Fractions and Mixed Numbers: Multiplication and Division

Transcription

1 Chapter Fractions and Mixed Numbers: Multiplication and Division Chapter Opener Puzzle Section. Introduction to Fractions and Mixed Numbers Section. Practice Exercises. Answers will vary.. (a) A fraction is a part of a whole unit. (b) The numerator of a fraction denotes the number of pieces of the whole being considered. (c) The denominator of a fraction denotes the number of equal pieces into which a whole unit is divided. (d) A fraction is a proper fraction if the numerator is less than the denominator. (e) An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. (f) A mixed number is a sum of a whole number and a fractional part of a whole.. 6 ; 6. ;. ; 0. ;. 0 ; 0. 0 ; 0. 0; undefined. 0; undefined.. Numerator: ; denominator:. Numerator: ; denominator:. Numerator: ; denominator: 6. Numerator ; denominator: 6..

2 Chapter Fractions and Mixed Numbers: Multiplication and Division or 0. Proper. Proper ;. ;. ; 6.. ; Proper. Proper. Improper. Improper. Improper 6. Improper

3 Section. Introduction to Fractions and Mixed Numbers eighths fifths + fourths + thirds

4 Chapter Fractions and Mixed Numbers: Multiplication and Division Divide the distance between 0 and into equal parts Divide the distance between 0 and into equal parts.. Divide the distance between 0 and into equal parts Divide the distance between 0 and into equal parts.. Divide the distance between 0 and into equal parts.. Divide the distance between 0 and into 6 equal parts.

5 Section. Prime Numbers and Factorization. 6 6 Divide the distance between and into 6 equal parts.. Divide the distance between and into equal parts. 0.. Divide the distance between and into equal parts. Divide the distance between and into equal parts.. False; whole numbers cannot be written as proper fractions.. True. True 6. True Section. Prime Numbers and Factorization Section. Practice Exercises. Answers will vary.. (a) A factor of a number n is a nonzero whole number that divides evenly into n. (b) A factorization of a number n is a product of factors that equals n. (c) A prime number is a whole number greater than that has only two factors (itself and ). (d) A composite number is a whole number greater than that is not prime. (e) The prime factorization of a number is the factorization in which every factor is a prime number.. ; ; 6 ; improper ; proper 6 ; 6 improper ;. For example: and

6 Chapter Fractions and Mixed Numbers: Multiplication and Division. For example: 0 and. For example: 6 and. For example: and. Product 0 Factor 0 Factor 6 Sum Product Factor Factor 6 Sum. A whole number is divisible by if it is an even number.. A whole number is divisible by 0 if its ones-place digit is 0.. A whole number is divisible by if the sum of its digits is divisible by. 0. A whole number is divisible by if its ones-place digit is or 0.. (a) No; is not even. (b) Yes; + is divisible by. (c) Yes; the ones-place digit is. (d) No; the ones-place digit is not (a) Yes; 00 is even. (b) No; is not divisible by. (c) Yes; the ones-place digit is 0. (d) Yes; the ones-place digit is 0.. (a) No; is not even. (b) No; + + is not divisible by. (c) No; the ones-place digit is not 0 or. (d) No; the ones-place digit is not 0.. (a) No; is not even. (b) No; + + is not divisible by. (c) No; the ones-place digit is not 0 or. (d) No; the ones-place digit is not (a) Yes; 0 is even. (b) Yes; is divisible by. (c) No; the ones-place digit is not 0 or. (d) No; the ones-place digit is not (a) Yes; 00 is even. (b) No; is not divisible by. (c) Yes; the ones-place digit is 0. (d) Yes; the ones-place digit is (a) Yes; 0 is even. (b) No; is not divisible by. (c) Yes; the ones-place digit is 0. (d) Yes; the ones-place digit is 0.. (a) No; is not even. (b) Yes; is divisible by. (c) Yes; the ones-place digit is. (d) No; the ones-place digit is not Yes, is divisible by Yes, 0 is divisible by.. Prime. Prime. Composite 0. Composite 6

7 Section. Prime Numbers and Factorization. Composite 6. Composite. 6. Prime. Prime. Neither 0. Neither Composite. Composite 6. Prime 60.. Prime. Composite Composite. There are two whole numbers that are neither prime nor composite, 0 and False; the square of any prime number is divisible by that prime number False; is not prime. 0. False; is not composite..,,,,,,,,,,,,,, 6..,,,,,,,,,,,,,,,,, 6, 6,,,. No, is not a prime number.. No, is not a prime number.. Yes 6. Yes is prime is prime.

8 Chapter Fractions and Mixed Numbers: Multiplication and Division 6.,,,, 6, 0.,,, 6,,.,,,, 6,.,,,.,,,,.,,,,, 6, 0,,, 0, 0, 60.,,,, 6,,, 6,, 6.,,,, 6,,,,,, 6,. No; 0 is not divisible by.. No; 6 is not divisible by.. Yes; 6 is divisible by. 0. Yes; 6 is divisible by.. Yes; is divisible by.. Yes; 0 is divisible by.. No; 6 is not divisible by.. No; is not divisible by.. Yes; is divisible by. 6. Yes; + + is divisible by.. No; is not divisible by.. No; is not divisible by.. Yes; is even and + + is divisible by. 0. Yes; 6 is even and is divisible by.. No; is not even.. No; is not divisible by. Section. Simplifying Fractions to Lowest Terms Section. Practice Exercises. Answers will vary.. (a) A fraction is said to be in lowest terms if the numerator and denominator share no common factor other than. (b) The largest number that divides evenly into the numerator and denominator is call their greatest common factor

9 Section. Simplifying Fractions to Lowest Terms False; 6. Two fractions are equivalent if they both represent the same part of a whole

10 Chapter Fractions and Mixed Numbers: Multiplication and Division undefined + 0 undefined

11 Section. Simplifying Fractions to Lowest Terms , 000, 000 (b) Jared sold the greater fractional part because 6 >.. (a) Lynette: Lisa: , , , , Heads: 0 Tails: (a) 6 (b) (a) (b) 6. (a) Jonathan: Jared: 6 (b) Lisa has completed more of her course because >.. (a) Raymond: 0 0 Travis: (b) Raymond read the greater fractional part because 0 >. 6. (a) (b) 6 6. (a) 00,000,000 (b) 6,000,000 (c) 6, 000, , 000, (a) 00,000,000 (b),000,000 (c) 00, 000, 000, 000, (d) times greater 6

12 Chapter Fractions and Mixed Numbers: Multiplication and Division. For example, 6,, 6 0. For example,,, 6. For example, 6,, 6. For example, 0,, Section. Multiplication of Fractions and Applications Section. Practice Exercises. Pages 6; answers will vary... A power of one-tenth is 0 whole-number power. raised to a.. Numerator: 0; denominator: 0. Numerator: ; denominator: 6 6. Numerator: ; denominator: 6. Numerator: 00; denominator:

13 Section. Multiplication of Fractions and Applications # # $ %$ % ' ' # # 6 $ %$ % 0 ' ' 0 0 # $ % ' # 6 $ % ' # # 6 $ %$ % ' ' # # $ %$ % ' ' # # $ %$ % ' ' # # $ %$ % ' '

14 Chapter Fractions and Mixed Numbers: Multiplication and Division $ # 0% 0 ' 0 ' 0 ' 0 ' 0 ' 0 ' 0 ' 0 ' 0,000,000, $ % # # 0 ' $ % # # # 0 ' ,000 6 $ % # # # # # 0 ' ,000, $ % # ' $ % # ' 6 $ % # # ' 6 $ % # # ' $ # % # $ % ' ' $ # % # $ % ' ' $ # % $ % # ' ' 0 # # $ % $ % 00 ' 0 ' # 6 $ % ' # $ % ' 6 6

15 Section. Multiplication of Fractions and Applications # $ % # '. A bh () $ % # # yd ' # $ % # 6 ' 6 6. A bh () 6 $ # % ' ' 6 or mm 6.. A l w cm 6.. A l w m 0.. in. A l w A bh ()() cm A bh ()() 0 in. A bh ()() m A bh $ %() # # ft ' 6 0. A l w ft. A ()() + ()() + +6 yd. A ()() + ()() m. A (6) $ # % + (6) $ # % ' + ' ' + ' + cm. A () $ # % + () $ # % ' + ' ' + ' + m 6

16 Chapter Fractions and Mixed Numbers: Multiplication and Division The amount left is 0 gal. 0,000,000 The cost is $0. Jim ate of the pizza for breakfast. of the sample has O negative blood.,,000,,000,,000 6,0,000 There are 6,0,000 viewers... (a) 0 6 (0)(6) Frankie mowed left to mow. (b). (a). 6.. (b) $ % # 6 ' $ % # ' yd. He has 0 yd 0. or Nancy spends or hr a day.. First place: Second place: $ Third place: $00 $ ,,, 6 The next number is. 6,, The next number is. 66

17 Section. Division of Fractions and Applications 0. # $ % 6 # $ % 6 They are the same. 0. # $ % 6 # $ % 6 They are the same. Section. Division of Fractions and Applications Section. Practice Exercises. Page Answers will vary.. To find the reciprocal of a nonzero fraction, interchange the numerator and denominator (a) Yes, (b) Yes,. (c) Yes, 6.. (d) No, 0 is undefined. 6.. # $ % # 6 ' 6 # $ % # ' $ $ # % # % $ $ # % # %... No reciprocal exists. 6

18 Chapter Fractions and Mixed Numbers: Multiplication and Division 0. No reciprocal exists.... multiplying. multiplying

19 Section. Division of Fractions and Applications multiplies by 6, and 6 multiplies by. 6 So 6 6 and

20 Chapter Fractions and Mixed Numbers: Multiplication and Division 66. multiplies by, and multiplies by. So 6 and.. $ # % ' $ # % ' $ # % $ # % 6 $ # % ' $ # % 00 ' $ # % 6 $ # 0% ' 6 ' $ # % $ # % 0 ' 0 ' ' $ # % ' ' ' ' # 0 $ % ' ' $ # 0 % ' $ # % '. $ # % ' 6 6 ' ' ' ' ' ' ' 0

21 Section. Division of Fractions and Applications. 6 % # $ ' 0 6 % # $ ' The stack will be in. high. 6 0 Yes, the books will take up only 0 in % # $ ' % # $ ' Li wrapped packages She can sell 0 parcels of land. 6 cups of juice 6. (a). (a). (a) commercials in hr (b) 6 6 commercials in day commercials in hr (b) commercials in day 0, 000 0, , 000 0, 000 The down payment is $, , 000, 000 6, 000 Ricardo s mother will pay $6,000. (b) $,000 $6,000 $000 Ricardo will have to pay $000. (c) $0,000 $,000 $6,000 He will have to finance $6, cm 00

22 Chapter Fractions and Mixed Numbers: Multiplication and Division 0. (a). (a),000,000, The down payment is $ Althea s parents will pay $0. (b) $00 $0 $0 Althea will have to pay $0. (c) $,000 $00 $6,00 She will have to finance $6,00. She plans to sell acre.. (a).. ( + ) () Josh has read pages. (b) ( + ) He still must read pages. She can prepare samples. 6 6 Tony must make strikes.. The length is ft, because (b) She keeps of the land. or acres 6. The width is m, because Problem Recognition Exercises: Multiplication and Division of Fractions. (a) 6 6. (a) (b) 6 6 (b) (c) (c) (d) (d) 0 0 6

23 Problem Recognition Exercises: Multiplication and Division of Fractions. (a) (b) (c) (d). (a) (b) (c) (d). (a) (b) (c) (d) 6. (a) (b) 0 0 (c) 0 Undefined (d) (a) (b) (c) (d). (a) (b) (c) (d). (a) (b) (c) (d)

24 Chapter Fractions and Mixed Numbers: Multiplication and Division 0. (a) (b) (c) (d). (a) (a) (b) (c) (d). (a) (b) (b) (c) (d). (a) (b) (c) (d) (a) (b) (c) (d) 6. (a) % (c) # $ 6 ' (d) $ # 6% (b) (c) (d) ' $ # 6% $ # 6% ' 6 $ # % ' ' ' 6 $ # % % # $ ' ' ' $ # % ' $ # % '

25 Section.6 Multiplication and Division of Mixed Numbers Section.6 Multiplication and Division of Mixed Numbers Section.6 Practice Exercises. Chapter Review Exercises, pages 60 Chapter Test, pages 60 6 Cumulative Review Exercises, pages 6 6 Answers will vary Multiply the whole number by the denominator.. Add the result to the numerator.. Write the result from step over the denominator # $# $ ' % %

26 Chapter Fractions and Mixed Numbers: Multiplication and Division # $# $ % % ' $ # % $ # % 6 ' $ # % '0 ' 0 $ % # # ' $ # % $ # % ' $ # 0% $ # % 0 '. $ # 6% $ # % 6 ' 6. $ $ # % # % $ # % ' ' 6. 6 $ # % $ $ # % # % ' ' 6

27 Section.6 Multiplication and Division of Mixed Numbers Tabitha earned $. 0, ,00, 000 The land will cost Kurt $, Average Americans consume 6 lb Kayla is paid $0.

28 Chapter Fractions and Mixed Numbers: Multiplication and Division. (a) weeks old (b) weeks old Each child will inherit $ million The roll is 6 ft long. 6. (a) Lucy:.. Ricky: 0 0 Lucy earned $ more than Ricky. (b) + Together they earned $

29 Section.6 Multiplication and Division of Mixed Numbers is undefined. 0 0 $ $ # % # % $ # % ' ' $ # 6% $ $ # % # % 6 ' ' 6. 6 It takes gallons of gas for Sara to get to and from work. $ $ It costs Sara $ each day The perimeter of the garden is (0) + () ft bricks will be needed. 6 $ $6 The total cost is $6.

30 Chapter Fractions and Mixed Numbers: Multiplication and Division Chapter Review Exercises Section (a) (b) Improper. (a) 6 (b) Proper or or Section..,, 00., 0, 60, 00 0.,, 0, 60, 00. Prime. Composite Neither. Neither

31 Chapter Review Exercises ,,,, 6,,, 6,,.,,,,, 0, 6, 0, 0, 0 Section (a) (b) Section $ % # # # 0 ' ,

32 Chapter Fractions and Mixed Numbers: Multiplication and Division $ % # $ % $ # % # $ # % ' 0 ' ' 0 0 ' # 00 6 $ # % $ % # # 0 ' 0 ' # $ # $ ' % 0 % 000 A bh. A lw A () $ % 6 # # ft ' 0 A lw or m 0 0 A yd or Maximus requires or yd of lumber There are 00 African American students There are 00 Asian American students There are 00 Hispanic female students There are 0 Caucasian male students. Section Reciprocal does not exist Multiplying

33 Chapter Review Exercises bags of candy 0 0 hr $ $6 Amelia earned $ $ # % # $ % ' $ # % ' ' 6 $ # % 6 6 ' 6 6 ' ' ' The area is 60 or ft. Yes, he will have pieces, which is more than enough for his class... % # $ ' 6 6 Section.6 6. $ %$ 6 % # ' ' 0

34 Chapter Fractions and Mixed Numbers: Multiplication and Division. # $# $ ' % % # $ % # ' It will take gal. 0 There will be 0 pieces. Chapter Test. (a) (b) Proper. (a) 6. (a) (b) Improper (b) +. ;. is an improper fraction because the numerator is greater than or equal to the denominator

35 Chapter Test 0. (a) Composite (b) Neither (c) Prime (d) Neither (e) Prime (f) Composite. (a),,,,, (b). (a) Add the digits of the number. If the sum is divisible by, then the original number is divisible by. (b) Yes; and is divisible by.. (a) No; is not even. (b) Yes; is divisible by. (c) Yes; the digit in the ones-place is a. (d) No; the digit in the ones-place is not or 0,00, ,00, 000. (a) Christine: Brad: (b) Brad has the greater fractional part completed since >. 6 6 $ # % ' ' 6 ' ' 6 or

36 Chapter Fractions and Mixed Numbers: Multiplication and Division 6.. ( * $ * # % ). A bh () $ # % ' ( ' + * -, ), 6 ' 6 ' ' or cm is greater. quarter-pounders 0 0 dogs are female pure breeds. 0 They can build on a maximum of acre. Chapters Cumulative Review Exercises.,000; nineteen thousand, three hundred forty;,0; fifteen thousand, seven hundred seventy-one , R 6

37 Chapters Cumulative Review Exercises., 000, 000 0, 000 0,000,000, Yes; 6 and d. c 6 ( ) 6. Yes; $ # % # # ' 0 # $ # % #. ' and 6. b. e. a. (a) (b) or 0. (a) Proper (b) Improper (c) Improper.. 6 % $ ' # % # $ ' 6 A lw or m. (a),,,, 6, 0,, 0 (b). (a) (b) 0 0 or 60, , 000. A bh # $ % () ' ' ' ' 0 ft of the students are males from out of 0 state.