with a common denominator first.
Converting between forms
Divide the numerator by the denominator to turn a fraction into a decimal, then multiply by 100 for a percentage. So 3/4 = 0.75 = 75%. A percentage is just a fraction out of 100.
Key Facts & Formulas
- fraction → decimal: top ÷ bottom
- decimal → percentage: × 100
- percentage → fraction: over 100, then simplify
Tips
- Learn the common ones by heart: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/10 = 10%.
- Be careful: 0.5 means 50%, not 5%.
Adding, subtracting and multiplying fractions
To add or subtract, rewrite with a common denominator, then add or subtract the numerators only. To multiply, multiply the numerators and multiply the denominators. So 1/2 + 1/3 = 3/6 + 2/6 = 5/6, and 2/3 × 3/4 = 6/12 = 1/2.
Key Facts & Formulas
- a/b + c/d = (ad + bc)/(bd)
- a/b × c/d = ac/bd
Tips
- Never add the denominators when adding fractions.
- Simplify before multiplying to keep the numbers small.
Revision Checklist
- I can find equivalent fractions and simplify to simplest form
- I can convert between fractions, decimals and percentages
- I can add and subtract fractions with different denominators
- I can multiply simple fractions and find a percentage of an amount
Frequently Asked Questions
Why can't I just add the denominators?
The denominator tells you the size of each part. You can only add parts that are the same size, which is why you first rewrite both fractions with a common denominator.
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