Pythagorist
Ratios

Ratio Simplifier

Simplify two-part and three-part ratios to their simplest form. This calculator finds the HCF and divides both parts, showing every step of the working.

Simplified ratio

2 : 3

How it works

  1. Find the highest common factor (HCF)

    HCF(24,36)=12\text{HCF}(24, 36) = 12

    The HCF of 24 and 36 is 12.

  2. Divide both parts by the HCF

    24:36=2412:3612=2:324 : 36 = \frac{24}{12} : \frac{36}{12} = 2 : 3

    Divide each part of the ratio by 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3.

    Result:2 : 3

Simplifying Ratios

a:b:c=ah:bh:chwhere h=gcd⁡(a,b,c)a : b : c = \frac{a}{h} : \frac{b}{h} : \frac{c}{h} \quad \text{where } h = \gcd(a, b, c)
hhHCF of all ratio parts
a,b,ca, b, cThe parts of the ratio

Example substitution

6:9:12=2:3:4(HCF=3)6 : 9 : 12 = 2 : 3 : 4 \quad (\text{HCF} = 3)

HCF of 6, 9, 12 is 3. Divide each: 6÷3=2, 9÷3=3, 12÷3=4.

Worked examples

Simplify the ratio 15 : 25 : 35.

  1. 1
    Find HCF of 15, 25, 35: HCF = 5
  2. 2
    Divide all parts by 5: 15÷5=3, 25÷5=5, 35÷5=7
Answer: 3 : 5 : 7

Simplify the ratio 18 : 27.

  1. 1
    Find HCF of 18 and 27: HCF = 9
  2. 2
    Divide both parts by 9: 18÷9=2, 27÷9=3
Answer: 2 : 3

Frequently asked questions

How do you simplify a ratio?+

Find the HCF of all parts and divide each part by it.

How do you simplify 15:25?+

HCF(15,25) = 5. 15:25 = 3:5.

How do you simplify a three-part ratio?+

Find the HCF of all three numbers and divide each by it. E.g., 6:9:12 → HCF=3 → 2:3:4.

Can a ratio have decimals?+

Ratios should be written as whole numbers. If you have a decimal ratio, multiply all parts by a power of 10 to clear the decimals, then simplify.

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