Ratio Notation
Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations
What a learner can do afterwards
- Write a ratio from a word problem and simplify it (e.g. 12:8 = 3:2)
- Convert a ratio to equivalent fractions of a whole (e.g. 3:2 means 3/5 and 2/5)
- Simplify ratios involving decimals or fractions by finding a common multiplier
The lesson
A ratio compares two amounts using a colon, like 3:2. It means that for every 3 parts of the first amount, there are 2 parts of the second amount. Order matters: 3:2 is not the same as 2:3.
To simplify a ratio, divide every number in it by their greatest common factor. For the ratio 12:8, the greatest common factor of 12 and 8 is 4, so dividing both by 4 gives 3:2.
A ratio also tells you the fraction each part makes of the whole. For the ratio 3:2, add the parts together: 3 + 2 = 5. That means the first amount is 3/5 of the total, and the second amount is 2/5 of the total.
If a ratio has decimals or fractions, multiply both numbers by the same value first to make them whole numbers, then simplify as usual. For example, 1.5:3 becomes 3:6 after multiplying by 2, which simplifies to 1:2.
Write a ratio with a colon in the correct order, simplify it by dividing both numbers by their greatest common factor, and turn it into fractions by putting each part over the total number of parts.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.