<< Chapter < Page Chapter >> Page >
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 ( [link] )

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.

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

600 (598)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

(1,200)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

4,900 (4,944)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

3,800 (3,760)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

6,050 (6,017)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

6,700 (6,718)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

61,400 (61,337)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

89,700 (89,718)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

213,000 (213,022)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

3,900 (3,935)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

41 63 size 12{"41" cdot "63"} {}

2,400 (2,583)

Got questions? Get instant answers now!

38 81 size 12{"38" cdot "81"} {}

Got questions? Get instant answers now!

18 28 size 12{"18" cdot "28"} {}

600 (504)

Got questions? Get instant answers now!

52 21 size 12{"52" cdot "21"} {}

Got questions? Get instant answers now!

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

150,123 147,000 (150,123)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

47,278 48,000 (47,278)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

12,771 14,100 (12,711)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

12 814 size 12{"12" cdot "814"} {}

8,100 (9,768)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

90,000 (86,784)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

396,000 (386,496)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

180 ÷ 12 size 12{"180" div "12"} {}

18 (15)

Got questions? Get instant answers now!

309 ÷ 16 size 12{"309" div "16"} {}

Got questions? Get instant answers now!

286 ÷ 22 size 12{"286" div "22"} {}

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

Got questions? Get instant answers now!

527 ÷ 17 size 12{"527" div "17"} {}

Got questions? Get instant answers now!

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

50 (53)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

54 (51)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

130 (105)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

41.25 (44)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

42 (43)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

14.4 (14)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

60 (61)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

1,000 (992)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

48 . 06 + 23 . 11 size 12{"48" "." "06"+"23" "." "11"} {}

71.1 (71.17)

Got questions? Get instant answers now!

73 . 73 + 72 . 9 size 12{"73" "." "73"+"72" "." 9} {}

Got questions? Get instant answers now!

62 . 91 + 56 . 4 size 12{"62" "." "91"+"56" "." 4} {}

119.4 (119.31)

Got questions? Get instant answers now!

87 . 865 + 46 . 772 size 12{"87" "." "865"+"46" "." "772"} {}

Got questions? Get instant answers now!

174 . 6 + 97 . 2 size 12{"174" "." 6+"97" "." 2} {}

272 (271.8)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2,001 (2,020.952)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

4.16 (3.9596)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Estimation by clustering ( [link] )

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.

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Mental arithmetic- using the distributive property ( [link] )

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

15 33 size 12{"15" cdot "33"} {}

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

Got questions? Get instant answers now!

15 42 size 12{"15" cdot "42"} {}

Got questions? Get instant answers now!

35 36 size 12{"35" cdot "36"} {}

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

Got questions? Get instant answers now!

35 28 size 12{"35" cdot "28"} {}

Got questions? Get instant answers now!

85 23 size 12{"85" cdot "23"} {}

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

Got questions? Get instant answers now!

95 11 size 12{"95" cdot "11"} {}

Got questions? Get instant answers now!

30 14 size 12{"30" cdot "14"} {}

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

Got questions? Get instant answers now!

60 18 size 12{"60" cdot "18"} {}

Got questions? Get instant answers now!

75 23 size 12{"75" cdot "23"} {}

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

Got questions? Get instant answers now!

65 31 size 12{"65" cdot "31"} {}

Got questions? Get instant answers now!

17 15 size 12{"17" cdot "15"} {}

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

Got questions? Get instant answers now!

38 25 size 12{"38" cdot "25"} {}

Got questions? Get instant answers now!

14 65 size 12{"14" cdot "65"} {}

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

Got questions? Get instant answers now!

19 85 size 12{"19" cdot "85"} {}

Got questions? Get instant answers now!

42 60 size 12{"42" cdot "60"} {}

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

Got questions? Get instant answers now!

81 40 size 12{"81" cdot "40"} {}

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

85 97 size 12{"85" cdot "97"} {}

Got questions? Get instant answers now!

Estimation by rounding fractions ( [link] )

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.

3 8 + 5 6 size 12{ { {3} over {8} } + { {5} over {6} } } {}

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

Got questions? Get instant answers now!

7 16 + 1 24 size 12{ { {7} over {"16"} } + { {1} over {"24"} } } {}

Got questions? Get instant answers now!

7 15 + 13 30 size 12{ { {7} over {"15"} } + { {"13"} over {"30"} } } {}

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

Got questions? Get instant answers now!

14 15 + 19 20 size 12{ { {"14"} over {"15"} } + { {"19"} over {"20"} } } {}

Got questions? Get instant answers now!

13 25 + 7 30 size 12{ { {"13"} over {"25"} } + { {7} over {"30"} } } {}

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

Got questions? Get instant answers now!

11 12 + 7 8 size 12{ { {"11"} over {"12"} } + { {7} over {8} } } {}

Got questions? Get instant answers now!

9 32 + 15 16 size 12{ { {9} over {"32"} } + { {"15"} over {"16"} } } {}

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

Got questions? Get instant answers now!

5 8 + 1 32 size 12{ { {5} over {8} } + { {1} over {"32"} } } {}

Got questions? Get instant answers now!

2 3 4 + 6 3 5 size 12{2 { {3} over {4} } +6 { {3} over {5} } } {}

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

6 1 20 + 2 1 10 + 8 13 60 size 12{6 { {1} over {"20"} } +2 { {1} over {"10"} } +8 { {"13"} over {"60"} } } {}

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

Got questions? Get instant answers now!

5 7 8 + 1 1 4 + 12 5 12 size 12{5 { {7} over {8} } +1 { {1} over {4} } +"12" { {5} over {"12"} } } {}

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?

Ask