**Integers**

**Question 1.Using the number line write the integer which is:**

**(a)**3 more than 5

**(b)**5 more than -5

**(c)**6 less than 2

**(d)**3 less than -2

**Solution:(a)** We want to obtain integer 3 more than 5. So, we start from 5 and proceed 3 units to the right to obtain 8 as shown in the figure.

Hence, 3 more than 5 is 8.

**(b)**We want to obtain integer 5 more than -5. So, we start from -5 and proceed 5 units to the right to obtain 0 as shown in the figure.

Hence, 5 more than -5 is 0.

**(c)**We want to obtain an integer 6 less than 2. So, we start from 2 and proceed 6 units to the left of it to obtain -4 as shown in the figure.

Hence, 6 less than 2 is -4.

**(d)**We want to obtain an integer 3 less than -2. So, we start from -2 and proceed 3 units to the left of it to obtain -5 as shown in the figure.

Hence, 3 less than -2 is -5.

**Question 2.Use number line and add the following integers:**

**(a)**9 + (-6)

**(b)**5 + (-11)

**(c)**(-1) + (-7)

**(d)**(-5) + 10

**(e)**(-1) + (-2) + (-3)

**(f)**(-2) + 8 + (-4)

**Solution:(a)** First we move to the right of 0 by 9 steps reaching 9. Then we move 6 steps to the left of 9 reaching 3 as shown in the figure.

Thus, 9 + (-6) = 3.

**(b)**First we move to the right of 0 by 5 steps reaching 5. Then, we move 11 steps to the left of 5 reaching -6 as shown in the figure.

Thus, 5 + (-11) = -6.

**(c)**First we move to the left of 0 by 1 step reaching -1. Then we move 7 steps to* the left of -1 reaching -8 as shown in the figure.

Thus, (-1) + (-7) = -8.

**(d)**First we move to the left of 0 by 5 steps reaching -5. Then we move 10 steps to the right of -5 reaching 5 as shown in the figure.

Thus, (-5) + 10 = 5.

**(e)**First we move to the left of 0 by 1 step reaching -1. Then we move 2 steps to the left of -1 reaching -3. Again, we move 3 steps to the left of -3 reaching -6 as shown in the figure.

Thus, (-1) + (-2) + (-3) = -6.

**(f)**First we move to the left of 0 by 2 steps reaching -2. Then we move 8 steps to the right of -2 reaching 6. Again, we move 4 steps to the left of 6 reaching -2 as shown in the figure.

Thus, (-2) + 8 + (-4) = 2.

**Question 3.Add without using number line:**

**(a)**11 + (-7)

**(b)**(-13) + (+18)

**(c)**(-10) + (+19)

**(d)**(-250) + (+150)

**(e)**(-380)+ (-270)

**(f)**(-217) + (-100)

**Solution:(a)** 11 + (-7) = 4 + 7 + (-7)

= 4 + 0 = 4

**(b)**(-13) + (+18) = (-13) + (+13) + (+ 5)

= 0 + (+5) = 5

**(c)**(-10) + (+19) = (-10) + (+10) + (+9)

= 0 + (+9) = +9

**(d)**(-250) + (+150) = (-100) + (-150) + (+150)

= (-100) + 0 = -100

**(e)**(-380) + (-270) = -650

**(f)**(-217) + (-100) = -317

**Question 4.Find the sum of:**

**(a)**137 and -354

**(b)**-52 and 52

**(c)**-312, 39 and 192

**(d)**-50, – 200 and 300

**Solution:(a)** (+137) + (-354) = (+137) + (-137) + (-217)

= 0 + (-217) =-217

**(b)**(-52) + (+52) = 0

**(c)**(-312) + (+39) + (+192) = (-312) + (+231)

= (-81) + (-231) + (+231)

= (-81) + 0 = -81

**(d)**(-50) + (-200) + (+300) = (-250) + (+300)

= (-250) + (+250) + (+50)

= 0 + (+50) = +50

**Question 5.Find the sum:**

**(a)**(-7) + (-9) + 4 + 16

**(b)**(37) + (-2) + (-65) + (-8)

**Solution:****(a) **(-7) + (-9) + 4 + 16 = (-16) + 4 + 16

= (-16) + (+16) + 4 = 0 + 4 = 4**(b)** (37) + (-2) + (-65) + (-8) = 37 + (-75)

= 37+ (-37)+ (-38)

= 0 + (-38) = -38