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Ratio Word Problems
A ratio compares two amounts, like 3 red marbles for every 2 blue marbles (3:2). Most ratio problems can be solved by finding the value of one "part" and scaling up.
For: Grade 6 and 7 students.
The rules
- Add the parts of the ratio to find the total number of parts.
- Divide the total amount by the number of parts to find one part.
- Multiply one part by each number in the ratio.
- For a missing amount, scale both sides of the ratio by the same number.
Worked examples
Example 1: Share 35 stickers between Ana and Ben in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 35 ÷ 7 = 5.
- Ana: 3 × 5 = 15. Ben: 4 × 5 = 20.
Answer: Ana 15, Ben 20
Example 2: A recipe uses 2 cups of flour for every 3 eggs. How many eggs for 8 cups of flour?
- 8 cups is 4 times 2 cups.
- Multiply the eggs by 4 too: 3 × 4 = 12.
Answer: 12 eggs
Example 3: The ratio of boys to girls is 5:6 and there are 30 boys. How many girls?
- 30 ÷ 5 = 6, so one part is 6.
- Girls: 6 × 6 = 36.
Answer: 36 girls
Example 4: 3 notebooks cost $4.50. What is the cost of one notebook?
- Unit rate: 4.50 ÷ 3 = 1.50.
Answer: $1.50 each
Practice problems
- Share 24 in the ratio 1:3
- 4:7 = 12:?
- 5 pens cost $3. Cost of 15 pens?
- Cats to dogs is 2:5 with 15 dogs. Cats?
- Simplify the ratio 18:24
Show answers
- 6 and 18
- 21
- $9
- 6
- 3:4
Frequently asked questions
What is the difference between a ratio and a fraction?
A ratio compares part to part (3 red : 2 blue), while a fraction usually compares part to whole (3 of 5 marbles are red, so 3/5).
What is a unit rate?
A rate for one unit of something, such as dollars per item or miles per hour.
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