What your child learns
- Write a ratio three ways: 3 to 5, 3:5 and 3/5.
- Find equivalent ratios by multiplying or dividing both parts by the same number.
- Solve ratio problems with tables, tape diagrams and double number lines.
Common Core 6.RP.A.1 6.RP.A.3
A ratio compares two quantities. If a fruit bowl has 3 bananas and 5 apples, the ratio of bananas to apples is 3 to 5. Ratios show up everywhere in 6th grade and beyond: recipes, maps, speed, prices and percents all build on this one idea.
Equivalent ratios
Two ratios are equivalent when they describe the same relationship. Multiply or divide both numbers by the same amount and the ratio stays equivalent: 3:5 = 6:10 = 9:15.
Example 1: Lemonade with a ratio table
A recipe uses 2 cups of lemon juice for every 7 cups of water. How much water goes with 8 cups of lemon juice?
| Lemon juice (cups) | 2 | 4 | 6 | 8 |
|---|---|---|---|---|
| Water (cups) | 7 | 14 | 21 | 28 |
8 is 2 × 4, so multiply the water by 4 too: 7 × 4 = 28 cups of water.
Tape diagrams: when you know the total
Example 2: Sharing 40 stickers in the ratio 3:5
- Draw 3 equal boxes for Mia and 5 equal boxes for Leo. That is 8 boxes in total.
- 40 stickers ÷ 8 boxes = 5 stickers in each box.
- Mia gets 3 × 5 = 15 and Leo gets 5 × 5 = 25.
- Check: 15 + 25 = 40, and 15:25 simplifies to 3:5.
Double number lines: when the numbers keep growing
Example 3: Running pace
A runner covers 3 km every 15 minutes. How far does she run in 1 hour?
- Top line (km): 0, 3, 6, 9, 12. Bottom line (minutes): 0, 15, 30, 45, 60.
- 60 minutes lines up with 12 km.
Practice
- A class has 12 girls and 10 boys. Write the ratio of girls to boys three ways.
- Simplify the ratio 18:24.
- Is 4:6 equivalent to 10:15? Explain.
- A paint mix uses 3 parts blue to 2 parts white. How much white paint goes with 12 parts blue?
- Share 56 marbles in the ratio 3:4. How many does each person get?
- A car travels 90 miles in 2 hours. At the same rate, how far does it travel in 5 hours?
- The ratio of cats to dogs at a shelter is 5:3. There are 24 dogs. How many cats are there?
- A recipe needs 2 eggs for 12 muffins. How many eggs for 30 muffins?
Show answers
- 12 to 10, 12:10, 12/10 (simplified: 6:5)
- 3:4 (divide both by 6)
- Yes: 4:6 = 2:3 and 10:15 = 2:3
- 8 parts white (12 ÷ 3 = 4, and 2 × 4 = 8)
- 24 and 32 (56 ÷ 7 = 8)
- 225 miles (45 miles per hour)
- 40 cats (24 ÷ 3 = 8, and 5 × 8 = 40)
- 5 eggs (30 ÷ 12 = 2.5, and 2 × 2.5 = 5)
Common mistakes and quick fixes
- Adding instead of multiplying: 3:5 is not equivalent to 4:6. Add the same number and the relationship changes. Always multiply or divide.
- Mixing up the order: label each number with its word (girls, boys) before writing the ratio.
- Using the ratio numbers as the answer in sharing problems: first find the value of one part, then multiply.
Try it at home
Make a drink with a ratio, such as 1 part juice to 4 parts sparkling water. Ask your child to work out how much of each to use for 1 glass, then for the whole family, using a ratio table.
This guide matches Unit 1: Ratios in Level Up Math, Grade 6 (coming January 2027). Watch the Ratios and Percents video lesson next.
Questions parents ask
Is a ratio the same as a fraction?
Not quite. A fraction compares a part to a whole. A ratio can compare a part to a part (3 boys to 5 girls) or a part to a whole (3 boys out of 8 children).
Does the order in a ratio matter?
Yes. 3:5 and 5:3 describe different situations. The order of the numbers must match the order of the words.
When should students use a tape diagram?
Tape diagrams are best when you know the total or one part and need to find the others, for example sharing 40 stickers in the ratio 3:5.
