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Maths · Ratio & Proportion

Simplify ratios

Reduce ratios to their simplest form.

Not startedCAMBRIDGE · 7CBSE · VIIIB · MYP-1

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What does simplest form mean?

A ratio is in simplest form when the numbers in it share no common factors except 1. We divide all parts by their highest common factor (HCF) to simplify.

Finding the highest common factor

The HCF is the largest number that divides evenly into all parts of the ratio. List factors of each number, then pick the biggest one they share.

Dividing to simplify

Once you know the HCF, divide every number in the ratio by it. The result is the simplest form. For example, 8:12 becomes 2:3 when divided by 4.

Ratios with more than two parts

The same method works for three or more numbers. Find the HCF of all parts, then divide each by it. Check that no common factor remains.

Why simplify ratios?

Simpler numbers are easier to understand and compare. The ratio 2:3 shows the same relationship as 20:30 but is clearer and quicker to use.

Worked examples

  1. 1. Simplify the ratio 15:25.

    1. Find factors of 15: 1, 3, 5, 15.
    2. Find factors of 25: 1, 5, 25.
    3. The highest common factor is 5.
    4. Divide both parts by 5: 15÷5 = 3 and 25÷5 = 5.
    5. The simplest form is 3:5.

  2. 2. Simplify the ratio 12:18:30.

    1. Find the HCF of 12, 18 and 30.
    2. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
    3. The HCF is 6.
    4. Divide each part: 12÷6 = 2, 18÷6 = 3, 30÷6 = 5.
    5. The simplest form is 2:3:5.

  3. 3. Simplify the ratio 40:100.

    1. Find the HCF of 40 and 100.
    2. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
    3. The HCF is 20.
    4. Divide both parts: 40÷20 = 2 and 100÷20 = 5.
    5. The simplest form is 2:5.

Try it yourself

Simplify the ratio 24:36.

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