Problems Involving Difference of Positive and Negative Numbers

Q.

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

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

(2) 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 ?

(3) If the no. Of steps moved down is represented by negative integers and the no. Of steps moved up by positive integers , represent his moves in part 1 and 2 by completing the following; (1) -3+2-..... = -8 (2) 4-2+....... =8. In 1 the sum (-8) represent going down by eight steps. So, what will the sum 8 in 2 represent ?

Q.

Write a pair of integers whose difference gives an integer smaller than both the integers.

Q.

Find the sum of 153 and -302

Q.

If a = -8 , b = -7 , c = 6 verify thtt (a+b) + c = a + ( b + c )

Q.

Question 4(v)

Give expression for the following cases.

7 subtracted from - m

Q.

A car travelled 60 km towards the north direction from a point A. From there, it travelled 100 km in the south direction. How far is the car from point A now?

1. 40 km South

2. 40 km North

3. 160 km South

4. 160 km North

Q.

The sum of two integers is -5. If one of them is -3, then the other integer is?

1. -2

2. 7

3. 2

4. -7

Q.

What is the value of 2³?

Q.

The sum of two Integers is -56. If one Integer is -42 find other.

Q.

Find:

(i) (ii) (iii)

(iv) (v) (vi)

Q. A water tank has steps inside it.a monkeys sitting on the first step.the water level is at ninth step.
(1) he jumps 3 steps inside it and jumps back 2 steps up.in how many jumps will he heach the water level ?
(2)after drinking the water, the monkey wants to go back.for this he has jumped 5 steps up and then jumps back 3 steps down in every move.in how many jumps will he reach the top of the tank?

Q.

Simplify : (3a/10)+(2a/5)=(7a/25)+(29/25)

Q.

Simplify:5(x-4)-3(x-4)+7(x-4)

Q. Find the additive inverse of (6 - 11)

1. 6 + 11
2. - 6 - 11
3. 5
4. 9

Q. Find the additive inverse of:

(i) − 83
(ii) 256
(iii) 0
(iv) − 2001

Q. Find the additive inverse of:

(i) 5
(ii) −9
(iii) $\frac{3}{14}$
(iv) $\frac{-11}{15}$
(v) $\frac{15}{-4}$
(vi) $\frac{-18}{-13}$
(vii) 0
(viii) $\frac{1}{-6}$

Q.

Question 5 (i)

When a = 0, b = -1, find the value of the given expression:
2a + 2b

Q.

Find:

(i) (ii) (iii)

(iv) (v) (vi)

(vii) (viii)

Q.

Question 10(iii)
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.

(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.

60 - (- 20) - (- 3) = ?

1. 8

2. 92

3. -92

4. -8

Q.

Question 7 (iv)

Simplify these expressions and find their values if x = 3, a = -1, b = -2:
10 - 3b - 4 - 5b

Q. Find the additive inverse of:

(i) − 83
(ii) 256
(iii) 0
(iv) − 2001

Q.

Calculate the value of each of the following expressions.

$a+b$, when $a=-35$and $b=-75.$

Q.

Find:

(i) (ii) (iii)

(iv) (v) (vi)

Q.

Find the sum: $5+(-5)+5+(-5)+............$

If the number of terms is $40$.

Q.

Fill in the blanks with appropriate answers in the following:

(1)

(2)

(3)

(4)

(5)

(6)

Q. Solve each of the following equations by trial-and-error method:
(i) x + 3 = 12
(ii) x − 7 = 10
(iii) 4x = 28
(iv) $\frac{x}{2}+7=11$
(v) 2x + 4 = 3x
(vi) $\frac{x}{4}=12$
(vii) $\frac{15}{x}=3$
(viii) $\frac{x}{18}=20$

Q. Add the following rational numbers:

(i) $\frac{12}{7}\mathrm{and}\frac{3}{7}$
(ii) $\frac{-2}{5}\mathrm{and}\frac{1}{5}$
(iii) $\frac{3}{-8}\mathrm{and}\frac{1}{8}$
(iv) $\frac{-5}{11}\mathrm{and}\frac{7}{-11}$
(v) $\frac{9}{-13}\mathrm{and}\frac{-11}{-13}$
(vi) $\frac{-2}{9}\mathrm{and}\frac{-5}{9}$
(vii) $\frac{-17}{9}\mathrm{and}\frac{-11}{9}$
(viii) $\frac{-3}{7}\mathrm{and}\frac{5}{-7}$

Q.

The expression 21b - 32 + 7b - 20b on simplification gives

1. 32 - 8b

2. 8b + 32

3. 8b - 32

4. 24b

Q. What should be subtracted from $\frac{-3}{4}$ to get 1?