Calculus - Solutions

HW Set 7 Section 2.1 47 م 1 a) ((26+83)+54=(26+54)+83=80+83=163) b) \((4\times34)\times25=(4\times25)\times34=100\times34=3400\) c) \[256\times6=(200+50+6)\times6=(200\times b)+(50\times b)+(b\times6)\] \[=1200+300+36=1536\] d) \(288\div24=(240+48)\div24=10+2=12\) e) \[44\times56+56^{2}=(44+56)\times56=100\times56=5~600\] f) \[4\circ2\times12=4\circ2\times(10+2)=(402\times10)+(4\circ2\times2)\] = 4020+ 804 = 4824 2 a) [123+326+4+77=200+330=530] b) \[2\times6\times7\times5=10\times42=420\] c) \(3200\times34\div16=\frac{3200}{16}\times34=200\times34=6800\) can be viewed as can be viewed as) ( b) 62-39 = 63-40 23 add I to both c) \[48\times25=12\times(4\times25)=12\times100=1200\] d) alternatively, each 100 is four 25's \[500\div25=100\div5=20\] ( divide both by 5 So 500+25 = 5 x 4 = 20 e) 71-42 = 69-40 29 Subtract 2 from both f) \[180\div15=360\div30=120\div10=12\] double both divide both both by by 3 3 5 a) [78\times9=78\times(io-i)=780-78=702] b) \[37\times4=74\times2=148\] c) \[136\div8=68\div4=34\div2=17\] (to divide by 8, you can halve three times; \[136\rightarrow68\rightarrow34\rightarrow(17)\] 3 [197+568=200+565=765] d) 1500 ÷ 25 = 6000 ÷ 100 = 60 multiply both by 4 (1500 ÷ 25 = 300 ÷ 5 = 60) alternatively divide both by 5 e) 1575 ÷ 25 = (1500 + 75) ÷ 25 = 60 + 3 = 63 from part d f) 325 ÷ 5 = 650 ÷ 10 = 65 double both 6 Classify as either PV (Mental Math developing Place Value) DP (Mental Math developing the Distributive Prop) X (Not appropriate for Mental Math) a) PV 37 + 99 = 36 + 100 = 136 b) PV 20 x 40 = 800 c) DP 7 x 102 = 7 x (100 + 2) = 700 + 14 = 714 d) X 13 x 28 e) PV 326 - 98 = 328 - 100 = 228 add 2 to both f) X 337 + 879 g) DP 119 ÷ 7 = (70 + 49) ÷ 7 = 10 + 7 = 17 h) DP 3 x 32 = 3 x (30 + 2) = 90 + 6 = 96