Ratio Calculator
Ratios compare amounts: 3 : 5 means “for every 3 of one thing there are 5 of the other”. Simplify a ratio, find the missing number in a proportion, or split a total fairly.
Answer
Step by step
- Find the greatest common factor of 18, 24, 30: 6.
- Divide every part by 6: 3 : 4 : 5.
Answer: 3 : 4 : 5
Still stuck? Ask the tutor about these steps
How it works
divide every part by the GCFa : b = c : x → x = b × c ÷ aone part = T ÷ (a + b)Simplifying a ratio is like simplifying a fraction: divide all the parts by the same number. 18 : 24 : 30 ÷ 6 = 3 : 4 : 5.
In a proportion, the two ratios are equivalent. Cross-multiply, or find the scale factor between the known pair and apply it to the other.
To share in a ratio, count the total number of parts, find what one part is worth, then multiply for each share.
Order matters: 2 : 3 (boys : girls) is not the same as 3 : 2.
Worked example
Share $120 in the ratio 2 : 3 : 5.
- 2 + 3 + 5 = 10 parts
- One part = 120 ÷ 10 = 12
- Shares: 24, 36, 60
Frequently asked questions
How do you simplify a ratio?
Divide every part by their greatest common factor. 12 : 16 has a GCF of 4, so it simplifies to 3 : 4.
How do I solve a proportion?
Set the ratios as fractions and cross-multiply. For 3 : 5 = 12 : x, 3x = 60 so x = 20.
Can ratios have decimals?
Yes. Multiply every part by 10, 100… until they are whole numbers, then simplify. 1.5 : 2 becomes 15 : 20, which is 3 : 4.