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Fractions

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Fractions

Summary: Fractions represent parts of a whole, with equivalent fractions, mixed numbers, and the four operations forming the core of Year 7 fraction work. Tags: concepts math y7 fractions number Created: 2026-05-30 Last Updated: 2026-05-30

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A fraction has two parts: a numerator (top) and a denominator (bottom). The denominator tells you how many equal parts the whole is split into. The numerator tells you how many of those parts you have.

Equivalent Fractions

Two fractions are equivalent if they represent the same value. You can find an equivalent fraction by multiplying or dividing both the numerator and denominator by the same non-zero number.

Example: 3/4 = 6/8 = 9/12 = 12/16 — all are equivalent because each is obtained by multiplying top and bottom by the same number.

Simplifying Fractions

To simplify a fraction, divide both numerator and denominator by their highest common factor. A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

Example: Simplify 12/18. The HCF of 12 and 18 is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3. Answer: 2/3.

Mixed Numbers and Improper Fractions

An improper fraction has a numerator larger than its denominator (e.g. 11/4). A mixed number combines a whole number with a proper fraction (e.g. 2 3/4).

To convert an improper fraction to a mixed number: divide the numerator by the denominator — the quotient is the whole number, the remainder goes over the original denominator.

To convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place over the original denominator.

Comparing and Ordering Fractions

To compare fractions with different denominators, find a common denominator (usually the LCM) and convert each fraction.

Example: Compare 2/3 and 3/5. LCM of 3 and 5 is 15. 2/3 = 10/15, 3/5 = 9/15, so 2/3 > 3/5.

Adding and Subtracting Fractions

Same denominator: Add or subtract the numerators, keep the denominator the same.

Different denominators: Find a common denominator first, convert both fractions, then add or subtract.

  1. Find the LCM of the denominators
  2. Convert each fraction to an equivalent fraction with the LCM as denominator
  3. Add or subtract the numerators
  4. Simplify the result and convert to a mixed number if needed

Multiplying Fractions

Multiply the numerators together and the denominators together. Simplify the result.

Example: 3/4 × 2/5 = (3 × 2)/(4 × 5) = 6/20 = 3/10.

To multiply a fraction by an integer: write the integer as a fraction over 1, then multiply as above. For mixed numbers, convert to improper fractions first.

Dividing Fractions

To divide by a fraction, multiply by its reciprocal (flip the second fraction and multiply).

Example: 2/3 ÷ 5 = 2/3 × 1/5 = 2/15.

Fractions of an Amount

To find a fraction of a quantity, divide by the denominator and multiply by the numerator.

Example: Find 3/8 of 64. 64 ÷ 8 = 8, 8 × 3 = 24. Answer: 24.

Fractional Increase and Decrease

To increase an amount by a fraction: find the fraction of the amount and add it to the original. To decrease: find the fraction and subtract.

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