WORKSHEET ON INTEGERS

Evaluating Expressions with Positive and Negative Integers

1)  8 + - 5    Solution

2)  8 - - 5    Solution

3)  - 8 + - 5    Solution

4)  - 8 - - 5    Solution

5)  4 + - 9     Solution

6)  4 - - 9      Solution

7)  - 4 + - 9      Solution

8)  - 4 - - 9      Solution

9)  3 - - 2 + 4   Solution

10)  13 + - 5 - - 2        Solution

11)  - 6 - - 4 + - 5    Solution

12)  - 6 + - 1 - - 8     Solution

13)  5 - 12 - - 4      Solution

14)  8 - 15 + - 11     Solution

15)  3 - - 1 - - 5       Solution

16)  The list shows four bank account transactions in July. Find the change C in the account balance.

Solution

17)   Tell whether the sum is positive, negative, or zero without adding. Explain your reasoning.

a) −8 + 20

b)  30 + (−30)

c) −10 + (−18)

Solution

18)  Tell whether the statement is true or false. Explain your reasoning.

a) The sum of two negative integers is always negative.

b) An integer and its absolute value are always opposites.

Solution

Simplifying Positive and Negative Integers

Questions :

1)  8 - 2 × (-1)^{3     Solution}

2)  15 - 6 × (-3)     Solution

3)  - 2 × (3 - 5)^{2         Solution}

4)  5 - 14 ÷ (-2) + 1         Solution

5)  6 - 7 - (-2)^{2           Solution}

6)   (-2)² - (- 2)^{2          Solution}

7)  -5 - 15 ÷ (-3) Solution

8)  -12 + 3 × (-2)         Solution

9)  3 × (-2) - (-1) × 5     Solution

10)  (- 2)³ - (-2)^{2     Solution}

11)  15 - (-4)² × (-1)     Solution

12)  -16 ÷ (23 - (-9))    Solution

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

Solution

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

Solution

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

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

Solution

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

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

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

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

Word Problems Involving Positive and Negative integers

1)  When Steve woke up. His temperature was 102˚F. Two hours later it was 3˚Lower. What was his temperature then?

2)  An elevator is on the twentieth floor. It goes down 11 floors and then up 5 floors. What floor is the elevator on now ?

3)  A deep-sea exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?

4)  If it is 5˚ outside and the temperature will drop 17˚ in the next six hours, how cold will it get?

5)  Josie has $47 left on her checking account. If she writes a check for $55, what will Josie's balance be?

6)  Joe is playing a game with a regular die. If the number that turns up is even, he will gain 5 times the number that comes up. If it is odd, he will lose 10 times the number that come up. He tosses a 3. Express the results as an integers.

7)  It will be -12˚ tonight. The weatherman predicts it will be 25˚ warmer by noon tomorrow. What will the temperature be by noon tomorrow?

8)  The average temperature at the south pole is -45˚F. The average temperature on the Equator is 92˚F. How much warmer is the average temperature on the Equator than at the South Pole?

9)  The elevation of Mt. Everest is 29,028 feet. The elevation of the dead sea is -485 feet. What is the difference in the elevation between Mt. Everest and the Dead Sea?

10)  The temperature was -3˚c last night. It is now -4˚c. What was the change in temperature?

Solution

Answers :