Olympiad Test: Integers

Two 'pluses' make a plus, two 'minuses' make a plus. A plus and a minus make a minus.

−4 × (7)  = -28  [∵ (-) x (+) = (-)]

−45 ÷ 9 = −5

In this question, we have to multiply the integers with the same negative sign.

-5 x -6 = 30  [∵ (-) x (-) = +]

In multiplication, we have to multiply the sign of the integers also and then assign the obtained sign to the answer.
Negative sign multiplied by negative sign gives an overall positive sign.

LHS: (-8) + (-4) = -12
RHS: (-8) – (-4) = -4
⇒ -12 < -4 i.e. LHS<RHS
⇒ (- 8) + (- 4) < (- 8) – (- 4)

Thus, option C is correct.

Let other number be x.
⇒ x + (-109) = -112
⇒ x = -112 + 109 = -3

10 × (−3) = -30 [∵ (+) x (-) = -]

43 - (-17) = 60

-67 x (-1) = 67 [∵ (-) x (-) = +]

45 m above sea level = +45
25 m below sea level = -25
Therefore, 45 - (-25) = 70

 -2 x (-1) = 2 [∵ (-) x (-) = +]

25 ÷ -5 = - 5 [∵ (+/-) = -]

Temperature on Monday = -5°C
Temperature on Tuesday = Temperature on Monday - 2°C = -5°C - 2°C = -7°C

According to BODMAS,
6 × (−15 + 10) = 6 × (-5) = -30
[∵ -15 + 10 = -5]

If negative terms are multiplied odd times, then the result will always be negative.

Thus option B is correct.

Manish deposits amount = 2000
Manish withdraws amount = -1000
Balance of Manish's account = 2000 + (-1000) = Rs 1000

Thus option C is correct.

According to BODMAS,
- (-2) × (3 + 5) =  2 x 8 = 16 

When a positive integer and a negative integer are added, we may either get a negative integer or positive integer.
Example:  
5 + (-2) = 3
2 + (-5) = -3

(−12 - 3) = -15
(− 6 + 3) = -3
⇒ (−12 - 3) ÷ (− 6 + 3) = (-15) ÷ (-3) = 5

a = 20, b = 40, c = 80

According to BODMAS,
a x b + a x c = 20 x 40 + 20 x 80 = 800 + 1600 = 2400

 -140 x 8 = -1120