Class 6 Operations on whole Numbers Exercise 4.1

\begin{array}{l} \text {Q1. Fill in the blanks to make each of the following a true statement:} \\ (i) \quad 359+476=476 +\ldots \\ (ii) \quad \ldots +1952=1952+2008 \\ (iii) \quad 90758+0=\ldots \\ (iv) \quad 54321+(489+699)=489+(54321+\ldots \ldots) \\ \\\text {Sol. (i) } \quad 359+476=476+359 \quad \quad [\text {Using commutativity}] \\ (ii) \quad 2008+1952=1952+2008 \quad \quad [\text {Using commutativity}] \\ (iii) \quad 90758+0=90758 \quad \quad [\text {Using additive identity}] \\ (iv) \quad 54321+(489+699)=489+(54321+699) \quad \quad [\text {Using associativity}] \\ \\\text {Q2. Add each of the following and check by reversing the order of addends: } \\ (i) \quad 5628+39784 \\ (ii) \quad 923584+178 \\ (iii) \quad 15409+112 \\ (iv) \quad 2359+641 \\ \\\text {Sol. (i) } \quad 5628+39784=45412 \\ \text {By reversing the order of addends } \quad 39784+5628=45412 \\ (ii) \quad 923584+178 =923762 \\ \text {By reversing the order of addends } \quad 178+923584=923762 \\ (iii) \quad 15409+112=15521 \\ \text {By reversing the order of addends } \quad 112+15409=15521 \\ (iv) \quad 2359+641 =3000 \\ \text {By reversing the order of addends} \quad 641+2359=3000 \\ \\\text {Q3. Determine the sum by suitable rearrangements:} \\ (i) \quad 953+407+647 \\ (ii) \quad 15409+178+591+322 \\ (iii) \quad 2359+10001+2641+9999 \\ (iv) \quad 1+2+3+4+1996+1997+1998+1999 \\ (v) \quad 10+11+12+13+14+15+16+17+18+19+20 \\ \\\text {sol. (i) } \quad 953+407+647 \\ \text {We know that } \quad 53+47=100 \\ \Rightarrow 953+407+647 = (953+647)+407 \\ =1600+407 \\ =2007 \\ \\(ii) \quad 15409+178+591+322 \\ \text {We know that } \quad 409+91=500 \text { and } 78+22=100 \\ \Rightarrow 15409+178+591+322 = (15409+591)+(178+322) \\ =16000+500 \\ =16500 \\ \\(iii) \quad 2359+10001+2641+9999 \\ \text {We know that } \quad 59+41=100 \text { and } 99 + 1=100 \\\Rightarrow 2359+10001+2641+9999 = (2359+2641)+(10001+9999) \\ =5000+20000 \\ =25000 \\ \\(iv) \quad 1+2+3+4+1996+1997+1998+1999 \\ \text {We know that } \quad 99+1=100, 98+2=100, 97+3=100 \text { and } 96+4=100 \\\Rightarrow 1+2+3+4+1996+1997+1998+1999 \\ = (1+1999)+(2+1998)+(3+1997)+(4+1996) \\ =2000+2000+2000+2000 \\ =8000 \\ \\(v) \quad 10+11+12+13+14+15+16+17+18+19+20 \\ \text {We know that } \quad 10+20=30,1+9=10,2+8=10,3+7=10 \text { and } 4+6=10 \\ \Rightarrow 10+11+12+13+14+15+16+17+18+19+20 \\ = (10+20)+(11+19)+(12+18)+(13+17)+(14+16) \\ =30+30+30+30+30+15 \\ =150+15=165 \\ \\\text {Q4. Which of the following statements are true and which are false:} \\ \text {(i) The sum of two odd numbers is an odd number.} \\ \text {(ii) The sum of two odd numbers is an even number.} \\ \text {(iii) The sum of two even numbers is an even number.} \\ \text {(iv) The sum of two even numbers is an odd number.} \\ \text {(v) The sum of an even number and an odd number is an odd number.} \\ \text {(vi) The sum of an odd number and an even number is an even number.} \\ \text {(vii) Every whole number is a natural number.} \\ \text {(viii) Every natural number is a whole number.} \\ \text {(ix) There is a whole number which when added to a whole number, gives that number.} \\ \text {(x) There is a natural number which when added to a natural number, gives that number.} \\ \text {(xi) Commutativity and associativity are properties of whole numbers.} \\ \text {(xii) Commutativity and associativity are properties of addition of whole numbers. } \\ \\\text {Sol. (i) False. We know that, 1+3=4 where 4 is an even number.} \\ \text {(ii) True. We know that, 5+7=12 where 12 is an even number.} \\ \text {(iii) True. We know that, 2+4=6 where 6 is an even number.} \\ \text {(iv) False. We know that, 4+6=10 where 10 is an even number.} \\ \text {(v) True. We know that, 2+1=3 where 3 is an odd number.} \\ \text {(vi) False. We know that, 3+2=5 where 5 is an odd number.} \\ \text {(vii) False. Whole number starts from 0 whereas natural numbers start from 1.} \\ \text {(viii) True. All the natural numbers are also whole number.} \\ \text {(ix) True. We know that, 1+0=1 where 1 is a whole number.} \\ \text {(x) False. We know that 2+1=3 which is not that number.} \\ \text {(xi) False. Commutativity and associativity are not properties of whole numbers.} \\ \text {(xii) True. Commutativity and associativity are properties of addition of whole numbers.} \\ \\\end{array}