Class 6 Operations on whole Numbers Exercise 4.3-1

\begin{array}{l}\text {Q1. Fill in the blanks to make each of the following a true statement:} \\ (i) \quad 785 \times 0=\ldots \\ (ii) \quad 4567 \times 1=\ldots \\ (iii) \quad 475 \times 129=129 \times \ldots \\ (iv) \quad \ldots \ldots \times 8975=8975 \times 1243 \\ (v) \quad 10 \times 100 \times \ldots=10000 \\ (vi) \quad 27 \times 18=27 \times 9+27 \times \ldots +27 \times 5 \\ (vii) \quad 12 \times 45=12 \times 50-12 \times \ldots \\ (viii) \quad 78 \times 89=78 \times 100-78 \times \ldots + 78 \times 5 \\ (ix) \quad 66 \times 85=66 \times 90-66 \times \ldots – 66 \\ (x) \quad 49 \times 66+49 \times 34=49 \times(\ldots+ \ldots) \\ \\\text {Sol. } (i) \quad 785 \times 0=0 \\ (ii) \quad 4567 \times 1=4567 \quad \quad [\text {Based on Multiplicative identity}] \\(iii) \quad 475 \times 129=129 \times 475 \quad \quad [\text {Based on Commutativity}] \\(iv) \quad 1243 \times 8975=8975 \times 1243 \quad \quad [\text {Based on Commutativity}] \\(v) \quad 10 \times 100 \times 10=10000 \\(vi) \quad 27 \times 18 = 27 \times (9+4+5) \\ =27 \times 9+27 \times 4+27 \times 5 \\(vii) \quad 12 \times 45= 12 \times (50 -5) \\ =12 \times 50-12 \times 5 \\(viii) \quad 78 \times 89 = 78 \times (100 -16 +5)\\ =78 \times 100-78 \times 16+78 \times 5 \\(ix) \quad 66 \times 85 = 66 \times (90-4-1) \\ =66 \times 90-66 \times 4-66 \\(x) \quad 49 \times 66+49 \times 34=49 \times (66+34) \\ \\\text {Q2. Determine each of the following products by suitable rearrangements: } \\ (i) \quad 2 \times 1497 \times 50 \\ (ii) \quad 4 \times 358 \times 25 \\ (iii) \quad 495 \times 625 \times 16 \\ (iv) \quad 625 \times 20 \times 8 \times 50 \\ \\\text {Sol. } (i) \quad 2 \times 1497 \times 50 \\ =(2 \times 50) \times 1497 \\ =100 \times 1497 \\ =149700 \\ \\(ii) \quad 4 \times 358 \times 25 \\ =(4 \times 25) \times 358 \\ =100 \times 358 \\ =35800 \\ \\(iii) \quad 495 \times 625 \times 16 \\ =(625 \times 16) \times 495 \\ =10000 \times 495 \\ =4950000 \\ \\(iv) \quad 625 \times 20 \times 8 \times 50 \\ =(625 \times 8) \times (20 \times 50) \\ =5000 \times 1000 \\ =5000000 \\ \\\text {Q3. Using distributivity of multiplication over addition of whole numbers, } \\ \text {find each of the following products:} \\ (i) \quad 736 \times 103 \\ (ii) \quad 258 \times 1008 \\ (iii) \quad 258 \times 1008 \\ \\\text {Sol. } (i) \quad 736 \times 103 =736 \times (100+3) \\ =(736 \times 100)+(736 \times 3) \quad \quad [\text {Using distributivity}] \\ =73600+2208 =75808 \\ \\(ii) \quad 258 \times 1008 =258 \times (1000+8) \\ =(258 \times 1000)+(258 \times 8) \quad \quad [\text {Using distributivity}] \\ =258000+2064 =260064 \\ \\(iii) \quad 258 \times 1008 =258 \times (1000+8) \\ =(258 \times 1000)+(258 \times 8) \quad \quad [\text {Using distributivity}] \\ =258000+2064 =260064 \\ \\\text {Q4. Find each of the following products:} \\ (i) \quad 736 \times 93 \\ (ii) \quad 816 \times 745 \\ (iii) \quad 2032 \times 613 \\ \\\text {Sol. } (i) \quad 736 \times 93 =736 \times (100-7) \\ =(736 \times 100)-(736 \times 7) \quad \quad [\text {Using distributivity}] \\ =73600-5152 =68448 \\ \\(ii) \quad 816 \times 745 =816 \times (750-5) \\ =(816 \times 750)-(816 \times 5) \quad \quad [\text {Using distributivity}] \\ =612000-4080 =607920 \\ \\(iii) \quad 2032 \times 613 =2032 \times (600+13) \\ =(2032 \times 600)-(2032 \times 13) \quad \quad [\text {Using distributivity}] \\ =1219200-26416=1245616 \\ \\\text {Q5. Find the values of each of the following using properties:} \\ (i) \quad 493 \times 8+493 \times 2 \\ (ii) \quad 24579 \times 93+7 \times 24579 \\ (iii) \quad 1568 \times 184-1568 \times 84 \\ (iv) \quad 15625 \times 15625-15625 \times 5625 \\ \\\text {Sol. } (i) \quad 493 \times 8 + 493 \times 2 \\ =493 \times (8+2) \quad \quad [\text {Using distributivity}] \\ =493 \times 10 =4930 \\ \\(ii) \quad 24579 \times 93+7 \times 24579 \\ =24579 \times (93+7)\quad \quad [\text {Using distributivity}] \\ =24579 \times 100 =2457900 \\ \\(iii) \quad 1568 \times 184 – 1568 \times 84 \\ =1568 \times(184-84) \quad \quad [\text {Using distributivity}] \\ =1568 \times 100 =156800 \\ \\(iv) \quad 15625 \times 15625- 15625 \times 5625 \\ =15625 \times (15625-5625) \quad \quad [\text {Using distributivity}] \\ =15625 \times 10000 =156250000 \\ \\\text {Q6. Determine the product of:} \\ \text {(i) the greatest number of four digits and the smallest number of three digits.} \\ \text {(ii) the greatest number of five digits and the greatest number of three digits.} \\ \\\text {Sol (i) We know that greatest four digit number } =9999 \\ \text {And, the smallest three digit number } =100 \\ \therefore \text {Product of the greatest four-digit number and the smallest three-digit number} \\ =9999 \times 100 =999900 \\ \\\text {(ii) We know that the greatest five digit number } =99999 \\ \text {And, greatest three digit number }=999 \\ \therefore \text {Product of the greatest five-digit number and the greatest three-digit number} \\ =99999 \times 999 \\ =99999 \times (1000 – 1) \\ =(99999 \times 1000)-(99999 \times 1) \quad \quad [\text {Using distributivity}] \\ =99999000-99999\\ =99899001 \\ \end{array}