#### Solved Examples and Worksheet for Application of Integers

Q1Jason's pet dog weighs 6 pounds. Which of the following integers best represents the situation?

A. - 6 pounds
B. + 60 pounds
C. + 6 pounds
D. - 60 pounds

Step: 1
Represent 6 pounds on number line as shown below.
Step: 2
So, the integer that represents the weight of Joe's pet dog is + 6.
Correct Answer is :   + 6 pounds
Q2A hot air-balloon was 24,000 ft high from ground level. It then descended by 600 ft. How high was it after descending?

A. 27,920 ft
B. 23,000 ft
C. 23,200 ft
D. 23,400 ft

Step: 1
The height of the hot air-balloon after descending = its height before descending - the height by which it descended.
Step: 2
= 24000 - 600
[Original expression.]
Step: 3
= 23,400 ft
[Subtract.]
Correct Answer is :   23,400 ft
Q3When Johnny read the thermometer this morning, it was 53° F. At 5 p.m., the temperature was 98.5°F. What was the increase in the temperature?
A. 151.5°
B. 45.5°
C. 55.5°
D. 35.5°

Step: 1
To find increase in temperature, subtract the morning temperature from the evening temperature.
Step: 2
98.5°F - 53°F = 45.5°
Step: 3
So, the temperature increased by 45.5°.
Q4Identify an integer to represent the temperature 3°C below 0°C.
A. + 3°C
B. - 3°C
C. + 6°C
D. 0°C

Step: 1
3°C below 0°C is a negative number.
Step: 2
So, 3°C below 0°C is represented as - 3°C.
Correct Answer is :   - 3°C
Q5The average winter temperature of Tundra zone is 15°C below zero. Which of the following integers represents the situation?

A. - 51°C
B. 0°C
C. +15°C
D. - 15°C

Step: 1
15°C below zero is a negative number.
Step: 2
So, 15°C below zero is - 15°C .
Correct Answer is :   - 15°C
Q6A scuba diver dives 48 m below sea level. Which of the following integers represents the situation?

A. - 4 m
B. 0 m
C. - 48 m
D. + 48 m

Step: 1
48 m below sea level is a negative number.
Step: 2
So, 48 m below sea level is represented as - 48 m.
Correct Answer is :   - 48 m
Q7The temperature of a juice in a refrigerator is - 9°C. When it is taken out from the refrigerator, the temperature increased by 6°C. What is the new temperature?

A. + 15°C
B. - 3°C
C. + 3°C
D. - 15°C

Step: 1
Temperature of the juice in the refrigerator = - 9°C
Step: 2
Rise in temperature of the juice = + 6°C
Step: 3
New temperature of the juice = (- 9°C) + (6°C) = - 9°C + 6°C
[For any positive integer x and y, - x + (+ y) = - x + y.]
Step: 4
= - 3°C
[Subtract and put the sign of the larger number.]
Step: 5
So, the new temperature of the juice is - 3°C.
Correct Answer is :   - 3°C
Q8During selection trials for the Olympic games, the qualifying time set for 100 meters sprint is 11 seconds. Jessica′s current speed for 100 meters sprint is 16 seconds. How much time should Jessica save in order to qualify?

A. 5 seconds
B. 4 seconds
C. 6 seconds
D. 7 seconds

Step: 1
Jessica takes 16 seconds, but the time to qualify is 11 seconds.
Step: 2
So, the time to be saved = 16 - 11
Step: 3
= 16 + (- 11)
[To subtract a positive integer, add its negative integer.]
Step: 4
= 5

Step: 5
Jessica should save 5 seconds in order to qualify for the Olympic games.
Correct Answer is :   5 seconds
Q9The temperature of a city in the morning was - 4°C and by the noon time it went up by 15°C. What would be the temperature of the city at noon?

A. + 11°C
B. + 19°C
C. - 11°C
D. + 15°C

Step: 1
Morning temperature of the city = - 4°C
Step: 2
Rise in the temperature = + 15°C
Step: 3
Noon temperature of the city = (- 4°C) + (+ 15°C) = - 4°C + 15°C
[For any positive integer x and y, - x + (+ y) = - x + y.]
Step: 4
= + 11°C
Step: 5
So, the noon temperature of the city would be + 11°C.
Correct Answer is :   + 11°C
Q10The scores obtained by James in a game are + 3, - 6 and - 3. Find the total score of James.

A. + 6
B. + 12
C. - 6
D. - 6

Step: 1
Scores of James are 3, - 6 and - 3.
Step: 2
James′s total score = 3 + (- 6) + (- 3)
Step: 3
= 3 - 9
Step: 4
= - 6
Step: 5
So, James′s total score is - 6.
Correct Answer is :   - 6
Q11The temperatures of Campbell′s bedroom, kitchen and refrigerator are 33°C, 35°C and - 13°C respectively. Find the sum of the temperatures.
A. 11°C
B. 15°C
C. 55°C
D. 81°C

Step: 1
Temperature of Campbell′s bedroom = 33°C
Step: 2
Temperature of Campbell′s kitchen = 35°C
Step: 3
Temperature of Campbell′s refrigerator = - 13°C
Step: 4
Sum of the temperatures = 33°C + 35°C + (- 13°C)
Step: 5
= 33°C + 35°C - 13°C
[For any positive integer x and y, x + (- y) = x - y]
Step: 6
= 68°C - 13°C
Step: 7
= 55°C
Step: 8
So, the sum of the temperatures is 55°C.
Q12John gained 6, 8 points in the first two rounds of a game. In the third round, he lost 8 points. Find his total score.

A. - 6
B. 22
C. - 10
D. 6

Step: 1
Points gained by John in the first two rounds are 6 and 8.
Step: 2
Points lost by John in the third round is 8 which can be represented as - 8.
Step: 3
John′s final score = (+ 6) + (+ 8) + (- 8)
Step: 4
= 6 + 8 + (- 8)
Step: 5
= 14 - 8
[For any positive integer x and y, x + (- y) = x - y]
Step: 6
= 6
Step: 7
So, John′s total score is 6.
Q13In a quiz competition a team has - 46 points in the third round and they gain 18 points in the next round. Find the points of the team after the fourth round.
A. - 38
B. + 31
C. - 28
D. + 64

Step: 1
Points in the third round = - 46
Step: 2
Points gained in the fourth round = + 18
Step: 3
Points of the team after fourth round = - 46 + 18 = - 28
[Subtract and put the sign of the larger number.]
Step: 4
So, the team's points after the fourth round is - 28.
Correct Answer is :   - 28
Q14A submarine was situated 270 m below sea level. If it ascends 75 m, what is its new position?

A. - 345 m
B. + 247 m
C. + 195 m
D. - 195 m

Step: 1
Initial position of the submarine = - 270 m
Step: 2
Submarine ascends = + 75 m
Step: 3
New position of the submarine = (- 270 m) + (+ 75 m) = - 270 m + 75 m
[For any positive integer x and y, - x + (+ y) = - x + y.]
Step: 4
= - 195 m
[Subtract and put the sign of the larger number.]
Step: 5
Therefore, the submarine′s new position is - 195 m.
Correct Answer is :   - 195 m
Q15A toy moves 6 m forward from a point A and then moves 3 m backward. What is the distance of the toy from the point A?
A. - 3 m
B. - 18 m
C. 9 m
D. 3 m

Step: 1
Distance moved forward from the point A by the toy = 6 m
Step: 2
Distance moved backward by the toy = - 3 m
Step: 3
Total distance of the toy from the point A = 6 m + (- 3 m) = 6 m - 3 m
[For any positive integer x and y, x + (- y) = x - y.]
Step: 4
= 3 m
[Subtract.]
Step: 5
So, the distance of the toy from the point A is 3 m.
Correct Answer is :   3 m
• Integer