Ratios, made simple.
A ratio compares quantities in a stated order. If a box contains 2 red pencils for every 3 blue pencils, the ratio of red to blue is 2:3. The order matters: blue to red is 3:2. A ratio tells you how the quantities relate, but you need another piece of information to know their actual totals.
Match the units
When comparing measurements of the same kind, first use the same unit. The ratio of 1 metre to 50 centimetres is 100:50, which simplifies to 2:1. Writing 1:50 would compare numbers in different units.
Simplify or scale
Divide both terms by the same common factor to simplify: 8:12 becomes 2:3. Multiply both terms by the same positive number to scale up: 2:3 becomes 10:15. The relationship stays the same.
Distinguish part from whole
A red-to-blue ratio of 2:3 contains 5 parts altogether. Red pencils are therefore 2/5 of all the pencils, not 2/3. The fraction 2/3 compares the red quantity with the blue quantity.
Share a total
Add the ratio terms to find the total number of parts. Divide the total quantity by that number, then multiply the value of one part by each term. Check that your shares add back to the original total.
Share 45 stickers between Asha and Kabir in the ratio 2:3.
- There are 2 + 3 = 5 equal parts.
- Each part contains 45 ÷ 5 = 9 stickers.
- Asha gets 2 × 9 = 18; Kabir gets 3 × 9 = 27.
- Check: 18 + 27 = 45.
Asha: 18 stickers. Kabir: 27 stickers.
Take it with you: Keep the order clear, add the parts, then scale the relationship to fit the question.