Pythagorist
Ratios

Ratio Calculator

Simplify ratios and share amounts in a given ratio. Enter two numbers and choose whether to simplify the ratio or divide a total quantity — with full step-by-step working shown.

Simplified ratio

3 : 2

How it works

  1. Find the highest common factor (HCF)

    HCF(12,8)=4\text{HCF}(12, 8) = 4

    The HCF of 12 and 8 is 4.

  2. Divide both parts by the HCF

    12:8=124:84=3:212 : 8 = \frac{12}{4} : \frac{8}{4} = 3 : 2

    Divide each part of the ratio by 4: 12 ÷ 4 = 3, 8 ÷ 4 = 2.

    Result:3 : 2

Ratio — simplify and share

a:b=agcd⁡(a,b):bgcd⁡(a,b)share=totala+b×parta : b = \frac{a}{\gcd(a,b)} : \frac{b}{\gcd(a,b)} \qquad \text{share} = \frac{\text{total}}{a+b} \times \text{part}
a:ba : bThe ratio to simplify
gcd(a,b)gcd(a,b)Greatest common divisor of a and b
totaltotalThe quantity to be shared

Example substitution

12:8=3:2(÷4 each)12 : 8 = 3 : 2 \quad (÷4 \text{ each})

Divide both parts by HCF (4): 12 ÷ 4 = 3, 8 ÷ 4 = 2. Simplified ratio = 3 : 2.

Worked examples

Simplify the ratio 24 : 36.

  1. 1
    Find the HCF of 24 and 36: HCF(24, 36) = 12
  2. 2
    Divide both parts by 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3
  3. 3
    Simplified ratio: 2 : 3
Answer: 2 : 3

Share £120 in the ratio 3 : 5.

  1. 1
    Total parts: 3 + 5 = 8 parts
  2. 2
    Value of one part: £120 ÷ 8 = £15
  3. 3
    Each share: First: 3 × £15 = £45. Second: 5 × £15 = £75
Answer: £45 and £75

Frequently asked questions

How do you simplify a ratio?+

Divide both parts by their HCF. E.g., 12:8 → HCF is 4 → 3:2.

How do you share an amount in a ratio?+

Add the ratio parts to find the total shares. Divide the amount by total shares to find one share. Multiply each ratio part by one share.

How do you share £60 in the ratio 2:3?+

Total parts = 5. One share = £60/5 = £12. Shares: £24 and £36.

What is an equivalent ratio?+

Ratios that simplify to the same value. E.g., 2:3, 4:6, and 6:9 are all equivalent.

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