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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.
$\text{419}+\text{582}$
$\text{926}+\mathrm{1,}\text{105}$
$\mathrm{5,}\text{026}+\mathrm{2,}\text{814}$
$\mathrm{1,}\text{186}+\mathrm{4,}\text{228}$
$\mathrm{8,}\text{305}+\text{484}$
$\mathrm{5,}\text{293}+\mathrm{8,}\text{007}$
$\text{92},\text{512}+\text{26},\text{071}$
$\text{87},\text{612}+\mathrm{2,}\text{106}$
89,700 (89,718)
$\text{42},\text{612}+\mathrm{4,}\text{861}$
$\text{487},\text{235}+\text{494}$
$\mathrm{3,}\text{704}+\mathrm{4,}\text{704}$
$\text{38}\cdot \text{81}$
$\text{52}\cdot \text{21}$
$\text{412}\cdot \text{807}$
$\text{62}\cdot \text{596}$
$\text{92}\cdot \text{336}$
$8\cdot \mathrm{2,}\text{106}$
$\text{374}\cdot \text{816}$
$\text{126}\cdot \mathrm{2,}\text{834}$
$\mathrm{3,}\text{896}\cdot \text{413}$
1,609,048 1,560,000 (1,609,048)
$\mathrm{5,}\text{794}\cdot \text{837}$
$\mathrm{6,}\text{311}\cdot \mathrm{3,}\text{512}$
22,050,000 (22,164,232)
$\mathrm{7,}\text{471}\cdot \mathrm{5,}\text{782}$
$\text{309}\xf7\text{16}$
$\text{527}\xf7\text{17}$
$\mathrm{1,}\text{728}\xf7\text{36}$
$\mathrm{2,}\text{562}\xf7\text{61}$
$\mathrm{3,}\text{618}\xf7\text{18}$
$\mathrm{7,}\text{476}\xf7\text{356}$
$\text{43},\text{776}\xf7\text{608}$
$\text{51},\text{492}\xf7\text{514}$
$\text{33},\text{712}\xf7\text{112}$
$\text{176},\text{978}\xf7\text{214}$
$\text{48}\text{.}\text{06}+\text{23}\text{.}\text{11}$
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)
$\text{87}\text{.}\text{865}+\text{46}\text{.}\text{772}$
$(\text{48}\text{.}3)(\text{29}\text{.}6)$
$(\text{87}\text{.}\text{11})(\text{23}\text{.}2)$
2,001 (2,020.952)
$(\text{107}\text{.}\text{02})(\text{48}\text{.}7)$
$(1\text{.}\text{07})(\text{13}\text{.}\text{89})$
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.
$\text{38}+\text{51}+\text{41}+\text{48}$
$2(\text{40})+2(\text{50})=\text{180}$ (178)
$\text{19}+\text{73}+\text{23}+\text{71}$
$\text{27}+\text{62}+\text{59}+\text{31}$
$2(\text{30})+2(\text{60})=\text{180}$ (179)
$\text{18}+\text{73}+\text{69}+\text{19}$
$\text{83}+\text{49}+\text{79}+\text{52}$
$2(\text{80})+2(\text{50})=\text{260}$ (263)
$\text{67}+\text{71}+\text{84}+\text{81}$
$\text{16}+\text{13}+\text{24}+\text{26}$
$3(\text{20})+1(\text{10})=\text{70}$ (79)
$\text{34}+\text{56}+\text{36}+\text{55}$
$\text{14}+\text{17}+\text{83}+\text{87}$
$2(\text{15})+2(\text{80})=\text{190}$ (201)
$\text{93}+\text{108}+\text{96}+\text{111}$
$\text{18}+\text{20}+\text{31}+\text{29}+\text{24}+\text{38}$
$3(\text{20})+2(\text{30})+\text{40}=\text{160}$ (160)
$\text{32}+\text{27}+\text{48}+\text{51}+\text{72}+\text{69}$
$\text{64}+\text{17}+\text{27}+\text{59}+\text{31}+\text{21}$
$2(\text{60})+2(\text{20})+2(\text{30})=\text{220}$ (219)
$\text{81}+\text{41}+\text{92}+\text{38}+\text{88}+\text{80}$
$\text{87}+\text{22}+\text{91}$
$2(\text{90})+\text{20}=\text{200}$ (200)
$\text{44}+\text{38}+\text{87}$
$\text{19}+\text{18}+\text{39}+\text{22}+\text{42}$
$3(\text{20})+2(\text{40})=\text{140}$ (140)
$\text{31}+\text{28}+\text{49}+\text{29}$
$\text{88}+\text{86}+\text{27}+\text{91}+\text{29}$
$3(\text{90})+2(\text{30})=\text{330}$ (321)
$\text{57}+\text{62}+\text{18}+\text{23}+\text{61}+\text{21}$
For problems 91-110, compute each product using the distributive property.
$\text{15}\cdot \text{33}$
$\text{15}(\text{30}+3)=\text{450}+\text{45}=\text{495}$
$\text{15}\cdot \text{42}$
$\text{35}\cdot \text{36}$
$\text{35}(\text{40}-4)=\text{1400}-\text{140}=\mathrm{1,}\text{260}$
$\text{35}\cdot \text{28}$
$\text{85}\cdot \text{23}$
$\text{85}(\text{20}+3)=\mathrm{1,}\text{700}+\text{225}=\mathrm{1,}\text{955}$
$\text{95}\cdot \text{11}$
$\text{30}\cdot \text{14}$
$\text{30}(\text{10}+4)=\text{300}+\text{120}=\text{420}$
$\text{60}\cdot \text{18}$
$\text{75}\cdot \text{23}$
$\text{75}(\text{20}+3)=\mathrm{1,}\text{500}+\text{225}=\mathrm{1,}\text{725}$
$\text{65}\cdot \text{31}$
$\text{17}\cdot \text{15}$
$\text{15}(\text{20}-3)=\text{300}-\text{45}=\text{255}$
$\text{38}\cdot \text{25}$
$\text{14}\cdot \text{65}$
$\text{65}(\text{10}+4)=\text{650}+\text{260}=\text{910}$
$\text{19}\cdot \text{85}$
$\text{42}\cdot \text{60}$
$\text{60}(\text{40}+2)=\mathrm{2,}\text{400}+\text{120}=\mathrm{2,}\text{520}$
$\text{81}\cdot \text{40}$
$\text{15}\cdot \text{105}$
$\text{15}(\text{100}+5)=\mathrm{1,}\text{500}+\text{75}=\mathrm{1,}\text{575}$
$\text{35}\cdot \text{202}$
$\text{45}\cdot \text{306}$
$\text{45}(\text{300}+6)=\text{13},\text{500}+\text{270}=\text{13},\text{770}$
$\text{85}\cdot \text{97}$
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.
$\frac{3}{8}+\frac{5}{6}$
$\frac{1}{2}+1=1\frac{1}{2}\left(1\frac{5}{\text{24}}\right)$
$\frac{7}{\text{16}}+\frac{1}{\text{24}}$
$\frac{7}{\text{15}}+\frac{\text{13}}{\text{30}}$
$\frac{1}{2}+\frac{1}{2}=1\left(\frac{\text{27}}{\text{30}}\text{or}\frac{9}{\text{10}}\right)$
$\frac{\text{14}}{\text{15}}+\frac{\text{19}}{\text{20}}$
$\frac{\text{13}}{\text{25}}+\frac{7}{\text{30}}$
$\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\left(\frac{\text{113}}{\text{150}}\right)$
$\frac{\text{11}}{\text{12}}+\frac{7}{8}$
$\frac{9}{\text{32}}+\frac{\text{15}}{\text{16}}$
$\frac{1}{4}+1=1\frac{1}{4}\left(\frac{\text{39}}{\text{32}}\text{or}1\frac{7}{\text{32}}\right)$
$\frac{5}{8}+\frac{1}{\text{32}}$
$2\frac{3}{4}+6\frac{3}{5}$
$2\frac{3}{4}+6\frac{1}{2}=9\frac{1}{4}\left(9\frac{7}{\text{20}}\right)$
$4\frac{5}{9}+8\frac{1}{\text{27}}$
$\text{11}\frac{5}{\text{18}}+7\frac{\text{22}}{\text{45}}$
$\text{11}\frac{1}{4}+7\frac{1}{2}=\text{18}\frac{3}{4}\left(\text{18}\frac{\text{23}}{\text{30}}\right)$
$\text{14}\frac{\text{19}}{\text{36}}+2\frac{7}{\text{18}}$
$6\frac{1}{\text{20}}+2\frac{1}{\text{10}}+8\frac{\text{13}}{\text{60}}$
$6+2+8\frac{1}{4}=\text{16}\frac{1}{4}\left(\text{16}\frac{\text{11}}{\text{30}}\right)$
$5\frac{7}{8}+1\frac{1}{4}+\text{12}\frac{5}{\text{12}}$
$\text{10}\frac{1}{2}+6\frac{\text{15}}{\text{16}}+8\frac{\text{19}}{\text{80}}$
$\text{10}\frac{1}{2}+7+8\frac{1}{4}=\text{25}\frac{3}{4}\left(\text{25}\frac{\text{27}}{\text{40}}\right)$
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