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Cumulative Review Strategies

A free Pre-Algebra lesson from the “Cumulative Review and Test Prep” unit, with a worked example and practice problems including step-by-step solutions.

Cumulative review mixes topics without telling you which skill to use. Start by identifying the topic, estimate a reasonable answer, then solve carefully. This routine prepares you for placement tests, course exams, and Algebra I readiness checks.

What you'll learn

Why it matters: Mixed practice mirrors how every test and standardized exam is built. The strategy is to identify which tool each problem is asking for, then apply it.

Worked example

Problem. A rectangle is 7.5 feet long and 4 feet wide. What is its area?

  1. The word area tells us to multiply length by width.
  2. 7.5 x 4 = 30.
  3. The area is 30 square feet.

Answer: 30

Practice problems

1. Compute -6 + 14 - 5.

Show solution
  1. Number Review: First identify exactly what the question is asking: Compute -6 + 14 - 5.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. First -6 + 14 = 8.
  4. Then 8 - 5 = 3.
  5. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.

Answer: 3

2. Compute 4.6 + 2.75.

Show solution
  1. Number Review: First identify exactly what the question is asking: Compute 4.6 + 2.75.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Write 4.6 as 4.60.
  4. 4.60 + 2.75 = 7.35.
  5. Check the result by substituting or estimating: the response should match 7.35 and make sense in the original problem.

Answer: 7.35

3. Find 35% of 80.

Show solution
  1. Fraction and Percent Review: First identify exactly what the question is asking: Find 35% of 80.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. 35% is 0.35.
  4. 0.35 x 80 = 28.
  5. Check the result by substituting or estimating: the response should match 28 and make sense in the original problem.

Answer: 28

4. Solve 7/10 = x/50.

Show solution
  1. Proportional Reasoning: First identify exactly what the question is asking: Solve 7/10 = x/50.
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. 10 is multiplied by 5 to get 50.
  4. 7 x 5 = 35.
  5. Check the result by substituting or estimating: the response should match 35 and make sense in the original problem.

Answer: 35

5. Which quadrant contains (4, -9)?

Choices: Quadrant I · Quadrant II · Quadrant III · Quadrant IV

Show solution
  1. Coordinate Review: First identify exactly what the question is asking: Which quadrant contains (4, -9)?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Positive x and negative y is Quadrant IV.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Quadrant IV

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