MATH 074 REVIEW FOR CHAPTER 2 and 3 - Sections , ( Fractions) a) 18: b) 20: c) 48: d) 60: e) 59:

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1 MATH 074 REVIEW FOR CHAPTER 2 and 3 - Sections , ( Fractions) A. Can you list all the factors of a given number? 1. List all the factors of each of the following numbers. a) 18: b) 20: c) 48: d) 60: e) 59: B. Can you determine whether a given number is prime or composite? 2. Indicate whether each given number is prime or composite. a) 10: b) 17: c) 27: d) 39: e) 51: f) 41: 3. Write all the prime numbers between 8 and 21: 4. Write all the composite numbers between 17 and 31: 5. Write all the prime numbers between 50 and 70: C. Can you write the prime factorization of any given composite number? 6. Write the prime factorization of each of the following composite numbers. a) 28: b) 36: c) 48: d) 84: e) 210: f) 300: g) 80: h) 720: D. Can you find the Least Common Multiple (LCM) of two or more numbers? 7. Find the LCM in each case. a) 8 and 12: b) 16 and 24: c) 18 and 30: d) 5, 7, and 9: e) 8, 10 and 20: f) 18, 24, and 48: g) 56, 63 and 72: E. Can you express each mixed number as an improper fraction and each improper fraction as a mixed number? 8. Write each mixed number as an improper fraction. a) : b) : c) : d) :

2 9. Write each improper fraction as a mixed number. a) : b) : c) : d) : e) : F. Can you write Equivalent Fractions? 10. Write as an equivalent fraction whose denominator is 56: 11. Write as an equivalent fraction whose denominator is 84: 12. Write as an equivalent fraction whose numerator is 98: 13. Write as an equivalent fraction whose numerator is 40: G. Can you write a fraction in simplest form? OR Can you simplify a fraction? OR Can you write a fraction reduced to lowest terms? 14. Simplify each of the following fractions. That is, reduce each of the following fractions to lowest terms. d) e) f) g) h) i) j) H. Can you compare fractions? That is, given two or more fractions, can you arrange from smallest to largest? 15. Between each pair of fractions, insert the appropriate sign <, =, or >, to get a true statement. d) e) f) 16. Arrange each of the following from smallest to largest. Page_2

3 I. Can you solve simple application problems involving fractions? 17. In a club, there are 28 male members and 35 female members. What fraction of the total membership are females? Write your answer in simplest form. 18. A baseball player got 25 hits in 45 times at bat. What fraction of his times at bat did he not get a hit? Write your answer in simplest form. J. Can you add and subtract proper fractions? 19. Add or subtract as indicated. Reduce your answer to lowest terms. (Hint: First simplify each fraction) a) b) c) d) e) f) g) h) i) j) k) l) m) n) o) p) K. Can you add and subtract mixed numbers? 20. Add or subtract as indicated. Whenever possible, express your answer as a mixed number. Page_3

4 d) e) f) g) h) i) j) k) l) m) n) L. Can you solve simple application problems involving addition and subtraction of fractions? 21. Find the perimeter of the rectangle whose length is feet and the width is feet. 22. You are driving to a town 27 miles away. If you have already driven miles, how far away is the town? M. Can you multiply and divide proper fractions? 23. Multiply or divide as indicated. Reduce your answer to lowest terms. d) e) f) g) h) i) j) k) l) m) n) o) Page_4

5 N. Can you multiply and divide mixed numbers? 24. Multiply or divide as indicated. Whenever possible, express your answer as a mixed number. d) e) f) g) h) i) j) k) l) O. Can you simplify expressions involving mixed operations of fractions? 25. Simplify. Whenever possible, express your answer as a mixed number. a) b) c) d) P. Can you solve simple application problems involving multiplication and division of fractions? 26. Each dose of aspirin weighs grain. If you have 30 grains of aspirin on hand, how many doses can you administer? 27. Find the cost of buying carpeting at per square foot for the rectangular hallway whose length is 15 feet and the width is 12 feet. 28. A 40-acre field is to be subdivided equally into acre lots. How many such lots can be formed from the field? 29. On each page of a report, there are 220 words. If the report is pages long, how many words does it contain? Page_5

6 MATH 074 ANSWERS TO REVIEW PROBLEMS FROM CHAPTER 2 and 3 1. a) 1, 2, 3, 6, 9, 18 b) 1, 2, 4, 5, 10, 20 c) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 d) 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 e) 1, a) composite b) prime c) composite d) composite e) composite f) prime 3. 11, 13, 17, , 20, 21, 22, 24, 25, 26, 27, 28, , 59, 61, d) e) f) g) h) 7. a) 24 b) 48 c) 90 d) 315 e) 40 f) 144 g) d) 9. d) e) d) e) f) 6 g) h) i) j) 15. a) < b) = c) < d) = e) > f) < a) b) 1 c) d) e) f) Page_6

7 g) h) i) j) k) l) m) n) o) p) 20. d) e) f) g) h) 45 i) j) k) l) m) n) o) 21. feet 22. miles 23. d) 1 e) f) g) h) i) j) k) l) m) n) 35 o) d) e) f) 21 g) h) i) j) k) l) 25. d) doses 27. $ lots words Page_7