Number Foundations Checkpoint
A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint mixes the number skills from the first unit. Expect integers, fractions, ratios, unit rates, and percents in the same set, just like they appear in real math work.
What you'll learn
- Review integers, fractions, ratios, and percents
- Choose efficient strategies across number topics
- Build readiness for algebraic reasoning
Worked example
Problem. A jacket costs 80 dollars and is 25% off. What is the sale price?
- Find 25% of 80. Since 25% is 1/4, 1/4 of 80 is 20.
- Subtract the discount from the original price.
- 80 - 20 = 60, so the sale price is 60 dollars.
Answer: 60
Practice problems
1. Compute -9 + 14.
Show solution
- Integer Review: First identify exactly what the question is asking: Compute -9 + 14.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- The signs are different.
- 14 - 9 = 5, and the positive number has the larger distance from zero.
- Check the result by substituting or estimating: the response should match 5 and make sense in the original problem.
Answer: 5
2. Compute 6 - 15.
Show solution
- Integer Review: First identify exactly what the question is asking: Compute 6 - 15.
- For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
- Rewrite as 6 + -15.
- 15 is farther from zero, so the answer is negative.
- 15 - 6 = 9.
- Check the result by substituting or estimating: the response should match -9 and make sense in the original problem.
Answer: -9
3. Which fraction is equivalent to 9/12?
Choices: 3/4 · 4/3 · 1/3 · 9/4
Show solution
- Fraction Review: First identify exactly what the question is asking: Which fraction is equivalent to 9/12?
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- Divide 9 and 12 by 3.
- 9/12 simplifies to 3/4.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: 3/4
4. Compute 1/4 + 3/8.
Show solution
- Fraction Review: First identify exactly what the question is asking: Compute 1/4 + 3/8.
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- Rewrite 1/4 as 2/8.
- 2/8 + 3/8 = 5/8.
- Check the result by substituting or estimating: the response should match 5/8 and make sense in the original problem.
Answer: 5/8
5. A car travels 210 miles in 3 hours. What is the speed in miles per hour?
Show solution
- Ratios and Rates: First identify exactly what the question is asking: A car travels 210 miles in 3 hours. What is the speed in miles per hour?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Divide miles by hours.
- 210 divided by 3 is 70.
- Check the result by substituting or estimating: the response should match 70 and make sense in the original problem.
Answer: 70
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