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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. In Cumulative Review and Test Prep, 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: 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.
  4. Connect the calculation back to Cumulative Review Strategies so the method, not just the arithmetic, is clear.

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.
  5. Write the final response in the form requested by the prompt.

Answer: Quadrant IV

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