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Proficiency Exam

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 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.

Exercise 1

((Reference)) 3,716 + 6,7893,716 + 6,789 size 12{"3,716 "+" 6,789"} {}

Solution

10,500 (10,505)

Exercise 2

((Reference)) 8,821 + 9,2178,821 + 9,217 size 12{"8,821 "+" 9,217"} {}

Solution

18,000 (18,038)

Exercise 3

((Reference)) 7,316 - 2,3057,316 - 2,305 size 12{"7,316 - 2,305"} {}

Solution

5,000 (5,011)

Exercise 4

((Reference)) 110,812 - 83,406110,812 - 83,406 size 12{"110,812 - 83,406"} {}

Solution

28,000 (27,406)

Exercise 5

((Reference)) 82 ⋅ 3882 ⋅ 38 size 12{"82 " cdot " 38"} {}

Solution

3,200 (3,116)

Exercise 6

((Reference)) 51 ⋅ 9251 ⋅ 92 size 12{"51 " cdot " 92"} {}

Solution

4,500 (4,692)

Exercise 7

((Reference)) 48 ⋅ 6,01248 ⋅ 6,012 size 12{"48 " cdot " 6,012"} {}

Solution

300,000 (288,576)

Exercise 8

((Reference)) 238 ÷ 17238 ÷ 17 size 12{"238 "÷" 17"} {}

Solution

12 (14)

Exercise 9

((Reference)) 2,660 ÷ 282,660 ÷ 28 size 12{"2,660 "÷" 28"} {}

Solution

90 (95)

Exercise 10

((Reference)) 43.06 + 37.9443.06 + 37.94 size 12{"43" "." "06 "+" 37" "." "94"} {}

Solution

81 (81.00)

Exercise 11

((Reference)) 307.006 + 198.0005307.006 + 198.0005 size 12{"307" "." "006 "+" 198" "." "0005"} {}

Solution

505 (505.0065)

Exercise 12

((Reference)) (47.2)(92.8)(47.2)(92.8) size 12{ \( "47" "." 2 \) \( "92" "." 8 \) } {}

Solution

4,371 (4,380.16)

Exercise 13

((Reference)) 58 + 91 + 61 + 8858 + 91 + 61 + 88 size 12{"58 "+" 91 "+" 61 "+" 88"} {}

Solution

260+290=300260+290=300 size 12{2 left ("60" right )+2 left ("90" right )="300"} {} (298)

Exercise 14

((Reference)) 43 + 39 + 89 + 9243 + 39 + 89 + 92 size 12{"43 "+" 39 "+" 89 "+" 92"} {}

Solution

2(40)+2(90)=2602(40)+2(90)=260 size 12{2 \( "40" \) +2 \( "90" \) ="260"} {} (263)

Exercise 15

((Reference)) 81 + 78 + 27 + 7981 + 78 + 27 + 79 size 12{"81 "+" 78 "+" 27 "+" 79"} {}

Solution

30+3(80)=27030+3(80)=270 size 12{"30"+3 \( "80" \) ="270"} {} (265)

Exercise 16

((Reference)) 804 + 612 + 801 + 795+ 606804 + 612 + 801 + 795+ 606 size 12{"804 "+" 612 "+" 801 "+" 795"+" 606"} {}

Solution

3(800)+2(600)=3,6003(800)+2(600)=3,600 size 12{3 \( "800" \) +2 \( "600" \) =3,"600"} {} (3,618)

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

Exercise 17

((Reference)) 25⋅ 1425⋅ 14 size 12{"25" cdot " 14"} {}

Solution

25(10+4)=250+100=35025(10+4)=250+100=350 size 12{"25" \( "10"+4 \) ="250"+"100"="350"} {}

Exercise 18

((Reference)) 15 ⋅ 8315 ⋅ 83 size 12{"15 " cdot " 83"} {}

Solution

15(80+3)=1,200+45=1,24515(80+3)=1,200+45=1,245 size 12{"15" \( "80"+3 \) =1,"200"+"45"=1,"245"} {}

Exercise 19

((Reference)) 65 ⋅ 9865 ⋅ 98 size 12{"65 " cdot " 98"} {}

Solution

65(100−2)=6,500−130=6,37065(100−2)=6,500−130=6,370 size 12{"65" \( "100" - 2 \) =6,"500" - "130"=6,"370"} {}

Exercise 20

((Reference)) 80 ⋅ 10780 ⋅ 107 size 12{"80 " cdot " 107"} {}

Solution

80(100+7)=8,000+560=8,56080(100+7)=8,000+560=8,560 size 12{"80" \( "100"+7 \) =8,"000"+"560"=8,"560"} {}

Exercise 21

((Reference)) 400 ⋅ 215400 ⋅ 215 size 12{"400 " cdot " 215"} {}

Solution

400(200+15)=80,000+6,000=86,000400(200+15)=80,000+6,000=86,000 size 12{"400" \( "200"+"15" \) ="80","000"+6,"000"="86","000"} {}

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

Exercise 22

((Reference)) 1516+581516+58 size 12{ { {"15"} over {"16"} } + { {5} over {8} } } {}

Solution

1+12=1121+12=112 size 12{1+ { {1} over {2} } =1 { {1} over {2} } } {}19161916 size 12{ left (1 { {9} over {"16"} } right )} {}

Exercise 23

((Reference) ) 125+1120+1730125+1120+1730 size 12{ { {1} over {"25"} } + { {"11"} over {"20"} } + { {"17"} over {"30"} } } {}

Solution

0+12+12=10+12+12=1 size 12{0+ { {1} over {2} } + { {1} over {2} } =1} {}147300147300 size 12{ left (1 { {"47"} over {"300"} } right )} {}

Exercise 24

((Reference)) 8916+141128916+14112 size 12{8 { {9} over {"16"} } +"14" { {1} over {"12"} } } {}

Solution

812+14=2212812+14=2212 size 12{8 { {1} over {2} } +"14"="22" { {1} over {2} } } {}223148223148 size 12{ left ("22" { {"31"} over {"48"} } right )} {}

Exercise 25

((Reference)) 549+11736+6512549+11736+6512 size 12{5 { {4} over {9} } +1 { {"17"} over {"36"} } +6 { {5} over {"12"} } } {}

Solution

512+112+612=1312512+112+612=1312 size 12{5 { {1} over {2} } +1 { {1} over {2} } +6 { {1} over {2} } ="13" { {1} over {2} } } {}13131313 size 12{ left ("13" { {1} over {3} } right )} {}

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