Question

Complete the following addition table :

SECOND NUMBER

F I R S T N U M B E R	$+$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
	$-4$
	$-3$
	$-2$
	$-1$
	$0$
	$1$
	$2$
	$3$
	$4$

Now from the above table answer the following :

(a) List the pair of integers whose sum is zero.

(b) What do you observe in the row corresponding to zero as the first number and in the column corresponding to zero as the second number ?

(c) Is $(-4)+3=3+(-4)$? Is $3+(-1)=(-1)+3$?

(d) Is $(-2)+(-3)$ an integer?

Answer 1

On Adding the first number with the second number of this table we get the complete table as -

SECOND NUMBER

F I R S T N U M B E R	$+$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
	$-4$	$-8$	$-7$	$-6$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$
	$-3$	$-7$	$-6$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$	$1$
	$-2$	$-6$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$
	$-1$	$-5$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$
	$0$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
	$1$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$
	$2$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
	$3$	$-1$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
	$4$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$

from the above table ,

(a) On closely observing from the table , the pair of integers whose sum is zero are $(-4,4),(-3,3),(-2,2),(-1,1),(0,0),(1,-1),(2,-2),(3,-3),(4,-4).$

(b) We observe in the row corresponding to zero as the first number that the second number is the answer itself. When we add zero to a number , the other number itself will be the answer.We observe in the column corresponding to zero as the second number that the first number is the answer itself. When we add zero to a number , the other number itself will be the answer.

(c)Yes, $(-4)+3=3+(-4)$ as $(-4)+3=-1$and $3+(-4)=-1.$

also, $3+(-1)=(-1)+3$as $3+(-1)=2$ and $(-1)+3=2$ .

(d )Yes ,$(-2)+(-3)$ is an integer because $(-2)+(-3)=-5$ and $-5$ is an integer.