Addition and Subtraction of Integers

Q.

The temperature at $12$ noon was $10°C$ above zero. If it decreases at the rate of $2°C$ per hour until midnight, at what time would the temperature be $8°C$ below zero? What would be the temperature at mid-night?

Q.

Question 2(a)
Write a pair of negative integers whose difference gives 8.

Q.

A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the $9^{th}$ step.

(i) He jumps $3$ steps down and then jumps back $2$ steps up. In how many jumps will he reach the water level?

Q. In a test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer.
i. Radhika answered all the questions, scored 30 marks and got 10 correct answers
ii. Jay also answered all the questions, scored (-12) marks though he got 4 correct answers.
How many incorrect answers had they attempted?

1. 22
2. 24
3. 26
4. 28

Q.

In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack’s scores in five successive rounds were $25,-5,-10,15,$ , what was his total at the end?

Q.

Mohan deposits $₹2000$ in his bank account and withdraws$₹1642$ from it, the next day. If withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal.

Q.

Question 2(c)
Write a negative integer and a positive integer whose difference is -3.

Q.

Write five pairs of integers $(a,b)$ such that $a÷b=-3$. One such pair is $(6,-2)$ because $6÷(-2)=(-3)$.

Q.

In a class test containing $10$ questions, $5$ marks are awarded for every correct answer and $(-2)$ marks are awarded for every incorrect answer and $0$ for questions not attempted. Reshma gets five correct answers and five incorrect answers, what is her score?

Q.

A car cover a distance of 300 km with some speed. If the speed is increased by 10 km/hr, it will cover the same distance in one hour less. Find the speed of car.

Q.

Which of the following statements is not true?

1. When two positive integers are added, we always get a positive integer.
2. When two negative integers are added, we always get a negative integer.
3. When a positive integer and a negative integer are added, we always get a negative integer.
4. Additive inverse of an integer $2$ is $(-2)$ and additive inverse of $(-2)$ is $2$.

Q.

Is this statement true or false . For subtraction , we add the Additive inverse of the integer that is being subtracted , to the other integer. Please explain in detail.

Q.

Question 136

The highest point measured above sea level is the summit of Mt. Everest, which is 8848 m above sea level and the lowest point is challenger deep at the bottom of Mariana Trench which is 10911 m below sea level. What is the vertical distance between these two points?

Q.

Write two integers, which are smaller than $-5$ but their difference is $-5$.

Q.

Question 131

A green grocer had a profit of Rs. 47 on Monday, a loss of Rs. 12 on Tuesday and loss of Rs. 8 on Wednesday. Find his net profit or loss in 3 days.

Q.

Question 119 (i)

Write a positive integer and a negative integer whose sum is a negative integer.

Q. A man walked 3 km towards North then 8 km towards South. What is his final position with respect to his initial position?

1. 5 km towards East
2. 3 km towards South
3. 8 km towards North
4. 5 km towards South

Q.

If $p$ times the $pth$ term of an A.P is equal to $q$ times the $qth$ term of an A.P. then $(p+q)th$ term is:

1. $0$

2. $1$

3. $2$

4. $3$

Q.

Sana and Fatima participated in an apple race. The race was conducted in $6$ parts. In the first part, Sana won by $10$ seconds. In the second part, she lost by $1$ min, then won by $20$ seconds in the third part and lost by $25$ seconds in the fourth part, she lost by $37$ seconds in the fifth part and won by $12$ seconds in the last part. Who won the race finally?

Q. Question 3
In a quiz, team A scored - 40, 10, 0 and team B scored 10, 0, - 40 in three successive rounds.
(i) Which team scored more?
(ii) Can we say that we can add integers in any order?

Q.

The sum of two rational numbers is-7\12 .If one number is 13\24 find the other

Q.

Question 119 (ix)

Write two negative integers whose difference is 7.

Q. Question 3
At Srinagar temperature was $-5^{\circ }C$ on Monday and then it dropped by $2^{\circ }C$ on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by $4^{\circ }C$. What was the temperature on Wednesday?

Q.

A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step.

(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?

(ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?

(iii) If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following; (a) − 3 + 2 − … = − 8 (b) 4 − 2 + … = 8. In (a) the sum (− 8) represents going down by eight steps. So, what will the sum 8 in (b) represent?

Q.

What must be subtracted from $-3$ to get $-9$?

Q.

Subtract the first integer from the second in each case I) -3, 6

Q.

Question 8(ii)
Verify a−(−b) = a + b for the following values of a and b.
a = 118, b =125

Q. A certain freezing process requires that room temperature be lowered from ${40}^{o}C$ at the rate of $5^{o}C$ every hour. What will be the room temperature $10$ hours after the process begins?

Q.

Use the sign of $>,<$ or $=$ in the box to make the statements true.
$(-3)+7-\left(19\right)\square 15-8+(-9)$

Q. The temperature at $12$ noon was ${10}^o$C above zero. If it decreases at the rate of $2^o$C per hour until midnight, at what time would the temperature be $8^o$C below zero? What would be the temperature at midpoint?