Fractions

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p. 1

unit 3 linear equations name adding and subtracting fractions 2 directions solve 72

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p. 2

appendix b answer keys transparency/guided practice book answers 54

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p. 3

unit 2 linear equations name adding and subtracting fractions directions calculate 30

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appendix b answer keys transparency/guided practice book answers 67

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p. 5

2 how to · · · · · · · · · · · · · · · · · subtract fractions facts to know subtracting fractions with the same denominators when fractions have the same denominators subtract the numerators only and place the total over the denominator sample from a bag that contained 7 pound of birdseed margery poured 3 of a pound into the bird ­ ­ 8 8 feeder how much birdseed is left step 1 step 2 step 3 subtract the numerators write the answer over the denominator reduce the final answer 7­3=4 4 ­ 8 4 pound 1 pound ­ ­ 8 2 more on finding common denominators sometimes you must change more than one denominator to add or subtract for example how would you solve this problem sample 1 ­ 1 ­ ­ 2 3 these fractions have different denominators you cannot subtract them nor can only one denominator be changed because 2 won t divide into 3 evenly and 3 won t divide into 2 evenly therefore you must find a common denominator a number that both 2 and 3 will divide into evenly there are three methods for finding a common denominator method 1 check the largest denominator in the problem to find out whether it can be divided evenly by the other denominators in the problem ­1=2 ­ ­ 1­1 3 6 sample ­ ­ 3 6 ­1=1 ­ ­ 6 can be evenly divided by 3 so there s no need to look for another number 6 6 1 ­ method 2 multiply the denominators together to find a common denominator 6 3­2 sample ­ ­ 4 3 step 1 multiply the denominators the number 12 ­ 3 ­ 9 4 12 is the common denominator 2 ­­ 8 step 2 raise each fraction to 12ths 3 12 1 step 3 subtract the new fractions 12 method 3 go through the multiplication table of the largest denominator sample 5 ­ 1 ­ ­ 9 6 5 10 step 1 go through the multiplication table of the largest ­ 9 18 denominator 9 ­1 ­ 3 step 1 9 x 1 9 which cannot be divided evenly by 6 6 18 25 1 7 step 1 9 x 2 18 which can be divided evenly by 6 and 9 18 18 step 2 raise each fraction to 18ths step 3 subtract the new fractions 9 .

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p. 6

2 how to · · · · · · · · · · · · · · · · · subtract fractions facts to know cont subtracting fractions with different denominators when subtracting fractions with different denominators find a common denominator sample lupe walks 1 mile to the train she stops for coffee at tom s restaurant which is 3 mile to ­ ­ 2 8 the train how much further does she have to walk after tom s you ll have to subtract 3 from 1 but they don t have common denominators ­ ­ 8 2 step 1 find the least common denominator the numbers 2 and 8 1=4 ­ ­ 2 8 both evenly divisible by 8 ­3=3 ­ ­ step 2 raise 1 to eighths ­ 8 8 2 1 mile step 3 subtract the fractions using the least common denominator ­ 8 subtracting fractions from a whole number when subtracting fractions from the whole number 1 you must change the number 1 to a fraction with the same numerator and denominator as the denominator in the fraction sample ian took one cup of sugar from a bag he only used 3 cup to make ice tea ­ 4 how much sugar is left step 1 change 1 to a fraction using the same number for the 1=4 ­ 4 numerator and denominator as the denominator of the 3=3 ­­ ­ 4 4 original fraction 1 cup 4 cup ­ 4 1 cup left ­ step 2 subtract the fractions 4 when subtracting a fraction from a whole number larger than 1 you must regroup sample 3 ­ 3 ­ 8 3=28 ­ step 1 regroup by changing 3 to 2 8 ­ 8 8 8 3=­3 remeber 1 ­ ­­ ­ 8 8 8 step 2 subtract 25 ­ 8 subtracting mixed numbers you can subtract mixed numbers provided the fractions have the same denominators sample 4 1 ­ 1 3 ­ ­ 3 4 4 4 4 1 4 3 12 ­ step 1 find the lowest common denominator 3 12 12 12 9 9 9 4 ­ 1 3 1 ­ 1 ­ step 2 since you can t subtract from 4 12 12 12 12 4 regroup 1 as 12 from the 4 add it to 12 12 step 3 subtract the fractions then subtract the whole numbers 10 3 16 12 9 ­1 12 7 2 12

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p. 7

2 practice · · · · · · · · · · · · · · · subtracting fractions directions subtract the fractions remember to reduce the fractions to lowest terms 1 4 ­ 2 ­ ­ 5 17 ­ 11 9 1 ­ 1 ­ ­ 13 5 ­ ­ 5 5 5 23 23 2 6 6 18 9 4 2 ­ 10 10 6 20 ­ 17 21 21 10 7 ­ 1 ­ ­ 8 4 14 19 ­ 1 ­ 20 4 7 6 3 ­ 12 12 7 7 ­ 3 ­ ­ 8 8 7 ­ 11 ­ 1 10 5 15 3 ­ 1 ­ ­ 4 2 4 6 ­ 2 ­ ­ 7 7 7 6 8 ­ 15 15 ­ ­ 12 1 ­ 1 4 8 16 13 ­ 7 15 30 directions subtract the fraction from the whole number 17 53 ­ 4 ­ 3 ­ 4 19 43 ­ 4 ­ 3 ­ 8 21 12 3 ­ 4 ­ 12 25 23 53 ­ 4 ­ 1 ­ 4 25 13 3 ­ 4 ­ 11 22 18 73 ­ 4 1 ­ 16 20 10 3 ­ 4 ­ 5 ­ 7 22 83 ­ 4 9 ­ 12 24 25 3 ­ 4 ­ 14 17 26 53 ­ 4 ­ 5 ­ 7 11 .

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p. 8

2 practice · · · · · · · · · · · · · · · subtracting fractions keys to subtracting fractions · if the denominators in the fractions are not alike find the lowest common denominator · regroup if a minuend the number you subtract from is a whole number or the fraction in a minuend is smaller than the fraction in a subtrahend the number being subtracted · subtract the fractions first and then subtract the whole numbers directions subtract the mixed numbers remember reduce to the lowest term 1 97 ­ 8 5 ­6­ 8 7 6 7 ­5 10 2 9 15 10 7 ­ 7 10 8 93 ­ 8 ­23 ­ 8 3 14 19 24 5 ­8 24 9 4 7 11 4 ­3 11 4 11 5 ­ 6 ­51 ­ 6 10 4 8 13 5 ­6 13 5 67 ­ 8 ­33 ­ 8 11 61 ­ 4 ­31 ­ 3 6 53 ­ 8 ­14 ­ 7 12 10 3 ­ 5 ­83 ­ 4 12

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p. 9

1 .50 ­ 50 2 page 8 1 1 3/4 2 1 4/5 3 1 1/3 4 1 3/5 5 2 1/5 6 1 3/4 7 2 1/7 8 2 1/5 9 2 1/8 10 5 11 7/4 12 8/5 13 9/4 14 23/8 15 17/5 16 13/3 17 17/3 18 23/2 19 41/8 20 53/12 21 1/2 22 2/3 23 1/4 24 2/3 25 1/3 26 6/13 27 1/2 28 1/3 29 2/3 30 1/2 31 3/15 32 9/12 33 4/16 34 6/40 35 25/35 36 6/36 37 12/18 38 10/45 39 3/4 40 5/7 41 1 42 3 1/3 43 1 1/7 44 4 45 2 1/2 46 7 2/3 47 1 3/8 48 25/28 49 31/36 50 14 1/12 51 2 52 1 4/5 53 11 11/24 54 14 16/35 55 1 7/10 page 11 1 2/5 2 1/2 3 1/12 4 4/7 5 6/23 6 1/7 7 1/2 8 1/15 9 1/3 10 5/8 11 1/2 12 1/8 13 5/9 14 7/10 15 1/4 16 19/30 17 4 1/4 18 6 15/16 19 3 5/8 20 9 2/7 21 11 13/25 22 7 1/4 23 4 3/4 24 24 3/17 25 12 1/2 26 4 2/7 page 12 1 3 1/4 2 8 1/5 3 6 7/12 4 6 2/3 5 3 1/2 6 3 3/7 7 3/10 8 6 5/8 9 3 7/11 10 1 12/13 11 2 11/12 12 1 17/20 13 2 13/18 14 8 5/12 15 10 3/4 16 7 13/15 17 8 5/6 18 7 27/40 page 15 1 3/8 2 2/21 3 9/40 · · · · · · · · · · · · · · · · · · · · · · answer key 4 6/35 5 1/6 6 1/6 7 2/7 8 2/9 9 1/4 10 3/4 11 1/4 12 1/6 13 3/20 14 35/72 15 1/8 16 1/10 17 1/5 18 2/9 19 3/5 20 1/2 21 1/5 22 2/27 23 3/7 24 15/154 25 11/16 26 1/8 27 4/39 28 2/7 29 11/30 30 4/47 31 17/611 32 7/5,600 page 16 1 1 1/4 2 2 2/3 3 1 1/6 4 3 3/5 5 1 5/7 6 3/10 7 6 1/8 8 2 2/5 9 8/9 10 1 1/8 11 3 1/3 12 3 1/3 13 5 1/3 14 4 2/3 15 2 2/5 16 7/16 17 2 1/2 18 1 1/35 19 1 7/18 20 5/6 21 8 22 2 4/33 23 2 2/3 24 5 3/5 25 9 26 3 1/8 27 9 5/7 28 4/21 page 19 1 11/14 2 1 13/18 3 14/19 4 82/87 5 18/29 6 1 1/4 7 2/3 8 5 9 3/4 10 3/4 11 2 1/6 12 3/7 13 5/12 14 8/9 15 1 5/27 16 3/10 17 3 1/9 18 6 1/4 19 9 3/4 20 1/4 21 25/133 22 5/64 23 2 31/32 24 33 3/4 25 18/175 26 1/32 27 150 28 7 1/2 29 4 2/27 30 10 page 20 1 5/6 2 4/9 3 15/16 4 2 4/7 5 2/5 6 4 7 1/2 8 1 9 4 10 2 1/3 11 2/9 12 4/15 13 4 14 1/12 15 7/16 16 6 2/3 17 2/15 18 6 19 10 20 18 21 10 1/2 22 9 1/3 23 12 24 13 1/2 25 10 2/3 26 7 27 4 4/5 28 3 1/3 29 7 1/2 30 7/20 31 4 2/3 32 9 33 1 5/6 34 1 1/4 35 1 page 24 1 nine tenths 2 three hundred six thousandths 3 forty-two thousandths 4 six and three hundredths 5 eighty and seven tenths 6 two hundred thirty-four and six hundred twelve thousandths 7 sixty-eight and thirty-five ten thousandths 8 one thousand two hundred thirtyfour ten thousandths 9 one and two hundred thirtyfour thousandths 10 twelve and thirtyfour hundredths 11 .43 12 40.03 13 .017 14 86.6 15 .0508 16 5.04 17 12.140 12.404 12.444 12,400 18 0.96 0.9666 10.96 109.6 19 0.055 0.5 0.505 0.55 47 .

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p. 10

unit 2 linear equations name mixed fractions directions calculate 34

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p. 11

appendix b answer keys guided practice book answers cont 68

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p. 12

unit 3 linear equations name mixed fractions directions solve 76

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p. 13

unit 3 linear equations mixed fractions cont 77

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p. 14

appendix b answer keys guided practice book/assessment answers cont 55

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p. 15

unit 3 linear equations name multiplying and dividing fractions 2 directions solve 73

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