RS Aggarwal Solutions Class 6 Chapter 3 Whole Numbers Exercise 3B

     

EXERCISE-3B

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Question 1

Q.1. Fill in the blanks to make each of the following a true statements:

(i) $458+639=639+\ldots .$.

(ii) $864+2006=2006+\ldots .$.

(iii) $1946+\ldots \ldots=984+1946$

(iv) $8063+0=$ $\qquad$

(v) $53501+(574+799)=574+(53501+\ldots \ldots .$.

Ans. (i) $458+639=639+458$

(Commulative law)

(ii) $864+2006=2006+864$

(Commulative law)

(iii) $1946+984=984+1946$

(Commulative law)

(iv) $8063+0=8063$

(Additive property of zero)

(v) $53501+(574+799)=574+(53501+799)$

(Associative law)

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Question 2

Q.2. Add the following numbers and check by reversing the order of the addents :
(i) $16509+114$
(ii) $2359+548$
(iii) $19753+2867$

Ans.
(i) $16509+114=16623$
Check : $16623-114=16509$ which is given.
(ii) $2359+548=2907$
Check : $2907-2359=548$ which is given
(iii) $19753+2867=22620$
Check : $22620-19753=2867$ which is given

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Question 3

Q.3. Find the sum : $(1546+498)+3589$. Also, find the sum : $1546+(498+3589)$.

Are the two sums equal ? State the property satisfied.
Ans.
$\begin{aligned}
& (1546+498)+3589=2044+3589 \\
& =5633
\end{aligned}$
and $1546+(498+3589)=1546+4087$
$=5633$

Yes, the above two sum are equal.
The property used is associative law of addition.

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Question 4

Q.4. Determine each of the sums given below using suitable rearrangement.
(i) $953+707+647$
(ii) $1983+647+217+353$
(iii) $15409+278+691+422$
(iv) $3259+10001+2641+9999$
(v) $1+2+3+4+96+97+98+99$
(vi) $2+3+4+5+45+46+47+48$


Ans.

(i) 953 +  707 + 647

= (953 + 647) + 707

(by associative law)

= 1600 + 707 = 2307

(ii) 1983+647+217+353

= (1983+217) + (647+353)

= 2200 + 1000 = 3200

(iii) $15409+278+691+422$
$=(15409+691)+(278+422)$
(by associative law)
$=16100+700=16800$

(iv) $3259+10001+2641+9999$
$=(3259+2641)+(10001+9999)$
(by associative law)
= 5900 + 20000 = 25900

(v) 1+2+3+4+96+97+98+99

= (1 + 99) + (2 + 98) + (3 + 97) + (4 + 96)

= (100 + 100) + (100 + 100)

= 200 + 200 = 400

(vi) 2+3+4+5+45+46+47+48
= (2 + 48) + (3 + 47) + (4 + 46) + (5 + 45)

= (50 + 50) + (50 + 50) 

= 100 + 100 = 200

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Question 5

Q.5. Find the sum by short method:
(i) $6784+9999$
(ii) $10578+99999$

Ans. 

(i) $6784+9999=(6784-1)+(9999+1)$
(Adding and subtracting 1)
$=6783+10000=16783$

(ii) $10578+99999$
(Adding and subtracting 1 )
$\begin{aligned}
& =(10578-1)+(99999+1) \\
& =10577+100000=110577
\end{aligned}$

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Question 6

Q.6. For any whole numbers $a, b, c$, is it true that $(a+b)+c=a+(c+b)$ ? Give reasons.

Ans. Yes it is true, by the property of associative law of addition.

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Question 7

Q.7. Complete each one of the following magic squares by supplying the missing numbers:

(i) $\begin{array}{|l|l|l|}\hline & 9 & 2 \\\hline & 5 & \\\hline 8 & & \\\hline\end{array}$

(ii) $\begin{array}{|c|c|c|}\hline 16 & 2 & \\\hline & 10 & \\\hline & & 4 \\\hline\end{array}$

(iii) $\begin{array}{|l|l|l|l|}\hline 2 & 15 & 16 & \\\hline 9 & 12 & & \\\hline & & 7 & 10 \\\hline 14 & & & 17 \\\hline\end{array}$

(iv) $\begin{array}{|c|c|c|c|}\hline & 18 & 17 & 4 \\\hline & & 14 & 11 \\\hline & 9 & 10 & \\\hline 19 & & & 16 \\\hline\end{array}$

Ans.

The magic squares given are completed as under :

(i) $\begin{array}{|l|l|l|} \hline 4 & 9 & 2 \\ \hline 3 & 5 & 7 \\ \hline 8 & 1 & 6 \\ \hline \end{array}$

In each row/column, the sum = 15

(ii) $\begin{array}{|c|c|c|} \hline 16 & 2 & 12 \\ \hline 6 & 10 & 14 \\ \hline 8 & 18 & 4 \\ \hline \end{array}$

In each row/column, the sum = 30

(iii) $\begin{array}{|c|c|c|c|} \hline 2 & 15 & 16 & 5 \\ \hline 9 & 12 & 11 & 6 \\ \hline 13 & 8 & 7 & 10 \\ \hline 14 & 3 & 4 & 17 \\ \hline \end{array}$

In each rows/column, the sum = 38

(iv) $\begin{array}{|c|c|c|c|} \hline 7 & 18 & 17 & 4 \\ \hline 8 & 13 & 14 & 11 \\ \hline 12 & 9 & 10 & 15 \\ \hline 19 & 6 & 5 & 16 \\ \hline \end{array}$

In each row/column, the sum $=46$

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Question 8

Q.8. Write (T) for true and (F) for false for each of the following statements :
(i) The sum of two odd numbers is an odd number.
(ii) The sum of two even numbers is an even number.
(iii) The sum of an even number and an odd number is an odd number.

Ans.
(i) The sum of two odd numbers is an odd number ( F )
As sum of two odd numbers is always an even number
(ii) The sum of two even number is an even number ( T )
(iii) The sum of an even number and an odd number is an odd number (T)