SIMPLIFYING POSITIVE AND NEGATIVE INTEGERS

Problem 1 :

8 - 2 × (-1)³

Solution :

Problem 2 :

15 - 6 × (-3)

Solution :

Problem 3 :

- 2 × (3 - 5)²

Solution :

Problem 4 :

5 - 14 ÷ (-2) + 1

Solution :

Problem 5 :

6 - 7 - (-2)²

Solution :

Problem 6 :

 (-2)² - (- 2)²

Solution :

Problem 7 :

-5 - 15 ÷ (-3)

Solution :

Problem 8 :

-12 + 3 × (-2)

Solution :

Problem 9 :

3 × (-2) - (-1) × 5

Solution :

Problem 10 :

(- 2)³ - (-2)²

Solution :

Problem 11 :

15 - (-4)² × (-1)

Solution :

Problem 12 :

-16 ÷ (23 - (-9))

Solution :

Problem 13 :

The temperature was -7^oC and it has fallen a further 18^oC. What is the temperature
now?

Solution :

Current temperature = -7^oC

The terperature fallen = 18^oC

Temperature now = -7 - 18

= -25^oC

Problem 14 :

A submarine is 23 m below sea level and dives a further 36 m. How deep is it now?

Solution :

The height below the sea level = -23 m

Divies further = -36 m

Deepness now = -23 - 36

= -59 m

So, the height of the submarine below the sea is 59 m.

Problem 15 :

A bird flying 9 m above a lake suddenly drops 10.5 m to catch a fish. How far under the surface was the fish? 

Solution :

The distance under the surface = 9 - 10.5

= -1.5 m

So, the fish is at 1.5 m under the surface.

Problem 16 :

You deposit $50 in your savings account. One week later, you withdraw $20. Write each amount as an integer

Solution :

• Amount deposit = +50
• Amount withdrawl = -20

Problem 17 :

You go down 8 floors in an elevator. Your friend goes up 5 floors in an elevator. Write each amount as an integer.

Solution :

• Going down 8 floors, then distance covered by you is -8
• Going up 5 floors, then distance covered by your friend is +5.

Problem 18 :

The depths of two scuba divers exploring a living coral reef are shown.

a) Write an integer for the position of each diver relative to sea level.

b) Which integer in part (a) is greater?

c) Which integer in part (a) has the greater absolute value? Compare this absolute value with the depth of that diver.

Solution :

a) The divers are at the positions 14 ft and 18 ft below the sea level. Then their positions are -14 and -18.

b) The divers who is at 18 ft deeper is greater.

c) |-14| = 14

|-18| = 18

18 > 14

Comparing the above the depth of diver who is 18 ft below the sea is greater.

Problem 19 :

The summit elevation of a volcano is the elevation of the top of the volcano relative to sea level. The summit elevation of the volcano Kilauea in Hawaii is 1277 meters. The summit elevation of the underwater volcano Loihi in the Pacific Ocean is −969 meters. Which summit is closer to sea level?

Solution :

The volcano Kilauea in Hawaii is above the sea level which has the height of 1277 meters.

So, +1277 m

The underwater volcano Loihi in the Pacific Ocean is below the sea level which has the height of 969 m

So, -969 m

The underwater volcano Loihi in the Pacific Ocean is closer to the sea level.

Problem 20 :

Determine whether the statement is true or false. Explain your reasoning.

i) If x < 0, then ∣ x ∣= −x.

ii)  The absolute value of every integer is positive.

Solution :

i) If x < 0, then ∣ x ∣ = −x.

False, when x is lesser than 0, then will get -x. |-x| = x.

ii)  The absolute value of every integer is positive.

True, absolute value of every integer will be positive.