Ratio, Proportion & Rates of Change
Grade 3-4Simplifying Ratios
A ratio is simplified the same way as a fraction, by dividing every part by their highest common factor, and the only extra step comes from making sure every part is measured in a comparable way first. This lesson covers simplifying two-part and three-part ratios, simplifying ratios with different units, decimals or fractions, and writing a ratio in the form 1:n or n:1.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Simplifying a two-part ratio
Find the highest common factor of both parts of the ratio, then divide both parts by it.
12:18: the highest common factor of 12 and 18 is 6, so 12:18 simplifies to 2:3.
Simplifying a three-part ratio
The same method works for a ratio with three (or more) parts: find the highest common factor of all the parts, then divide every part by it.
6:9:15: the highest common factor of 6, 9 and 15 is 3, so 6:9:15 simplifies to 2:3:5.
Simplifying ratios with units, decimals or fractions
If a ratio compares two different units, convert both parts to the same unit first. If a ratio contains decimals, multiply every part by the same power of 10 to make them whole numbers. If a ratio contains fractions, multiply every part by the common denominator to clear the fractions. Then simplify as normal.
40 cm : 1 m: convert 1 m to 100 cm, giving 40:100, which simplifies to 2:5. 0.4:1.6: multiply both parts by 10 to get 4:16, which simplifies to 1:4.
Writing a ratio in the form 1:n or n:1
To write a ratio as 1:n, divide both parts by whatever the first part is. To write it as n:1, divide both parts by whatever the second part is. Unlike fully simplifying, the answer does not need to use whole numbers.
4:24 in the form 1:n: divide both parts by 4, giving 1:6. 15:6 in the form n:1: divide both parts by 6, giving 2.5:1.
Worked Examples
Three exam-style questions, fully solved.
Simplify the ratio 12:18.
Easy- 1.Find the highest common factor of 12 and 18: 6
- 2.Divide both parts by 6
Answer: 2:3
Write the ratio 40 cm : 1 m in its simplest form.
Medium- 1.Convert both parts to the same unit: 1 m = 100 cm, giving 40:100
- 2.Find the highest common factor of 40 and 100: 20
- 3.Divide both parts by 20
Answer: 2:5
Write the ratio 1/2 : 1/3 in its simplest form, using whole numbers.
Hard- 1.Multiply both parts by the common denominator, 6: (1/2 × 6) : (1/3 × 6)
- 2.Simplify: 3:2
- 3.Check the highest common factor of 3 and 2 is 1, so it is already fully simplified
Answer: 3:2
Avoid These
The most common mistakes students make.
Dividing only one part of the ratio by the common factor, instead of dividing every part by the same number.
Forgetting to convert both quantities to the same units before simplifying, leaving units like cm and m mixed together.
Stopping at a partially simplified ratio instead of finding the highest common factor and reaching the fully simplified form.
When simplifying a ratio with decimals or fractions, multiplying only some of the parts by the same amount instead of every part.
Confusing the forms 1:n and n:1, and dividing by the wrong part of the ratio.
FAQ
Questions parents and students ask.
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