Math · Ratios & measurement
Ratios and Proportions
Estimated time includes reading and one quiz. Take the time you need.
Start here: key ideas
- A ratio compares two quantities in a stated order.
- Equivalent ratios multiply or divide both quantities by the same nonzero number.
- A proportion states that two ratios are equal.
- A relationship is proportional only when its unit ratio stays constant.
What you’ll be able to do
- Write ratios in equivalent forms while keeping units in the same order.
- Solve proportions by scaling and verify them with cross-products.
- Recognize when two quantities are not proportional.
A ratio compares two quantities in a stated order. Equivalent ratios multiply or divide both quantities by the same nonzero number.
Optional review
If you’d like to review the basics, visit Fractions: Operations and Mixed Numbers. You can start this lesson without completing those first.
Keep the comparison and units in order
A ratio is a comparison by division. “3 red tubes for every 5 blue tubes” can be written 3 to 5, 3:5, or 3/5. The order matters because 3/5 describes red compared with blue, while 5/3 describes blue compared with red. Include units when they differ: 120 miles/3 hours, not just 120/3.
A part-to-part ratio compares categories. With 2 red and 3 blue tubes, red:blue is 2:3. A part-to-whole ratio compares a category with the total: red:all is 2:(2+3)=2:5.
To simplify a ratio, divide both terms by the same common factor. For 18:24, divide both by 6 to get 3:4. Simplifying does not change the comparison.
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