Question

Use the number line and add the following integers:
(i) 9 + (−6)
(ii) (−3) + 7
(iii) 8 + (−8)
(iv) (−1) + (−3)
(v) (−4) + (−7)
(vi) (−2) + (−8)
(vii) 3 + (−2) + (−4)
(viii) (−1) + (−2) + (−3)
(ix) 5 + (−2) + (−6)

Answer 1

i) On the number line, we start from 0 and move 9 steps to the right to reach a point A. Now, starting from A, we move 6 steps to the left to reach point B.


B represents the integer 3.
$\therefore$ 9 + (−6) = 3

(ii) On the number line, we start from 0 and move 3 steps to the left to reach point A. Now, starting from A, we move 7 steps to the right to reach point B.
B represents the integer 4.
$\therefore$ (−3) + 7 = 4



(iii) On the number line, we start from 0 and move 8 steps to the right to reach point A. Now, starting from A, we move 8 steps to the left to reach point B.
B represents the integer 0.
$\therefore$ 8 + (−8) = 0


(iv) On the number line, we start from 0 and move 1 step to the left to reach point A. Now, starting from A, we move 3 steps to the left to reach point B.
B represents the integer −4.
$\therefore$ (−1) + (−3) = −4


(v) On the number line, we start from 0 and move 4 steps to the left to reach point A. Now, starting from A, we move 7 steps to the left to reach point B.
B represents the integer −11.
$\therefore$ (−4) + (−7) = −11



(vi) On the number line, we start from 0 and move 2 steps to the left to reach point A. Now, starting from A, we move 8 steps to the left to reach point B.
B represents the integer −10.
$\therefore$ (−2) + (−8) = −10


(vii) On the number line, we start from 0 and move 3 steps to the right to reach point A. Now, starting from A, we move 2 steps to the left to reach point B. Again, starting from B, we move 4 steps to the left to reach point C.
C represents the integer −3.
$\therefore$ 3 + (−2) + (−4) = −3



(viii) On the number line, we start from 0 and move 1 step to the left to reach point A. Now, starting from A, we move 2 steps to the left to reach point B. Again, starting from B, we move 3 steps to the left to reach point C.
C represents the integer −6.
$\therefore$ (−1) + (−2) + (−3) = −6



(ix) On the number line, we start from 0 and move 5 steps to the right to reach point A. Now, starting from A, we move 2 steps to the left to reach point B. Again, starting from B, we move 6 steps to the left to reach point C.
C represents the integer −3.
$\therefore$ 5 + (−2) + (−6) = −3