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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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Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
Kizito
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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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