Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION

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1 Name: Instructor: Date: Section: Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION 2.1 Factorizations Learning Objectives a Determine whether one number is a factor of another, and find the factors of a number. b Find some multiples of a number, and determine whether a number is divisible by another. c Given a number from 1 to 100, tell whether it is prime, composite, or neither. d Find the prime factorization of a composite number. Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 4. multiple divisible prime composite 1. A number is a of another if it is the product of the number and some natural number. 2. A number has exactly two different factors. 3. A number a is by another number b if there is a number c such that bc = a. 4. A number has more than two different factors. Objective a Determine whether one number is a factor of another, and find the factors of a number. Determine whether the second number is a factor of the first ; ;

2 Find all the factors of the number Objective b Find some multiples of a number, and determine whether a number is divisible by another. Multiply by 1, 2, 3, and so on, to find 10 multiples of the number Determine whether the first number is divisible by the second number ; ; ,807;

3 Name: Instructor: Date: Section: Objective c Given a number from 1 to 100, tell whether it is prime, composite, or neither. Determine whether the number is prime, composite, or neither Objective d Find the prime factorization of a composite number. Find the prime factorization of the number

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5 Name: Instructor: Date: Section: Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION 2.2 Divisibility Learning Objectives a Determine whether a number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, or 10. Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 4. divisible divisible by 3 divisible by 5 even 1. A number is divisible by two if it is. 2. If a number has a ones digit of 0 or 5, then it is. 3. A number is if the sum of its digits is divisible by three. 4. A number a is by another number b if there is a number c such that a = b c. Objective a Determine whether a number is divisible by 2, 3, 4, 5, 6, 7, 8, 9, or 10. Consider the following numbers for Exercises ,956 12, Which of the above are divisible by 2? Which of the above are divisible by 3? Which of the above are divisible by 4? Which of the above are divisible by 5? 8. 27

6 9. Which of the above are divisible by 6? Which of the above are divisible by 7? Which of the above are divisible by 8? Which of the above are divisible by 9? Which of the above are divisible by 10? 13. Consider the following numbers for Exercises , , Which of the above are divisible by 2? Which of the above are divisible by 3? Which of the above are divisible by 4? Which of the above are divisible by 5? Which of the above are divisible by 6? Which of the above are divisible by 7? Which of the above are divisible by 8? Which of the above are divisible by 9? Which of the above are divisible by 10?

7 Name: Instructor: Date: Section: Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION 2.3 Fractions and Fraction Notation Learning Objectives a Identify the numerator and the denominator of a fraction and write fraction notation for part of an object. b Simplify fraction notation like n n to 1, 0 n to 0, and n to n. 1 Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 2. numerator denominator 1. In a fraction, the tell us the unit into which we are partitioning an object. 2. The of a fraction tells us the number of equal parts we are considering. Objective a Identify the numerator and the denominator of a fraction and write fraction notation for part of an object. Identify the numerator and the denominator

8 What part of the object is shaded? Find the ratios. 8. Dan delivers flowers for a florist. On Valentine s Day, he had 50 deliveries scheduled. By 11AM he had delivered 21 orders. What is the ratio of a. orders delivered to the total number of orders? 8. a. b. orders delivered to orders not delivered? b. c. orders not delivered to the total number of orders? c. 30

9 Name: Instructor: Date: Section: 9. Ruben sells cotton candy at a baseball game. He had 100 bags to sell. At the seventh inning stretch he had sold 79 bags. What is the ratio of a. bags sold to the total number of bags? 9. a. b. bags sold to bags not sold? b. c. bags not sold to the total number of bags? c. Objective b Simplify fraction notation like n n to 1, 0 n to 0, and n to n. 1 Simplify

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11 Name: Instructor: Date: Section: Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION 2.4 Multiplication and Applications Learning Objectives a Multiply a fraction by a fraction, and multiply a fraction by a whole number. b Solve applied problems involving multiplication of fractions. Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 3. area solve check 1. To an equation means to find all values of a variable that make the equation true. 2. The of a rectangle is length times width. 3. We can sometimes a solution by repeating calculations, finding the solution in a different manner, or seeing if the solution is reasonable. Objective a Multiply a fraction by a fraction, and multiply a fraction by a whole number. Multiply

12 Objective b Solve applied problems involving multiplication of fractions. Solve. 11. If each bag contains 5 8 bag contain? lb of seed, how much does half a If it takes 3 cup sugar to make one batch of cookies, how 4 much does it take to make 3 batches?

13 Name: Instructor: Date: Section: 13. How many in. wide? in. wide books can be placed on a shelf A water bottle can hold 5 8 cup. How much will the water 14. bottle hold when it is 1 2 full? 15. It takes 1 yard of dental floss for each patient. How many 2 yards of floss are needed by a dental hygienist for 9 patients? A rectangular table top measures 5 8 m long by 3 8 m wide. 16. What is the area? 35

14 17. The recipe for macaroni salad calls for 1 3 cup of 17. mayonnaise. How much is needed to make 1 2 of the recipe? 18. Seven of 53 high school band members play in a college band. Three of 79 college band members play in a community band. What fractional part of high school band members play in a community band?

15 Name: Instructor: Date: Section: Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION 2.5 Simplifying Learning Objectives a Multiply a number by 1 to find fraction notation with a specified denominator. b Simplify fraction notation. c Use the test for equality to determine whether two fractions name the same number. Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 3. canceling equivalent simplest 1. is a shortcut for removing a factor of 1, which must be used with caution. 2. Two fractions are if they name the same number. 3. A fraction is in form if the numerator and the denominator are the smallest whole numbers possible. Objective a Multiply a number by 1 to find fraction notation with a specified denominator. Find another name for the given number, but with the denominator indicated. Use multiplying by ? = ? = ? = ? =

16 Objective b Simplify fraction notation. Simplify Objective c Use the test for equality to determine whether two fractions name the same number. Use = or for to write a true sentence

17 Name: Instructor: Date: Section: Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION 2.6 Multiplying, Simplifying, and Applications Learning Objectives a Multiply and simplify using fraction notation. b Solve applied problems involving multiplication of fractions. Objective a Multiply and simplify using fraction notation. Multiply and simplify

18 Objective b Solve applied problems involving multiplication of fractions. Solve. 7. Jackson s tuition was $5200. A loan was obtained for 7 8 of the tuition. How much was the loan? A house worth $297,000 is assessed for 2 3 What is the assessed value of the home? of its value A recipe for pizza crust calls for 1 3 cup of oil. Juan is 9. making 1 2 of the recipe. How much oil should he use? 10. Telemarketers have determined that 1 3 of phone numbers 10. will change in 2 years. A business has a phone list of 3510 people. After two years, how many phone numbers on the list will be incorrect? 11. On a map, 1 in. represents 180 mi. What distance does 3 in. represent? The pitch of a screw is 5 in. How far will it go into a 32 piece of oak when it is turned 6 complete rotations clockwise?

19 Name: Instructor: Date: Section: Chapter 2 FRACTION NOTATION: MULTIPLICATION AND DIVISION 2.7 Division and Applications Learning Objectives a Find the reciprocal of a number. b Divide and simplify using fraction notation. c Solve equations of the type a x= b and x a = b, where a and b may be fractions. d Solve applied problems involving division of fractions. Key Terms Use the vocabulary terms listed below to complete each statement in Exercises 1 2. Terms may be used more than once. reciprocal n 0 1. The number zero has no because is not defined. 2. We find the of a fraction by interchanging the numerator and the denominator. Objective a Find the reciprocal of a number. Find the reciprocal of each number

20 Objective b Divide and simplify using fraction notation. Divide and simplify

21 Name: Instructor: Date: Section: Objective c Solve equations of the type a x = b and x a = b, where a and b may be fractions. Solve x = y = m = n = p = x =

22 Objective d Solve applied problems involving division of fractions. Solve. 22. A pair of children s shorts requires 2 yd of cotton. How 3 many pairs of shorts can be made from 24 yd of cotton? How many 3 -cup sugar bowls can be filled from 15 cups of sugar? 24. A bucket had 14 L of water in it when it was 2 3 much could it hold when full? full. How A tank had 20 L of gasoline in it when it was 5 6 much could it hold when full? full. How Matthew Le is going to a Penn State football game. After driving 192 kilometers (km), he has completed 3 5 of the 26. trip. How long is the total trip? How many kilometers are left to drive? 27. A piece of cable 7 meters (m) long is to be cut into 14 8 pieces of the same length. What is the length of each piece?