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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)

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

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

(1,200)

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

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

4,900 (4,944)

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

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

3,800 (3,760)

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

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

6,050 (6,017)

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

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

6,700 (6,718)

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

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

61,400 (61,337)

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

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

89,700 (89,718)

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

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

213,000 (213,022)

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

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

3,900 (3,935)

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

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

2,400 (2,583)

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

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

600 (504)

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

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

150,123 147,000 (150,123)

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

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

47,278 48,000 (47,278)

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

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

12,771 14,100 (12,711)

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

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

8,100 (9,768)

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

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

90,000 (86,784)

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

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

396,000 (386,496)

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

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

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

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

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

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

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

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180 ÷ 12 size 12{"180" div "12"} {}

18 (15)

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309 ÷ 16 size 12{"309" div "16"} {}

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286 ÷ 22 size 12{"286" div "22"} {}

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

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527 ÷ 17 size 12{"527" div "17"} {}

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

50 (53)

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

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

54 (51)

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

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

130 (105)

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

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

41.25 (44)

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

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

42 (43)

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

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

14.4 (14)

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

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

60 (61)

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

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

1,000 (992)

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

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

71.1 (71.17)

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

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

119.4 (119.31)

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

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

272 (271.8)

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

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

2,001 (2,020.952)

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

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

4.16 (3.9596)

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

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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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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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)

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

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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)

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

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

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

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

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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)

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

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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)

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

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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"} {}

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

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

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

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

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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"} {}

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

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

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

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

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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"} {}

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

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

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

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

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

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

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

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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"} {}

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

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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"} {}

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

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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"} {}

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

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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 )} {}

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

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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 )} {}

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

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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 )} {}

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

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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 )} {}

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

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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 )} {}

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

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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 )} {}

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

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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 )} {}

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

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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 )} {}

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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