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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. In Proportional Reasoning, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

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?

  1. 25% is one fourth.
  2. One fourth of 48 is 12.
  3. 48 - 12 = 36.
  4. Connect the calculation back to Cumulative Review: Number and Ratio Skills so the method, not just the arithmetic, is clear.

Answer: 36

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response). Counts include repeated prompts and variants.

Practice problems

1. Compute -6 x 7.

Show solution
  1. Different signs give a negative product.
  2. 6 x 7 = 42.

Answer: -42

2. Compute -48 divided by -8.

Show solution
  1. Same signs give a positive quotient.
  2. 48 divided by 8 is 6.

Answer: 6

3. Compute 1/2 + 2/5.

Show solution
  1. Use 10 as a common denominator.
  2. 1/2 = 5/10 and 2/5 = 4/10.
  3. 5/10 + 4/10 = 9/10.

Answer: 9/10

4. Compute 2 1/3 + 1 1/6.

Show solution
  1. Rewrite 1/3 as 2/6.
  2. 2/6 + 1/6 = 3/6 = 1/2.
  3. 2 + 1 = 3.

Answer: 3 1/2

5. Compute 8.4 - 2.75.

Show solution
  1. Write 8.4 as 8.40.
  2. 8.40 - 2.75 = 5.65.

Answer: 5.65

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