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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is a proficiency exam to the chapter "Techniques of Estimation." Each problem is accompanied with a reference link pointing back to the module that discusses the type of problem demonstrated in the question. The problems in this exam are accompanied by solutions.

Proficiency exam

For problems 1 - 16, estimate each value. After you have made an estimate, find the exact value. Results may vary.

( [link] ) 3,716 + 6,789 size 12{"3,716 "+" 6,789"} {}

10,500 (10,505)

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( [link] ) 8,821 + 9,217 size 12{"8,821 "+" 9,217"} {}

18,000 (18,038)

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( [link] ) 7,316 - 2,305 size 12{"7,316 - 2,305"} {}

5,000 (5,011)

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( [link] ) 110,812 - 83,406 size 12{"110,812 - 83,406"} {}

28,000 (27,406)

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( [link] ) 82 38 size 12{"82 " cdot " 38"} {}

3,200 (3,116)

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( [link] ) 51 92 size 12{"51 " cdot " 92"} {}

4,500 (4,692)

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( [link] ) 48 6,012 size 12{"48 " cdot " 6,012"} {}

300,000 (288,576)

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( [link] ) 238 ÷ 17 size 12{"238 "÷" 17"} {}

12 (14)

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( [link] ) 2,660 ÷ 28 size 12{"2,660 "÷" 28"} {}

90 (95)

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( [link] ) 43 . 06 + 37 . 94 size 12{"43" "." "06 "+" 37" "." "94"} {}

81 (81.00)

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( [link] ) 307 . 006 + 198 . 0005 size 12{"307" "." "006 "+" 198" "." "0005"} {}

505 (505.0065)

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( [link] ) ( 47 . 2 ) ( 92 . 8 ) size 12{ \( "47" "." 2 \) \( "92" "." 8 \) } {}

4,371 (4,380.16)

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( [link] ) 58 + 91 + 61 + 88 size 12{"58 "+" 91 "+" 61 "+" 88"} {}

2 60 + 2 90 = 300 size 12{2 left ("60" right )+2 left ("90" right )="300"} {} (298)

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( [link] ) 43 + 39 + 89 + 92 size 12{"43 "+" 39 "+" 89 "+" 92"} {}

2 ( 40 ) + 2 ( 90 ) = 260 size 12{2 \( "40" \) +2 \( "90" \) ="260"} {} (263)

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( [link] ) 81 + 78 + 27 + 79 size 12{"81 "+" 78 "+" 27 "+" 79"} {}

30 + 3 ( 80 ) = 270 size 12{"30"+3 \( "80" \) ="270"} {} (265)

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( [link] ) 804 + 612 + 801 + 795 + 606 size 12{"804 "+" 612 "+" 801 "+" 795"+" 606"} {}

3 ( 800 ) + 2 ( 600 ) = 3, 600 size 12{3 \( "800" \) +2 \( "600" \) =3,"600"} {} (3,618)

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For problems 17-21, use the distributive property to obtain the exact result.

( [link] ) 25 14 size 12{"25" cdot " 14"} {}

25 ( 10 + 4 ) = 250 + 100 = 350 size 12{"25" \( "10"+4 \) ="250"+"100"="350"} {}

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( [link] ) 15 83 size 12{"15 " cdot " 83"} {}

15 ( 80 + 3 ) = 1, 200 + 45 = 1, 245 size 12{"15" \( "80"+3 \) =1,"200"+"45"=1,"245"} {}

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( [link] ) 65 98 size 12{"65 " cdot " 98"} {}

65 ( 100 2 ) = 6, 500 130 = 6, 370 size 12{"65" \( "100" - 2 \) =6,"500" - "130"=6,"370"} {}

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( [link] ) 80 107 size 12{"80 " cdot " 107"} {}

80 ( 100 + 7 ) = 8, 000 + 560 = 8, 560 size 12{"80" \( "100"+7 \) =8,"000"+"560"=8,"560"} {}

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( [link] ) 400 215 size 12{"400 " cdot " 215"} {}

400 ( 200 + 15 ) = 80 , 000 + 6, 000 = 86 , 000 size 12{"400" \( "200"+"15" \) ="80","000"+6,"000"="86","000"} {}

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For problems 22-25, estimate each value. After you have made an estimate, find the exact value. Results may vary.

( [link] ) 15 16 + 5 8 size 12{ { {"15"} over {"16"} } + { {5} over {8} } } {}

1 + 1 2 = 1 1 2 size 12{1+ { {1} over {2} } =1 { {1} over {2} } } {} 1 9 16 size 12{ left (1 { {9} over {"16"} } right )} {}

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( [link] ) 1 25 + 11 20 + 17 30 size 12{ { {1} over {"25"} } + { {"11"} over {"20"} } + { {"17"} over {"30"} } } {}

0 + 1 2 + 1 2 = 1 size 12{0+ { {1} over {2} } + { {1} over {2} } =1} {} 1 47 300 size 12{ left (1 { {"47"} over {"300"} } right )} {}

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( [link] ) 8 9 16 + 14 1 12 size 12{8 { {9} over {"16"} } +"14" { {1} over {"12"} } } {}

8 1 2 + 14 = 22 1 2 size 12{8 { {1} over {2} } +"14"="22" { {1} over {2} } } {} 22 31 48 size 12{ left ("22" { {"31"} over {"48"} } right )} {}

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( [link] ) 5 4 9 + 1 17 36 + 6 5 12 size 12{5 { {4} over {9} } +1 { {"17"} over {"36"} } +6 { {5} over {"12"} } } {}

5 1 2 + 1 1 2 + 6 1 2 = 13 1 2 size 12{5 { {1} over {2} } +1 { {1} over {2} } +6 { {1} over {2} } ="13" { {1} over {2} } } {} 13 1 3 size 12{ left ("13" { {1} over {3} } 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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