Ratios turn up in recipes, maps, paint mixes and screen sizes. The two jobs you meet most often are reducing a ratio to something readable, and scaling it to a new size.
Simplifying a ratio
Divide both parts by their greatest common factor. For 24:36 the GCF is 12, so the ratio is 2:3. Both versions mean the same thing: for every 2 of the first quantity there are 3 of the second.
Solving a proportion
A proportion says a:b = c:x. Cross-multiply: x = b × c ÷ a. If a recipe uses 3 parts flour to 5 parts water, and you have 12 parts flour, then x = 5 × 12 ÷ 3 = 20 parts water. The calculator gives this as 3:5 = 12:20.
Using the calculator
- Choose simplify or proportion.
- To simplify, enter the two parts of the ratio.
- To solve a proportion, enter a, b and c. The tool finds the missing fourth number.
Neither value in a ratio can be zero, and in a proportion a cannot be zero, because the answer would involve dividing by zero.
Examples from daily life
- Screens: 1920:1080 simplifies to 16:9. Resizing an image to 1280 wide keeps the shape if height scales to 720.
- Maps: if 2 cm on the map is 5 km on the ground, 7 cm is 17.5 km.
- Mixing: a 1:4 cordial dilution means 1 part cordial to 4 parts water, which is 5 parts in total, not 4.
Frequently asked questions
Can I simplify a ratio with decimals?
Multiply both parts by the same power of ten to make them whole numbers, then simplify. 1.5:4.5 becomes 15:45, which is 1:3.
What is the difference between a ratio and a fraction?
A fraction compares a part to the whole. A ratio compares parts to each other, so 2:3 means 2 of one thing for 3 of another, while the fraction of the whole would be 2/5 and 3/5.