Grade 6 · Free math lesson
Ratios & Proportions
After this lesson, you will be able to write ratios and solve proportion problems using cross-multiplication.
Practice Ratios & Proportions freeSkills in this unit
Pick a skill to try three free questions on just that.
- Ratio language and equivalent ratios
- Unit rates
- Ratio tables and double number lines
- Percent of a quantity
- Finding the whole from a part and a percent
- Converting measurement units with ratios
- Proportional relationships and the constant of proportionality
- Solving proportions in word problems
What Is a Ratio?
A ratio compares two amounts. You write it as 3:2, which means 'for every 3 of one thing, there are 2 of another.'
Example: In a bag with 4 red apples and 6 green apples, the ratio of red to green is 4:6.
Remember: Think of a ratio like a recipe — it tells you how much of each ingredient to use.
Simplify the Ratio
You can shrink a ratio to its simplest form by dividing both numbers by the same amount. This makes it easier to compare.
Example: The ratio 4:6 can be simplified. Divide both by 2 to get 2:3.
Remember: Treat a ratio just like a fraction — find the biggest number that divides both sides evenly.
Solve a Proportion
A proportion says two ratios are equal. To find a missing number, cross-multiply and then divide.
Example: If 2:3 = 4:?, cross-multiply: 2 × ? = 3 × 4, so 2 × ? = 12, meaning ? = 6.
Remember: Cross-multiply means multiply the top of one side by the bottom of the other — like making an X.
Worked example
A recipe uses 2 cups of flour for every 3 cups of milk. How many cups of milk do you need for 8 cups of flour?
- 1Write the proportion: 2:3 = 8:?
- 2Cross-multiply: 2 × ? = 3 × 8, so 2 × ? = 24
- 3Divide both sides by 2: ? = 24 ÷ 2 = 12
Answer: You need 12 cups of milk.
The #1 mistake to avoid
Students flip the order of the ratio by accident — always write the numbers in the SAME order on both sides. If it's boys:girls on the left, keep it boys:girls on the right too.
Key takeaways
- A ratio compares two amounts and is written as A:B.
- You can simplify a ratio by dividing both numbers by the same value.
- A proportion sets two ratios equal — use cross-multiplication to find the missing number.
Master Ratios & Proportions — free
Interactive practice you solve by doing, an AI tutor when you're stuck, and mastery you can't fake. No credit card.
Start practicing free