Master Ratios and Proportions with Pre-Algebra review games.
This unit covers writing ratios, solving proportions and unit rates — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers writing ratios, solving proportions and unit rates — essential concepts for Pre-Algebra. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Writing Ratios
A ratio compares two quantities and can be written three ways: as a fraction (a/b), with a colon (a:b), or in words (a to b). Ratios must be simplified to lowest terms on exams. Order matters — the ratio of a to b is not the same as b to a.
Key Points
- Always write the ratio in the same order the problem lists the quantities
- Simplify by dividing both parts by their GCF
- Ratios can compare part-to-part or part-to-whole
- A ratio has no units when both quantities share the same unit
A class has 12 boys and 18 girls. Write the ratio of boys to girls in simplest form.
Set up the ratio in the stated order: 12/18. Divide both by GCF 6 to get 2/3. The simplified ratio of boys to girls is 2:3.
2 Solving Proportions
A proportion states that two ratios are equal (a/b = c/d). To solve for a missing value, use cross-multiplication: multiply the numerator of each fraction by the denominator of the other, then solve the resulting equation. Always check that your answer makes the two ratios equivalent.
Key Points
- Cross-multiply to eliminate fractions: a × d = b × c
- Isolate the variable by dividing both sides
- Check your answer by substituting back and confirming the ratios are equal
- Set up the proportion so matching units are in the same position (top/bottom)
Solve for x: 3/4 = x/20
Cross-multiply: 3 × 20 = 4 × x, giving 60 = 4x. Divide both sides by 4 to get x = 15. Check: 3/4 = 15/20, and both simplify to 3/4, confirming the answer.
3 Unit Rates
A unit rate expresses a ratio with a denominator of 1, showing how much of one quantity exists per single unit of another. To find a unit rate, divide the numerator by the denominator. Unit rates are used to compare prices, speeds, and other real-world quantities.
Key Points
- Divide to make the denominator equal to 1
- Label the unit rate clearly (e.g., miles per hour, dollars per item)
- To compare rates, convert both to unit rates first
- The better deal is the lower unit price (cost per single item)
A car travels 150 miles in 3 hours. What is the unit rate in miles per hour?
Write the rate as a fraction: 150 miles / 3 hours. Divide both by 3 to get 50/1, or 50 miles per hour. The unit rate is 50 mph, meaning the car travels 50 miles for every 1 hour.
Questions, answered.
What is Ratios and Proportions?
Ratios and Proportions is Unit 3 of Pre-Algebra, covering writing ratios, solving proportions and unit rates.
How to study for Pre-Algebra Unit 3?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 25+ review questions across 5 different game modes.