Cumulative Review: Number and Ratio Skills
A free Pre-Algebra lesson from the “Proportional Reasoning” unit, with a worked example and practice problems including step-by-step solutions.
Spaced review keeps earlier skills active while new topics are added. This review mixes number foundations, fraction fluency, decimal operations, percents, and proportional reasoning so students practice choosing the method.
What you'll learn
- Review integers, fractions, decimals, percents, and ratios
- Choose efficient number strategies
- Prepare for mixed checkpoints
Why it matters: These number and ratio skills appear together every time you split a bill, compare prices, or scale a recipe. A quick warm-up across all of them keeps the connections solid.
Worked example
Problem. A price of 48 dollars is discounted by 25%. What is the sale price?
- 25% is one fourth.
- One fourth of 48 is 12.
- 48 - 12 = 36.
Answer: 36
Practice problems
1. Compute -6 x 7.
Show solution
- Integer Review: First identify exactly what the question is asking: Compute -6 x 7.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- Different signs give a negative product.
- 6 x 7 = 42.
- Check the result by substituting or estimating: the response should match -42 and make sense in the original problem.
Answer: -42
2. Compute -48 divided by -8.
Show solution
- Integer Review: First identify exactly what the question is asking: Compute -48 divided by -8.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- Same signs give a positive quotient.
- 48 divided by 8 is 6.
- Check the result by substituting or estimating: the response should match 6 and make sense in the original problem.
Answer: 6
3. Compute 1/2 + 2/5.
Show solution
- Fraction Review: First identify exactly what the question is asking: Compute 1/2 + 2/5.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- Use 10 as a common denominator.
- 1/2 = 5/10 and 2/5 = 4/10.
- 5/10 + 4/10 = 9/10.
- Check the result by substituting or estimating: the response should match 9/10 and make sense in the original problem.
Answer: 9/10
4. Compute 2 1/3 + 1 1/6.
Show solution
- Mixed Number Review: First identify exactly what the question is asking: Compute 2 1/3 + 1 1/6.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- Rewrite 1/3 as 2/6.
- 2/6 + 1/6 = 3/6 = 1/2.
- 2 + 1 = 3.
- Check the result by substituting or estimating: the response should match 3 1/2 and make sense in the original problem.
Answer: 3 1/2
5. Compute 8.4 - 2.75.
Show solution
- Decimal Review: First identify exactly what the question is asking: Compute 8.4 - 2.75.
- For decimals, keep place value aligned and use estimation to make sure the decimal point is reasonable.
- Write 8.4 as 8.40.
- 8.40 - 2.75 = 5.65.
- Check the result by substituting or estimating: the response should match 5.65 and make sense in the original problem.
Answer: 5.65
Practice this interactively with instant feedback and an AI tutor.
Practice Cumulative Review: Number and Ratio Skills Take the free placement check