# 8.6 Exercise supplement

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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.

## 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.

$\text{286}+\text{312}$

600 (598)

$\text{419}+\text{582}$

$\text{689}+\text{511}$

(1,200)

$\text{926}+1,\text{105}$

$1,\text{927}+3,\text{017}$

4,900 (4,944)

$5,\text{026}+2,\text{814}$

$1,\text{408}+2,\text{352}$

3,800 (3,760)

$1,\text{186}+4,\text{228}$

$5,\text{771}+\text{246}$

6,050 (6,017)

$8,\text{305}+\text{484}$

$3,\text{812}+2,\text{906}$

6,700 (6,718)

$5,\text{293}+8,\text{007}$

$\text{28},\text{481}+\text{32},\text{856}$

61,400 (61,337)

$\text{92},\text{512}+\text{26},\text{071}$

$\text{87},\text{612}+2,\text{106}$

89,700 (89,718)

$\text{42},\text{612}+4,\text{861}$

$\text{212},\text{413}+\text{609}$

213,000 (213,022)

$\text{487},\text{235}+\text{494}$

$2,\text{409}+1,\text{526}$

3,900 (3,935)

$3,\text{704}+4,\text{704}$

$\text{41}\cdot \text{63}$

2,400 (2,583)

$\text{38}\cdot \text{81}$

$\text{18}\cdot \text{28}$

600 (504)

$\text{52}\cdot \text{21}$

$\text{307}\cdot \text{489}$

150,123 147,000 (150,123)

$\text{412}\cdot \text{807}$

$\text{77}\cdot \text{614}$

47,278 48,000 (47,278)

$\text{62}\cdot \text{596}$

$\text{27}\cdot \text{473}$

12,771 14,100 (12,711)

$\text{92}\cdot \text{336}$

$\text{12}\cdot \text{814}$

8,100 (9,768)

$8\cdot 2,\text{106}$

$\text{192}\cdot \text{452}$

90,000 (86,784)

$\text{374}\cdot \text{816}$

$\text{88}\cdot 4,\text{392}$

396,000 (386,496)

$\text{126}\cdot 2,\text{834}$

$3,\text{896}\cdot \text{413}$

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

$5,\text{794}\cdot \text{837}$

$6,\text{311}\cdot 3,\text{512}$

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

$7,\text{471}\cdot 5,\text{782}$

$\text{180}÷\text{12}$

18 (15)

$\text{309}÷\text{16}$

$\text{286}÷\text{22}$

$\text{14}\frac{1}{2}$ (13)

$\text{527}÷\text{17}$

$1,\text{007}÷\text{19}$

50 (53)

$1,\text{728}÷\text{36}$

$2,\text{703}÷\text{53}$

54 (51)

$2,\text{562}÷\text{61}$

$1,\text{260}÷\text{12}$

130 (105)

$3,\text{618}÷\text{18}$

$3,\text{344}÷\text{76}$

41.25 (44)

$7,\text{476}÷\text{356}$

$\text{20},\text{984}÷\text{488}$

42 (43)

$\text{43},\text{776}÷\text{608}$

$7,\text{196}÷\text{514}$

14.4 (14)

$\text{51},\text{492}÷\text{514}$

$\text{26},\text{962}÷\text{442}$

60 (61)

$\text{33},\text{712}÷\text{112}$

$\text{105},\text{152}÷\text{106}$

1,000 (992)

$\text{176},\text{978}÷\text{214}$

$\text{48}\text{.}\text{06}+\text{23}\text{.}\text{11}$

71.1 (71.17)

$\text{73}\text{.}\text{73}+\text{72}\text{.}9$

$\text{62}\text{.}\text{91}+\text{56}\text{.}4$

119.4 (119.31)

$\text{87}\text{.}\text{865}+\text{46}\text{.}\text{772}$

$\text{174}\text{.}6+\text{97}\text{.}2$

272 (271.8)

$\left(\text{48}\text{.}3\right)\left(\text{29}\text{.}6\right)$

$\left(\text{87}\text{.}\text{11}\right)\left(\text{23}\text{.}2\right)$

2,001 (2,020.952)

$\left(\text{107}\text{.}\text{02}\right)\left(\text{48}\text{.}7\right)$

$\left(0\text{.}\text{76}\right)\left(5\text{.}\text{21}\right)$

4.16 (3.9596)

$\left(1\text{.}\text{07}\right)\left(\text{13}\text{.}\text{89}\right)$

## 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.

$\text{38}+\text{51}+\text{41}+\text{48}$

$2\left(\text{40}\right)+2\left(\text{50}\right)=\text{180}$ (178)

$\text{19}+\text{73}+\text{23}+\text{71}$

$\text{27}+\text{62}+\text{59}+\text{31}$

$2\left(\text{30}\right)+2\left(\text{60}\right)=\text{180}$ (179)

$\text{18}+\text{73}+\text{69}+\text{19}$

$\text{83}+\text{49}+\text{79}+\text{52}$

$2\left(\text{80}\right)+2\left(\text{50}\right)=\text{260}$ (263)

$\text{67}+\text{71}+\text{84}+\text{81}$

$\text{16}+\text{13}+\text{24}+\text{26}$

$3\left(\text{20}\right)+1\left(\text{10}\right)=\text{70}$ (79)

$\text{34}+\text{56}+\text{36}+\text{55}$

$\text{14}+\text{17}+\text{83}+\text{87}$

$2\left(\text{15}\right)+2\left(\text{80}\right)=\text{190}$ (201)

$\text{93}+\text{108}+\text{96}+\text{111}$

$\text{18}+\text{20}+\text{31}+\text{29}+\text{24}+\text{38}$

$3\left(\text{20}\right)+2\left(\text{30}\right)+\text{40}=\text{160}$ (160)

$\text{32}+\text{27}+\text{48}+\text{51}+\text{72}+\text{69}$

$\text{64}+\text{17}+\text{27}+\text{59}+\text{31}+\text{21}$

$2\left(\text{60}\right)+2\left(\text{20}\right)+2\left(\text{30}\right)=\text{220}$ (219)

$\text{81}+\text{41}+\text{92}+\text{38}+\text{88}+\text{80}$

$\text{87}+\text{22}+\text{91}$

$2\left(\text{90}\right)+\text{20}=\text{200}$ (200)

$\text{44}+\text{38}+\text{87}$

$\text{19}+\text{18}+\text{39}+\text{22}+\text{42}$

$3\left(\text{20}\right)+2\left(\text{40}\right)=\text{140}$ (140)

$\text{31}+\text{28}+\text{49}+\text{29}$

$\text{88}+\text{86}+\text{27}+\text{91}+\text{29}$

$3\left(\text{90}\right)+2\left(\text{30}\right)=\text{330}$ (321)

$\text{57}+\text{62}+\text{18}+\text{23}+\text{61}+\text{21}$

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

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

$\text{15}\cdot \text{33}$

$\text{15}\left(\text{30}+3\right)=\text{450}+\text{45}=\text{495}$

$\text{15}\cdot \text{42}$

$\text{35}\cdot \text{36}$

$\text{35}\left(\text{40}-4\right)=\text{1400}-\text{140}=1,\text{260}$

$\text{35}\cdot \text{28}$

$\text{85}\cdot \text{23}$

$\text{85}\left(\text{20}+3\right)=1,\text{700}+\text{225}=1,\text{955}$

$\text{95}\cdot \text{11}$

$\text{30}\cdot \text{14}$

$\text{30}\left(\text{10}+4\right)=\text{300}+\text{120}=\text{420}$

$\text{60}\cdot \text{18}$

$\text{75}\cdot \text{23}$

$\text{75}\left(\text{20}+3\right)=1,\text{500}+\text{225}=1,\text{725}$

$\text{65}\cdot \text{31}$

$\text{17}\cdot \text{15}$

$\text{15}\left(\text{20}-3\right)=\text{300}-\text{45}=\text{255}$

$\text{38}\cdot \text{25}$

$\text{14}\cdot \text{65}$

$\text{65}\left(\text{10}+4\right)=\text{650}+\text{260}=\text{910}$

$\text{19}\cdot \text{85}$

$\text{42}\cdot \text{60}$

$\text{60}\left(\text{40}+2\right)=2,\text{400}+\text{120}=2,\text{520}$

$\text{81}\cdot \text{40}$

$\text{15}\cdot \text{105}$

$\text{15}\left(\text{100}+5\right)=1,\text{500}+\text{75}=1,\text{575}$

$\text{35}\cdot \text{202}$

$\text{45}\cdot \text{306}$

$\text{45}\left(\text{300}+6\right)=\text{13},\text{500}+\text{270}=\text{13},\text{770}$

$\text{85}\cdot \text{97}$

## 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.

$\frac{3}{8}+\frac{5}{6}$

$\frac{1}{2}+1=1\frac{1}{2}\left(1\frac{5}{\text{24}}\right)$

$\frac{7}{\text{16}}+\frac{1}{\text{24}}$

$\frac{7}{\text{15}}+\frac{\text{13}}{\text{30}}$

$\frac{\text{14}}{\text{15}}+\frac{\text{19}}{\text{20}}$

$\frac{\text{13}}{\text{25}}+\frac{7}{\text{30}}$

$\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\left(\frac{\text{113}}{\text{150}}\right)$

$\frac{\text{11}}{\text{12}}+\frac{7}{8}$

$\frac{9}{\text{32}}+\frac{\text{15}}{\text{16}}$

$\frac{5}{8}+\frac{1}{\text{32}}$

$2\frac{3}{4}+6\frac{3}{5}$

$2\frac{3}{4}+6\frac{1}{2}=9\frac{1}{4}\left(9\frac{7}{\text{20}}\right)$

$4\frac{5}{9}+8\frac{1}{\text{27}}$

$\text{11}\frac{5}{\text{18}}+7\frac{\text{22}}{\text{45}}$

$\text{11}\frac{1}{4}+7\frac{1}{2}=\text{18}\frac{3}{4}\left(\text{18}\frac{\text{23}}{\text{30}}\right)$

$\text{14}\frac{\text{19}}{\text{36}}+2\frac{7}{\text{18}}$

$6\frac{1}{\text{20}}+2\frac{1}{\text{10}}+8\frac{\text{13}}{\text{60}}$

$6+2+8\frac{1}{4}=\text{16}\frac{1}{4}\left(\text{16}\frac{\text{11}}{\text{30}}\right)$

$5\frac{7}{8}+1\frac{1}{4}+\text{12}\frac{5}{\text{12}}$

$\text{10}\frac{1}{2}+6\frac{\text{15}}{\text{16}}+8\frac{\text{19}}{\text{80}}$

$\text{10}\frac{1}{2}+7+8\frac{1}{4}=\text{25}\frac{3}{4}\left(\text{25}\frac{\text{27}}{\text{40}}\right)$

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Damian
yes that's correct
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I think
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The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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research.net
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sciencedirect big data base
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