EXERCISE-3D
Question 1
Q.1. Fill in the blanks to make each of the following a true statement :
(i) $246 \times 1=$ .....
(ii) $1369 \times 0=$ .......
(iii) $593 \times 188=188 \times$ .....
(iv) $286 \times 753=$ ........ $\times 286$
(v) $38 \times(91 \times 37)=$ ........ $\times(38 \times 37)$
(vi) $13 \times 100 \times$ ........ $=1300000$
(vii) $59 \times 66+59 \times 34=59 \times 1$ ....... + .......
(viii) $68 \times 95=68 \times 100-68 \times$ ......
Ans. (i) $246 \times 1=246$
(By multiplicative property of 1 )
(ii) $1369 \times 0=0$
(By multiplicative property of 0 )
(iii) $593 \times 188=188 \times 593$
(By commutative law of multiplicaton)
(iv) $286 \times 753=753 \times 286$
(By commutative law of multiplication)
(v) $38 \times(91 \times 37)=91 \times(38 \times 37)$
(By associative law of multiplication)
(vi) $13 \times 100 \times 1000=1300000$
(vii) $59 \times 66+59 \times 34=59 \times(66+34)$
(By distributive law of multiplication)
(viii) $68 \times 95=68 \times 100-68 \times 5$
Question 2
(i) $19 \times 17=17 \times 19$
(ii) $16 \times 32$ is a whole number
(iii) $(29 \times 36) \times 18=29 \times(36 \times 18)$
(iv) $1480 \times 1=1480$
(v) $1732 \times 0=0$
(vi) $72 \times 98+72 \times 2=72 \times(98+2)$
(vii) $63 \times 126-63 \times 26=63 \times(126-26)$
Ans. (i) Commutative law of multiplication
(ii) Closure property
(iii) Associative law of multiplication
(iv) Multiplicative property of 1
(v) Multiplicative property of 0
(vi) Distributive law of multiplication over addition in whole numbers
(vii) Distributive law of multiplication over subtraction in whole numbers
Question 3
(i) $647 \times 13+647 \times 7$
(ii) $8759 \times 94+8759 \times 6$
(iii) $7459 \times 999+7459$
(iv) $9870 \times 561-9870 \times 461$
(v) $569 \times 17+569 \times 13+569 \times 70$
(vi) $16825 \times 16825-16825 \times 6825$
Ans.
$\begin{aligned}
& \text { (i) } 647 \times 13+647 \times 7 \\
& =647 \times(13+7)=647 \times 20 \\
& =12940
\end{aligned}$
$\begin{aligned}
& \text { (ii) } 8759 \times 94+8759 \times 6 \\
& =8759 \times(94+6)=8759 \times 100 \\
& =875900
\end{aligned}$
$\begin{aligned}
& \text { (iii) } 7459 \times 999+7459 \\
& =7459 \times 999+7459 \times 1 \\
& =7459 \times(999+1)=7459 \times 1000 \\
& =7459000
\end{aligned}$
\begin{aligned}
& \text { (iv) } 9870 \times 561-9870 \times 461 \\
& =9870 \times(561-461)=9870 \times 100 \\
& =987000
\end{aligned}$
$\begin{aligned}
& \text { (v) } 569 \times 17+569 \times 13+569 \times 70 \\
& =569 \times(17+13+70)=569 \times 100 \\
& =56900
\end{aligned}$
$\begin{aligned}
& \text { (vi) } 16825 \times 16825-16825 \times 6825 \\
& =16825 \times(16825-6825) \\
& =16825 \times 10000=168250000
\end{aligned}$
Question 4
(i) $2 \times 1658 \times 50$
(ii) $4 \times 927 \times 25$
(iii) $625 \times 20 \times 8 \times 50$
(iv) $574 \times 625 \times 16$
(v) $250 \times 60 \times 50 \times 8$
(vi) $8 \times 125 \times 40 \times 25$
Ans.
(i) $2 \times 1658 \times 50=1658 \times(2 \times 50)$
(Associative law of multiplication)
$1658 \times 100=165800$
(ii) $4 \times 927 \times 25=927 \times(4 \times 25)$
(Associative law of multiplication)
$=927 \times 100=92700$
(iii) $625 \times 20 \times 8 \times 50$
(By associative law of multiplication)
$\begin{aligned}
& (625 \times 8) \times(20 \times 50) \\
& =5000 \times 1000=5000000
\end{aligned}$
(iv) $574 \times(625 \times 16)$
$=574 \times 10000=5740000$
(v) $250 \times 60 \times 50 \times 8$
$=(250 \times 8) \times(60 \times 50)$
(By associative law)
$=2000 \times 3000=6000000$
(vi) $8 \times 125 \times 40 \times 25$
$\begin{aligned}
& =(8 \times 125) \times(40 \times 25) \\
& =1000 \times 1000=1000000
\end{aligned}$
Question 5
distributive laws:
(i) $740 \times 105$
(ii) $245 \times 1008$
(iii) $947 \times 96$
(iv) $996 \times 367$
(v) $472 \times 1097$
(vi) $580 \times 64$
(vii) $439 \times 997$
(viii) $1553 \times 198$
Ans.
$\begin{aligned}
& \text { (i) } 740 \times 105=740 \times(100+5) \\
& =740 \times 100+740 \times 5 \\
& =74000+3700=77700
\end{aligned}$
$\begin{aligned}
& \text { (ii) } 245 \times 1008=245 \times(1000+8) \\
& =245 \times 1000+245 \times 8 \\
& =245000+1960=246960
\end{aligned}$
$\begin{aligned}
& \text { (iii) } 947 \times 96=947 \times(100-4) \\
& =947 \times 100-947 \times 4 \\
& =94700-3788=90912
\end{aligned}$
$\begin{aligned}
& \text { (iv) } 996 \times 367=367 \times(1000-4) \\
& =367 \times 1000-367 \times 4 \\
& =367000-1468=365532 \\
& \text { (v) } 472 \times 1097=472 \times(1100-3) \\
& =472 \times 1100-472 \times 3 \\
& =519200-1416=517784
\end{aligned}$
$\begin{aligned} & \text { (vi) } 580 \times 64=580 \times(60+4) \\ & =580 \times 60+580 \times 4 \\ & =34800+2320=37120 \\ & \text { (vii) } 439 \times 997=437 \times(1000-3) \\ & =439 \times 1000-439 \times 3 \\ & =439000-1317=437683 \\ & \text { (viii) } 1553 \times 198=1553 \times(200-2) \\ & =1553 \times 200-1553 \times 2 \\ & =310600-3106=307494\end{aligned}$
Question 6
Q.6. Find each of the following products, using distributive laws :
(i) $3576 \times 9$
(ii) $847 \times 99$
(iii) $2437 \times 999$
Ans. (i) $3576 \times 9=3576 \times(10-1)$
$\begin{aligned}
& =3576 \times 10-3576 \times 1 \\
& =35760-3576=32184
\end{aligned}$
$\begin{aligned}
& \text { (ii) } 847 \times 99=84 \times(100-1) \\
& =847 \times 100-847 \times 1 \\
& =84700-847=83853
\end{aligned}$
$\begin{aligned}
& \text { (iii) } 2437 \times 999=2437 \times(1000-1) \\
& =2437 \times 1000-2437 \times 1 \\
& =2437000-2437=2434563
\end{aligned}$
Question 6
(i) $3576 \times 9$
(ii) $847 \times 99$
(iii) $2437 \times 999$
Ans. (i) $3576 \times 9=3576 \times(10-1)$
$\begin{aligned}
& =3576 \times 10-3576 \times 1 \\
& =35760-3576=32184
\end{aligned}$
$\begin{aligned}
& \text { (ii) } 847 \times 99=84 \times(100-1) \\
& =847 \times 100-847 \times 1 \\
& =84700-847=83853
\end{aligned}$
$\begin{aligned}
& \text { (iii) } 2437 \times 999=2437 \times(1000-1) \\
& =2437 \times 1000-2437 \times 1 \\
& =2437000-2437=2434563
\end{aligned}$
Question 7
(i) $\begin{gathered}458 \\ \times 67 \\ \text { (ii) } 3709\end{gathered}$
(ii) $\begin{array}{r}3709 \\ \times 89 \\ \hline 4617\end{array}$
(iii) $\frac{\times 234}{\times 15208}$
(iv) $\begin{array}{r}15208 \\ \times 542 \\ \hline\end{array}$
Ans.
(i) $\begin{array}{r} 458 \\ \times 67 \\ \hline 3206 \\ 27480 \\ \hline 30686 \\ \hline \end{array}$
(ii) $\begin{array}{r} 3709 \\ \times 89 \\ \hline 33381 \\ 296720 \\ \hline 330101 \\ \hline \end{array}$
(iii) $\begin{array}{r}4617 \\ \times 234 \\ \hline 18468 \\ 138510 \\ 923400 \\ \hline 1080378 \\ \hline\end{array}$
(iv) $\begin{array}{r} 15208 \\ \times 542 \\ \hline 30416 \\ 608320 \\ 7604000 \\ \hline 8242736 \\ \hline \end{array}$
Question 8
Ans. Largest 3-digit number $=999$
Largest 5-digit number $=99999$
$\begin{aligned} & \text { Required product }=99999 \times 999 \\ & =99999 \times(1000-1) \\ & =99999 \times 1000-99999 \times 1 \\ & =99999000-99999 \\ & =9,98,99,001 \end{aligned}$
Question 9
Ans.
Speed of car $=75 \mathrm{~km}$ per hour
In 1 hour, distance covered by a car $=75 \mathrm{~km}$
$\therefore$ In 98 hours, distance will be covered
$\begin{aligned} & =75 \times 98 \\ & =75 \times(100-2)=75 \times 100-75 \times 2 \\ & =7500-150=7350 \mathrm{~km} \end{aligned}$
In 1 hour, distance covered by a car $=75 \mathrm{~km}$
$\therefore$ In 98 hours, distance will be covered
$\begin{aligned} & =75 \times 98 \\ & =75 \times(100-2)=75 \times 100-75 \times 2 \\ & =7500-150=7350 \mathrm{~km} \end{aligned}$
Question 10
Ans.
Cost of 1 set of VCR = Rs. 24350
Cost of 139 sets of VCR
$\begin{aligned} & \text { =Rs. } 24350 \times 139=\text { Rs. } 3384650 \\ & \begin{array}{r} 24350 \\ \times 139 \\ \hline 219150 \end{array} \\ & 730500 \\ & \frac{2435000}{3384650} \end{aligned}$
Question 11
Ans.
Cost of 1 house = Rs. 450000
Cost of 197 houses $=$ Rs. $450000 \times 197$
$\begin{aligned} & =\text { Rs. } 450000 \times(200-3) \\ & =\text { Rs. }(450000 \times 200-450000 \times 3) \\ & =\text { Rs. }(90000000-1350000)=\text { Rs. } 88650000 \end{aligned}$
Question 12
Ans.
Cost of each chair $=$ Rs. 1065
$\therefore$ Cost of 50 chairs $=$ Rs. $1065 \times 50$
$=$ Rs. 53250
Cost of each blackboard = Rs. 1645
$\therefore$ Cost of 30 blackboards $=$ Rs. $1645 \times 30$
$=$ Rs. 49350
Total cost of 50 chairs and 30 blackboards
$=\text { Rs. } 53250+49350=\text { Rs. } 102600$
Question 13
Ans. Number of students in 1 section $=45$
$\therefore$ Number of students in 6 sections
$=45 \times 6=270$
Monthly charges of 1 student $=$ Rs. 1650
$\therefore$ Total monthly incomes from the class VI
$=$ Rs. $270 \times 1650$
$=$ Rs. $(300-30) \times 1650$
$=$ Rs. $(1650 \times 300-1650 \times 30)$
$=$ Rs. $(495000-49500)=$ Rs. 445500
Question 14
Q.14. The product of two whole numbers is zero. What do you conclude?
Ans. Since the product of two whole numbers is zero
$\therefore$ From multiplicative property of zero, we conclude that one of the whole numbers is zero.
Question 15
Q.15. Fill in the blanks:
(i) Sum of two odd numbers is an ...... number.
(ii) Product of two odd numbers is an ...... number.
(iii) $a \times a=a \Rightarrow a=$ ?
Ans. (i) Sum of two odd numbers is an even number.
(ii) Product of two odd numbers is an odd number.
(iii) $a \times a=a \Rightarrow a=1$ as $1 \times 1=1$
$\therefore$ Number of students in 6 sections
$=45 \times 6=270$
Monthly charges of 1 student $=$ Rs. 1650
$\therefore$ Total monthly incomes from the class VI
$=$ Rs. $270 \times 1650$
$=$ Rs. $(300-30) \times 1650$
$=$ Rs. $(1650 \times 300-1650 \times 30)$
$=$ Rs. $(495000-49500)=$ Rs. 445500
Question 14
Ans. Since the product of two whole numbers is zero
$\therefore$ From multiplicative property of zero, we conclude that one of the whole numbers is zero.
Question 15
(i) Sum of two odd numbers is an ...... number.
(ii) Product of two odd numbers is an ...... number.
(iii) $a \times a=a \Rightarrow a=$ ?
Ans. (i) Sum of two odd numbers is an even number.
(ii) Product of two odd numbers is an odd number.
(iii) $a \times a=a \Rightarrow a=1$ as $1 \times 1=1$
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