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Techniques of Estimation: Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Techniques of Estimation" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise Supplement

Estimation by Rounding ((Reference))

For problems 1-70, estimate each value using the method of rounding. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary.

Exercise 1

286+312286+312 size 12{"286"+"312"} {}

Solution

600 (598)

Exercise 2

419+582419+582 size 12{"419"+"582"} {}

Exercise 3

689+511689+511 size 12{"689"+"511"} {}

Solution

(1,200)

Exercise 4

926+1,105926+1,105 size 12{"926"+1,"105"} {}

Exercise 5

1,927+3,0171,927+3,017 size 12{1,"927"+3,"017"} {}

Solution

4,900 (4,944)

Exercise 6

5,026+2,8145,026+2,814 size 12{5,"026"+2,"814"} {}

Exercise 7

1,408+2,3521,408+2,352 size 12{1,"408"+2,"352"} {}

Solution

3,800 (3,760)

Exercise 8

1,186+4,2281,186+4,228 size 12{1,"186"+4,"228"} {}

Exercise 9

5,771+2465,771+246 size 12{5,"771"+"246"} {}

Solution

6,050 (6,017)

Exercise 10

8,305+4848,305+484 size 12{8,"305"+"484"} {}

Exercise 11

3,812+2,9063,812+2,906 size 12{3,"812"+2,"906"} {}

Solution

6,700 (6,718)

Exercise 12

5,293+8,0075,293+8,007 size 12{5,"293"+8,"007"} {}

Exercise 13

28,481+32,85628,481+32,856 size 12{"28","481"+"32","856"} {}

Solution

61,400 (61,337)

Exercise 14

92,512+26,07192,512+26,071 size 12{"92","512"+"26","071"} {}

Exercise 15

87,612+2,10687,612+2,106 size 12{"87","612"+2,"106"} {}

Solution

89,700 (89,718)

Exercise 16

42,612+4,86142,612+4,861 size 12{"42","612"+4,"861"} {}

Exercise 17

212,413+609212,413+609 size 12{"212","413"+"609"} {}

Solution

213,000 (213,022)

Exercise 18

487,235+494487,235+494 size 12{"487","235"+"494"} {}

Exercise 19

2,409+1,5262,409+1,526 size 12{2,"409"+1,"526"} {}

Solution

3,900 (3,935)

Exercise 20

3,704+4,7043,704+4,704 size 12{3,"704"+4,"704"} {}

Exercise 21

41⋅6341⋅63 size 12{"41" cdot "63"} {}

Solution

2,400 (2,583)

Exercise 22

38⋅8138⋅81 size 12{"38" cdot "81"} {}

Exercise 23

18⋅2818⋅28 size 12{"18" cdot "28"} {}

Solution

600 (504)

Exercise 24

52⋅2152⋅21 size 12{"52" cdot "21"} {}

Exercise 25

307⋅489307⋅489 size 12{"307" cdot "489"} {}

Solution

150,123 147,000 (150,123)

Exercise 26

412⋅807412⋅807 size 12{"412" cdot "807"} {}

Exercise 27

77⋅61477⋅614 size 12{"77" cdot "614"} {}

Solution

47,278 48,000 (47,278)

Exercise 28

62⋅59662⋅596 size 12{"62" cdot "596"} {}

Exercise 29

27⋅47327⋅473 size 12{"27" cdot "473"} {}

Solution

12,771 14,100 (12,711)

Exercise 30

92⋅33692⋅336 size 12{"92" cdot "336"} {}

Exercise 31

12⋅81412⋅814 size 12{"12" cdot "814"} {}

Solution

8,100 (9,768)

Exercise 32

8⋅2,1068⋅2,106 size 12{8 cdot 2,"106"} {}

Exercise 33

192⋅452192⋅452 size 12{"192" cdot "452"} {}

Solution

90,000 (86,784)

Exercise 34

374⋅816374⋅816 size 12{"374" cdot "816"} {}

Exercise 35

88⋅4,39288⋅4,392 size 12{"88" cdot 4,"392"} {}

Solution

396,000 (386,496)

Exercise 36

126⋅2,834126⋅2,834 size 12{"126" cdot 2,"834"} {}

Exercise 37

3,896⋅4133,896⋅413 size 12{3,"896" cdot "413"} {}

Solution

1,609,048 1,560,000 (1,609,048)

Exercise 38

5,794⋅8375,794⋅837 size 12{5,"794" cdot "837"} {}

Exercise 39

6,311⋅3,5126,311⋅3,512 size 12{6,"311" cdot 3,"512"} {}

Solution

22,050,000 (22,164,232)

Exercise 40

7,471⋅5,7827,471⋅5,782 size 12{7,"471" cdot 5,"782"} {}

Exercise 41

180÷12180÷12 size 12{"180" div "12"} {}

Solution

18 (15)

Exercise 42

309÷16309÷16 size 12{"309" div "16"} {}

Exercise 43

286÷22286÷22 size 12{"286" div "22"} {}

Solution

14121412 size 12{"14" { {1} over {2} } } {} (13)

Exercise 44

527÷17527÷17 size 12{"527" div "17"} {}

Exercise 45

1,007÷191,007÷19 size 12{1,"007" div "19"} {}

Solution

50 (53)

Exercise 46

1,728÷361,728÷36 size 12{1,"728" div "36"} {}

Exercise 47

2,703÷532,703÷53 size 12{2,"703" div "53"} {}

Solution

54 (51)

Exercise 48

2,562÷612,562÷61 size 12{2,"562" div "61"} {}

Exercise 49

1,260÷121,260÷12 size 12{1,"260" div "12"} {}

Solution

130 (105)

Exercise 50

3,618÷183,618÷18 size 12{3,"618" div "18"} {}

Exercise 51

3,344÷763,344÷76 size 12{3,"344" div "76"} {}

Solution

41.25 (44)

Exercise 52

7,476÷3567,476÷356 size 12{7,"476" div "356"} {}

Exercise 53

20,984÷48820,984÷488 size 12{"20","984" div "488"} {}

Solution

42 (43)

Exercise 54

43,776÷60843,776÷608 size 12{"43","776" div "608"} {}

Exercise 55

7,196÷5147,196÷514 size 12{7,"196" div "514"} {}

Solution

14.4 (14)

Exercise 56

51,492÷51451,492÷514 size 12{"51","492" div "514"} {}

Exercise 57

26,962÷44226,962÷442 size 12{"26","962" div "442"} {}

Solution

60 (61)

Exercise 58

33,712÷11233,712÷112 size 12{"33","712" div "112"} {}

Exercise 59

105,152÷106105,152÷106 size 12{"105","152" div "106"} {}

Solution

1,000 (992)

Exercise 60

176,978÷214176,978÷214 size 12{"176","978" div "214"} {}

Exercise 61

48.06+23.1148.06+23.11 size 12{"48" "." "06"+"23" "." "11"} {}

Solution

71.1 (71.17)

Exercise 62

73.73+72.973.73+72.9 size 12{"73" "." "73"+"72" "." 9} {}

Exercise 63

62.91+56.462.91+56.4 size 12{"62" "." "91"+"56" "." 4} {}

Solution

119.4 (119.31)

Exercise 64

87.865+46.77287.865+46.772 size 12{"87" "." "865"+"46" "." "772"} {}

Exercise 65

174.6+97.2174.6+97.2 size 12{"174" "." 6+"97" "." 2} {}

Solution

272 (271.8)

Exercise 66

(48.3)(29.6)(48.3)(29.6) size 12{ \( "48" "." 3 \) \( "29" "." 6 \) } {}

Exercise 67

(87.11)(23.2)(87.11)(23.2) size 12{ \( "87" "." "11" \) \( "23" "." 2 \) } {}

Solution

2,001 (2,020.952)

Exercise 68

(107.02)(48.7)(107.02)(48.7) size 12{ \( "107" "." "02" \) \( "48" "." 7 \) } {}

Exercise 69

(0.76)(5.21)(0.76)(5.21) size 12{ \( 0 "." "76" \) \( 5 "." "21" \) } {}

Solution

4.16 (3.9596)

Exercise 70

(1.07)(13.89)(1.07)(13.89) size 12{ \( 1 "." "07" \) \( "13" "." "89" \) } {}

Estimation by Clustering ((Reference))

For problems 71-90, estimate each value using the method of clustering. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary.

Exercise 71

38+51+41+4838+51+41+48 size 12{"38"+"51"+"41"+"48"} {}

Solution

2(40)+2(50)=1802(40)+2(50)=180 size 12{2 \( "40" \) +2 \( "50" \) ="180"} {} (178)

Exercise 72

19+73+23+7119+73+23+71 size 12{"19"+"73"+"23"+"71"} {}

Exercise 73

27+62+59+3127+62+59+31 size 12{"27"+"62"+"59"+"31"} {}

Solution

2(30)+2(60)=1802(30)+2(60)=180 size 12{2 \( "30" \) +2 \( "60" \) ="180"} {} (179)

Exercise 74

18+73+69+1918+73+69+19 size 12{"18"+"73"+"69"+"19"} {}

Exercise 75

83+49+79+5283+49+79+52 size 12{"83"+"49"+"79"+"52"} {}

Solution

2(80)+2(50)=2602(80)+2(50)=260 size 12{2 \( "80" \) +2 \( "50" \) ="260"} {} (263)

Exercise 76

67+71+84+8167+71+84+81 size 12{"67"+"71"+"84"+"81"} {}

Exercise 77

16+13+24+2616+13+24+26 size 12{"16"+"13"+"24"+"26"} {}

Solution

3(20)+1(10)=703(20)+1(10)=70 size 12{3 \( "20" \) +1 \( "10" \) ="70"} {} (79)

Exercise 78

34+56+36+5534+56+36+55 size 12{"34"+"56"+"36"+"55"} {}

Exercise 79

14+17+83+8714+17+83+87 size 12{"14"+"17"+"83"+"87"} {}

Solution

2(15)+2(80)=1902(15)+2(80)=190 size 12{2 \( "15" \) +2 \( "80" \) ="190"} {} (201)

Exercise 80

93+108+96+11193+108+96+111 size 12{"93"+"108"+"96"+"111"} {}

Exercise 81

18+20+31+29+24+3818+20+31+29+24+38 size 12{"18"+"20"+"31"+"29"+"24"+"38"} {}

Solution

3(20)+2(30)+40=1603(20)+2(30)+40=160 size 12{3 \( "20" \) +2 \( "30" \) +"40"="160"} {} (160)

Exercise 82

32+27+48+51+72+6932+27+48+51+72+69 size 12{"32"+"27"+"48"+"51"+"72"+"69"} {}

Exercise 83

64+17+27+59+31+2164+17+27+59+31+21 size 12{"64"+"17"+"27"+"59"+"31"+"21"} {}

Solution

2(60)+2(20)+2(30)=2202(60)+2(20)+2(30)=220 size 12{2 \( "60" \) +2 \( "20" \) +2 \( "30" \) ="220"} {} (219)

Exercise 84

81+41+92+38+88+8081+41+92+38+88+80 size 12{"81"+"41"+"92"+"38"+"88"+"80"} {}

Exercise 85

87+22+9187+22+91 size 12{"87"+"22"+"91"} {}

Solution

2(90)+20=2002(90)+20=200 size 12{2 \( "90" \) +"20"="200"} {} (200)

Exercise 86

44+38+8744+38+87 size 12{"44"+"38"+"87"} {}

Exercise 87

19+18+39+22+4219+18+39+22+42 size 12{"19"+"18"+"39"+"22"+"42"} {}

Solution

3(20)+2(40)=1403(20)+2(40)=140 size 12{3 \( "20" \) +2 \( "40" \) ="140"} {} (140)

Exercise 88

31+28+49+2931+28+49+29 size 12{"31"+"28"+"49"+"29"} {}

Exercise 89

88+86+27+91+2988+86+27+91+29 size 12{"88"+"86"+"27"+"91"+"29"} {}

Solution

3(90)+2(30)=3303(90)+2(30)=330 size 12{3 \( "90" \) +2 \( "30" \) ="330"} {} (321)

Exercise 90

57+62+18+23+61+2157+62+18+23+61+21 size 12{"57"+"62"+"18"+"23"+"61"+"21"} {}

Mental Arithmetic- Using the Distributive Property ((Reference))

For problems 91-110, compute each product using the distributive property.

Exercise 91

15⋅3315⋅33 size 12{"15" cdot "33"} {}

Solution

15(30+3)=450+45=49515(30+3)=450+45=495 size 12{"15" \( "30"+3 \) ="450"+"45"="495"} {}

Exercise 92

15⋅4215⋅42 size 12{"15" cdot "42"} {}

Exercise 93

35⋅3635⋅36 size 12{"35" cdot "36"} {}

Solution

35(40−4)=1400−140=1,26035(40−4)=1400−140=1,260 size 12{"35" \( "40" - 4 \) ="1400" - "140"=1,"260"} {}

Exercise 94

35⋅2835⋅28 size 12{"35" cdot "28"} {}

Exercise 95

85⋅2385⋅23 size 12{"85" cdot "23"} {}

Solution

85(20+3)=1,700+225=1,95585(20+3)=1,700+225=1,955 size 12{"85" \( "20"+3 \) =1,"700"+"225"=1,"955"} {}

Exercise 96

95⋅1195⋅11 size 12{"95" cdot "11"} {}

Exercise 97

30⋅1430⋅14 size 12{"30" cdot "14"} {}

Solution

30(10+4)=300+120=42030(10+4)=300+120=420 size 12{"30" \( "10"+4 \) ="300"+"120"="420"} {}

Exercise 98

60⋅1860⋅18 size 12{"60" cdot "18"} {}

Exercise 99

75⋅2375⋅23 size 12{"75" cdot "23"} {}

Solution

75(20+3)=1,500+225=1,72575(20+3)=1,500+225=1,725 size 12{"75" \( "20"+3 \) =1,"500"+"225"=1,"725"} {}

Exercise 100

65⋅3165⋅31 size 12{"65" cdot "31"} {}

Exercise 101

17⋅1517⋅15 size 12{"17" cdot "15"} {}

Solution

15(20−3)=300−45=25515(20−3)=300−45=255 size 12{"15" \( "20" - 3 \) ="300" - "45"="255"} {}

Exercise 102

38⋅2538⋅25 size 12{"38" cdot "25"} {}

Exercise 103

14⋅6514⋅65 size 12{"14" cdot "65"} {}

Solution

65(10+4)=650+260=91065(10+4)=650+260=910 size 12{"65" \( "10"+4 \) ="650"+"260"="910"} {}

Exercise 104

19⋅8519⋅85 size 12{"19" cdot "85"} {}

Exercise 105

42⋅6042⋅60 size 12{"42" cdot "60"} {}

Solution

60(40+2)=2,400+120=2,52060(40+2)=2,400+120=2,520 size 12{"60" \( "40"+2 \) =2,"400"+"120"=2,"520"} {}

Exercise 106

81⋅4081⋅40 size 12{"81" cdot "40"} {}

Exercise 107

15⋅10515⋅105 size 12{"15" cdot "105"} {}

Solution

15(100+5)=1,500+75=1,57515(100+5)=1,500+75=1,575 size 12{"15" \( "100"+5 \) =1,"500"+"75"=1,"575"} {}

Exercise 108

35⋅20235⋅202 size 12{"35" cdot "202"} {}

Exercise 109

45⋅30645⋅306 size 12{"45" cdot "306"} {}

Solution

45(300+6)=13,500+270=13,77045(300+6)=13,500+270=13,770 size 12{"45" \( "300"+6 \) ="13","500"+"270"="13","770"} {}

Exercise 110

85⋅9785⋅97 size 12{"85" cdot "97"} {}

Estimation by Rounding Fractions ((Reference))

For problems 111-125, estimate each sum using the method of rounding fractions. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary.

Exercise 111

38+5638+56 size 12{ { {3} over {8} } + { {5} over {6} } } {}

Solution

12+1=112152412+1=1121524 size 12{ { {1} over {2} } +1=1 { {1} over {2} } left (1 { {5} over {"24"} } right )} {}

Exercise 112

716+124716+124 size 12{ { {7} over {"16"} } + { {1} over {"24"} } } {}

Exercise 113

715+1330715+1330 size 12{ { {7} over {"15"} } + { {"13"} over {"30"} } } {}

Solution

12+12=1  2730 or 91012+12=1  2730 or 910 size 12{ { {1} over {2} } + { {1} over {2} } =1 left ( { {"27"} over {"30"} } " or " { {9} over {"10"} } right )} {}

Exercise 114

1415+19201415+1920 size 12{ { {"14"} over {"15"} } + { {"19"} over {"20"} } } {}

Exercise 115

1325+7301325+730 size 12{ { {"13"} over {"25"} } + { {7} over {"30"} } } {}

Solution

12+14=3411315012+14=34113150 size 12{ { {1} over {2} } + { {1} over {4} } = { {3} over {4} } left ( { {"113"} over {"150"} } right )} {}

Exercise 116

1112+781112+78 size 12{ { {"11"} over {"12"} } + { {7} over {8} } } {}

Exercise 117

932+1516932+1516 size 12{ { {9} over {"32"} } + { {"15"} over {"16"} } } {}

Solution

14+1=1143932 or  173214+1=1143932 or  1732 size 12{ { {1} over {4} } +1=1 { {1} over {4} } left ( { {"39"} over {"32"} } " or "1 { {7} over {"32"} } right )} {}

Exercise 118

58+13258+132 size 12{ { {5} over {8} } + { {1} over {"32"} } } {}

Exercise 119

234+635234+635 size 12{2 { {3} over {4} } +6 { {3} over {5} } } {}

Solution

234+612=9149720234+612=9149720 size 12{2 { {3} over {4} } +6 { {1} over {2} } =9 { {1} over {4} } left (9 { {7} over {"20"} } right )} {}

Exercise 120

459+8127459+8127 size 12{4 { {5} over {9} } +8 { {1} over {"27"} } } {}

Exercise 121

11518+7224511518+72245 size 12{"11" { {5} over {"18"} } +7 { {"22"} over {"45"} } } {}

Solution

1114+712=18341823301114+712=1834182330 size 12{"11" { {1} over {4} } +7 { {1} over {2} } ="18" { {3} over {4} } left ("18" { {"23"} over {"30"} } right )} {}

Exercise 122

141936+2718141936+2718 size 12{"14" { {"19"} over {"36"} } +2 { {7} over {"18"} } } {}

Exercise 123

6120+2110+813606120+2110+81360 size 12{6 { {1} over {"20"} } +2 { {1} over {"10"} } +8 { {"13"} over {"60"} } } {}

Solution

6+2+814=16141611306+2+814=1614161130 size 12{6+2+8 { {1} over {4} } ="16" { {1} over {4} } left ("16" { {"11"} over {"30"} } right )} {}

Exercise 124

578+114+12512578+114+12512 size 12{5 { {7} over {8} } +1 { {1} over {4} } +"12" { {5} over {"12"} } } {}

Exercise 125

1012+61516+819801012+61516+81980 size 12{"10" { {1} over {2} } +6 { {"15"} over {"16"} } +8 { {"19"} over {"80"} } } {}

Solution

1012+7+814=25342527401012+7+814=2534252740 size 12{"10" { {1} over {2} } +7+8 { {1} over {4} } ="25" { {3} over {4} } left ("25" { {"27"} over {"40"} } right )} {}

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