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Comprehensive Review of Multiples, Factors, Fractions, and Equations

This document serves as a thorough revision guide covering key mathematical concepts such as multiples and factors, prime factorization, GCF & LCM, fractions, decimals, and proportions. It provides clear examples and answers, including how to find the first five multiples of 24, list factors, decompose numbers into prime factors, and perform operations with fractions. It also explains the conversions between decimals, fractions, and percentages, as well as solving basic equations and applying ratios. Ideal for students preparing for assessments.

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Comprehensive Review of Multiples, Factors, Fractions, and Equations

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  1. 2nd 9-Weeks Review

  2. Topic: Multiples & Factors Question: Find the first 5 multiples of 24. & List all of the factors of 24. Answer: Multiples: 24, 48, 72, 96, 120 Factors: 1, 2, 3, 4, 6, 8, 12, 24

  3. Topic: Prime Factorization Question: Decompose 102 into its prime factorization. Answer: 102 2 51 2 ∙ 3 ∙ 17 3 17

  4. Topic: Prime Factorization Question: Decompose 72 into its prime factorization using exponents. Answer: 72 4 18 23 ∙ 32 2 2 2 9 3 3

  5. Topic: GCF & LCM Question: Find the Greatest Common Factor of 36 & 84. Answer: 3 36 84 4 12 28 GCF = 3 ∙ 4 = 12 3 7

  6. Topic: GCF & LCM Question: Find the Lowest Common Multiple of 24 & 18. Answer: 2 24 18 3 12 9 LCM = 2 ∙ 3 ∙ 4 ∙ 3 = 72 4 3

  7. Topic: Using GCF & LCM Question: If hamburger buns come in packages of 8 and hamburger patties come in packages of 12. What is the least amount of hamburgers you can make buying whole packages of buns and patties? Answer: 2 8 12 2 4 6 LCM = 2 ∙ 2 ∙ 2 ∙ 3 = 24 2 3 24 hamburgers

  8. Topic: Equivalent Fractions Question: Find the equivalent fraction. 2 = 18 5 ? Answer: 2 = 18 5 45

  9. Topic: Mixed Numbers & Improper Fractions Question: Change the mixed number to an improper fraction. 5 ¾ Answer: 5 ¾ = 23 4

  10. Topic: Decimals to Fractions Question: Change the Decimal to a fraction. 0.88 Answer: 0.88 = 88 = 44 = 22 100 5025

  11. Topic: Fractions to Decimals Question: Change the fraction to a decimal. 1 9 Answer: 0.111 9 1.000 0.1 -9 10 -9 1

  12. Topic: Decimals to Percents Question: If you have $0.61 what percent of a dollar do you have? Answer: $0.61 = 61%

  13. Topic: Percents to Decimals Question: If you have 55% of a dollar, how much money is that? Answer: 55% = $0.55

  14. Topic: Percents to Fractions Question: Change the percent to a fraction. 40% Answer: 40% = 40 = 2 100 5

  15. Topic: Fractions to Percents Question: Change the fraction to a percent. 5 8 Answer: 5 = ? 5 ∙ 100 = 8 ∙ ? 8 100 500 = 8 ∙ ? 8 8 62.5% = ?

  16. Topic: Adding Fractions Question: Answer: 5 + 3 = 8 2 + 1 = 3 = 1 1+8 = 9 3 3 3

  17. Topic: Adding Fractions Question: Answer: 18 + 5 = 23 30 3030

  18. Topic: Subtracting Fractions Question: Answer: 32 - 21 = 11 56 56 56

  19. Topic: Subtracting Fractions Question: Answer: 3 9 116 233116 117 24 - 24 = 24 - 24 = 24

  20. Topic: Multiplying Fractions Question: Answer: 30 = 15 = 5 48 24 8

  21. Topic: Multiplying Fractions Question: Answer: 8 · 3 = 24 = 4 3 2 6

  22. Topic: Dividing Fractions Question: Answer: 3 · 5 = 15 =3 3 4 1 4 4

  23. Topic: Dividing Fractions Question: Answer: 17 · 12 = 204 = 51 8 10 80 20

  24. Topic: Solving Equations Question: Solve: ½ = ¾b Answer: 1 · 4 = 4 = 2 2 3 6 3

  25. Topic: Solving Equations Question: Solve: 1 + b = 5 6 8 Answer: 5 - 1 = 15 - 4 = 11 8 6 24 24 24

  26. Topic: Solving Equations Question: Solve: b – 7 = 24 8 5 Answer: 2 4 + 7 = 232 + 35 = 267 = 327 5 8 40 40 40 40

  27. Topic: Solving Equations Question: Solve: b ÷ 2 = 5 5 10 Answer: 5 · 2 = 10 = 1 10 5 50 5

  28. Topic: Ratios Question: A cake recipe calls for 2 cups sugar and 5 cups flour. If you want to reduce the recipe and only use 1 cup of sugar, how much flour do you need? Answer: 2.5 cups flour

  29. Topic: Rates Question: Which is the better buy? 6 video games for $67.92 3 video games for $33.60 Answer: Unit rate: 6 @ $11.32 each Unit rate: 3 @ $11.20 each 3 for $33.60 is the better buy

  30. Topic: Proportions Question: Set up and solve using a proportion. Suzie can run 2 miles in 22 minutes. How long will it take her to run 2 ½ miles? Answer: 22 min = ?___ 22 ∙ 2.5 = 2 ∙ ? 2 mile 2.5 miles 55 = 2 ∙ ? 2 2 27.5 = ? 27.5 minutes

  31. Topic: % of a number Question: On a $55.00 dinner bill you want to leave 15% tip. What is 15% of $55.00? Answer: ? = 15% 55 ∙ 15 = 100 ∙ ? or 55 or 100% ------- 55 100 825 = 100 ∙ ? ∙ .15 10% ------- 5.5 100 = 100 ∙ ? 275 5% ------- 2.75 $8.25 = ? +550 15% ------ 8.25 8.25 15% of $55.00 is $8.25

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