Page 279 - Ganit Kaushal

(b) 50 − (−40) – (−2) = 90 − (−2) [ 50 − (−40) = 90, Rule S3]
= 90 + 2 = 92 [By rule S3]
(c) 280 + (− 130) – 96 = 150 – 96 [By rule A3]
= 54 [By rule S1]
Alter: 280 – 130 – 96 = 280 – (130 + 96) (grouping negative and positive integers separately)
= 280 – 226 = 54 [By rule S1]
(d) –10025 + 149 = − [10025 – 149] [By rule A3]
= −9876
(e) 2884 + (−2884) = 0 [By rule A4]
(f) −522 + (−160) = −(522 + 160) [By rule A2]
= −682
Ex 2. A submarine is at 850 feet below sea level. If it rises by 175 feet, what is its new position?
Sol. Sea level can be taken as 0 feet. Since the submarine is below sea level, its starting position is −850 feet.
The movement is taken as +175. [ It’s going up]
The new position (target) = −850 + 175 = −675 feet.
[ Recall: Starting Position + Movement = Target Position]
Ex 3. When I am added to 3, the result is −14. Who am I?
Sol. This question can be visualised as: if the starting number is 3 and the target number is −14, then what
is the movement needed? Recall that, Target Number – Starting Number = Movement needed.
We get −14 − 3 = −17.
\ I am −17.

Exercise 10.2

1. Making use of the number line, evaluate the following:
(a) −9 + 5 (b) −3 + (−6) (c) −1 + (−2) + 2 (d) 7 + (−7)
(e) 5 + (−9) (f) (−2) + 7 + (−9)
2. Find the sum of the following:
(a) −588 and 488 (b) 2467 and −1325 (c) −5523 and 3258
3. Subtract:
(a) −1235 from 4532 (b) −789 from −1225 (c) −584 from 0
4. Using Brahmagupta’s rules, evaluate the following:
(a) −12 + (−98) – (−84) + (−7) (b) −17 – 18 – (−36)
(c) −12 + (−35) – (−125) – 170 (d) −129 + 129 – (−129) − 129
5. Subtract the sum of −3090 and 3320 from 999.
6. Subtract the sum of −1250 and −1138 from the sum of 1136 and 1272.
7. From the sum of 444 and −234, subtract −111.
8. The sum of two integers is – 241. If one of the integers is 563, determine the other.
9. A submarine is positioned at 800 feet below sea level. If it rises by 250 feet, what will be its new
position?
10. When I am added to −5, the result is 12. Who am I?
11. A monkey sits on a branch 20 feet above the ground. He swings 10 feet upwards, then climbs further
9 feet upwards and finally jumps down 15 feet. How much above the ground is the monkey now?

The Other Side of Zero 277