## NCERT Solutions for Class 6 Chapter 6: Integers

Exercise 6.1

**1. Write opposites of the following.**

**(a) Increase in weight**

**(b) 30 km north**

**(c) 80 m east**

**(d) Loss of Rs 700**

**(e) 100 m above sea level**

**Solutions:**

**(a) **The opposite of an increase in weight is a decrease in weight.

(b) The opposite of 30 km north is 30 km south.

(c) The opposite of 80 m east is 80 m west.

(d) The opposite of a loss of Rs 700 is a gain of Rs 700.

(e) The opposite of 100 m above sea level is 100 m below sea level.

**2. Represent the following numbers as integers with appropriate signs.**

**(a) An aeroplane is flying at the height of two thousand metres above the ground.**

**(b) A submarine is moving at a depth of eight hundred metres below sea level.**

**(c) A deposit of rupees two hundred.**

**(d) Withdrawal of rupees seven hundred.**

**Solutions:**

**(a) **+ 2000 m

(b) – 800 m

(c) + Rs 200

(d) – Rs 700

**3. Represent the following numbers on a number line.**

**(a) + 5**

**(b) – 10**

**(c) + 8**

**(d) – 1**

**(e) – 6**

**Solutions:**

**(a) + **5

(b) – 10

(c) + 8

(d) – 1

(e) – 6

**4. Adjacent figure is a vertical number line representing integers. Observe it and locate the following points.**

**(a) If point D is + 8, then which point is – 8?**

**(b) Is point G a negative integer or a positive integer?**

**(c) Write integers for points B and E.**

**(d) Which point marked on this number line has the least value?**

**(e) Arrange all the points in decreasing order of value.**

**Solutions:**

**(a) **If point D is +8, then point F is -8.

(b) Point G is a negative integer.

(c) Point B is 4, and point E is – 10.

(d) The least value on this number line is point E, as it represents – 10.

(e) The points in decreasing order of value are D, C, B, A, O, H, G, F, E.

**5. Following is the list of temperatures of five places in India on a particular day of the year.**

**Place Temperature**

**Siachin 10°C below 0°C ……………..**

**Shimla 2°C below 0°C ……………..**

**Ahmedabad 30°C above 0°C ……………..**

**Delhi 20°C above 0°C ……………..**

**Srinagar 5°C below 0°C ……………..**

**(a) Write the temperatures of these places in the form of integers in the blank column.**

**(b) Following is the number line representing the temperature in degree Celsius.**

**Plot the name of the city against its temperature.**

**(c) Which is the coolest place?**

**(d) Write the names of the places where temperatures are above 10°C.**

**Solutions:**

**(a)**

Siachin – 100 C

Shimla – 20 C

Ahmedabad + 300 C

Delhi + 200 C

Srinagar – 50 C

(b)

(c) Siachin is the coolest place.

(d) Ahmedabad and Delhi are the places where the temperatures are above 100C.

**6. In each of the following pairs, which number is to the right of the other on the number line?**

**(a) 2, 9**

**(b) – 3, – 8**

**(c) 0, – 1**

**(d) – 11, 10**

**(e) – 6, 6**

**(f) 1, – 100**

**Solutions:**

**(a) **9 lies to the right on the number line (9 > 2).

(b) – 3 lies to the right on the number line (- 3 > – 8).

(c) 0 lies to the right on the number line (0 > -1).

(d) 10 lies to the right on the number line (10 > -11).

(e) 6 lies to the right on the number line (6 > -6).

(f) 1 lies to the right on the number line (1 > -100).

**7. Write all the integers between the given pairs (write them in increasing order).**

**(a) 0 and – 7**

**(b) – 4 and 4**

**(c) – 8 and – 15**

**(d) – 30 and – 23**

**Solutions:**

**(a) **-6, -5, -4, -3, -2, -1 are the integers between 0 and -7.

(b) -3, -2, -1, 0, 1, 2, 3 are the integers between -4 and 4.

(c) -14, -13, -12, -11, -10, -9 are the integers between -8 and -15.

(d) -29, -28, -27, -26, -25, -24 are the integers between -30 and -23.

**8. (a) Write four negative integers greater than – 20.**

**(b) Write four integers less than – 10.**

**Solutions:**

**(a) **-19, -18, -17, -16 are the integers greater than -20.

(b) -11, -12, -13, -14 are the integers less than -10.

**9. For the following statements, write True (T) or False (F). If the statement is false, correct the statement.**

**(a) – 8 is to the right of – 10 on a number line.**

**(b) – 100 is to the right of – 50 on a number line.**

**(c) Smallest negative integer is – 1.**

**(d) – 26 is greater than – 25.**

**Solutions:**

**(a) **True, as (-8 > -10).

(b) False. (-50 is greater than -100). Hence, -100 lies to the left of -50 on the number line.

(c) False. -1 is the greater negative integer.

(d) False. -26 is smaller than -25.

**10. Draw a number line and answer the following.**

**(a) Which number will we reach if we move 4 numbers to the right of – 2?**

**(b) Which number will we reach if we move 5 numbers to the left of 1?**

**(c) If we are at – 8 on the number line, in which direction should we move to reach – 13?**

**(d) If we are at – 6 on the number line, in which direction should we move to reach – 1?**

**Solutions:**

**(a)**

If we move 4 numbers to the right of -2, we will reach 2.

(b)

If we move 5 numbers to the left of 1, we will reach -4.

(c)

-13 lies to the left of -8 on the number line. Hence, we should move towards the left direction.

(d)-1 lies to the right of -6 on the number line. So, we should move towards the right direction.

**Exercise 6.2**

**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**

**Solutions:**

**(a)**

Hence, 8

(b)** **

Hence, 0

(c)

Hence, -4

**(**d)

Hence, -5

**2. Use a 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)**

**Solutions:**

**(a)**

Hence, 3

(b)

Hence, -6

(c)

Hence, -8

(d)

Hence, 5

(e)

Hence, -6

(f)

Hence, 2

**3. Add without using a number line.**

**(a) 11 + (–7)**

**(b) (–13) + (+18)**

**(c) (–10) + (+19)**

**(d) (–250) + (+150)**

**(e) (–380) + (–270)**

**(f) (–217) + (–100)**

**Solutions:**

(a) 11 + (-7) = 4

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

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

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

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

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

**4. Find the sum of:**

**(a) 137 and – 354**

**(b) – 52 and 52**

**(c) – 312, 39 and 192**

**(d) – 50, – 200 and 300**

**Solutions:**

**(a) **137 and -354

(137) + (-354) = (137) + (-137) + (-217)

= 0 + (-217) [(137) + (-137) = 0]

= (-217)

= -217

(b) -52 and 52

(-52) + (+52) = 0 [(-a) + (+a) = 0]

(c) -312, 39 and 192

(-312) + (+39) + (+192) = (-231) + (-81) + (+39) + (+192)

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

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

= 0 + (-81) [(-a) + (+a) = 0]

= -81

(d) -50, -200 and 300

(-50) + (-200) + (+300) = (-50) + (-200) + (+200) + (+100)

= (-50) + 0 + (+100) [(-a) + (+a) = 0]

= (-50) + (+100)

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

= 0 + (+50) [(-a) + (+a) = 0]

= 50

**5. Find the sum.**

**(a) (–7) + (–9) + 4 + 16**

**(b) (37) + (–2) + (–65) + (–8)**

**Solutions:**

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

= (-7) + (-9) + 4 + (+7) + (+9)

= (-7) + (+7) + (-9) + (+9) + 4

= 0 + 0 + 4 [(-a) + (+a) = 0]

= 4

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

= (+37) + (-75)

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

= 0 + (-38) [(-a) + (+a) = 0]

= -38

Exercise 6.3

**1. Find**

**(a) 35 – (20)**

**(b) 72 – (90)**

**(c) (-15) – (-18)**

**(d) (-20) – (13)**

**(e) 23 – (-12)**

**(f) (-32) – (-40)**

**Solutions:**

**(a) **35 – (20)

**= **35 – 20

**= **15

(b) 72 – (90)

= 72 – 90

= -18

(c) (-15) – (-18)

= -15 + 18

= 3

(d) (-20) – (13)

= -20 – 13

= -33

(e) 23 – (-12)

= 23 + 12

= 35

(f) (-32) – (-40)

= -32 + 40

= 8

**2. Fill in the blanks with >, < or = sign.**

**(a) (–3) + (–6) ______ (–3) – (–6)**

**(b) (–21) – (–10) _____ (–31) + (–11)**

**(c) 45 – (– 11) ______ 57 + (– 4)**

**(d) (–25) – (–42) _____ (– 42) – (–25)**

**Solutions:**

**(a) **(-3) + (-6) = -9

(-3) – (-6) = -3 + 6 = 3

-9 < 3

Therefore, (-3) + (-6) < (-3) – (-6)

(b) -21 – (-10) = -21 + 10 = -11

-31 + (-11) = -42

-11 > -42

Therefore, (-21) – (-10) > (-31) + (-11)

(c) 45 – (-11) = 45 + 11 = 56

57 + (-4) = 57 – 4 = 53

56 > 53

Therefore, 45 – (-11) > 57 + (-4)

(d) (-25) – (-42) = -25 + 42 = 17

-42 – (-25) = -42 + 25 = -17

17 > -17

Therefore, (-25) – (-42) > (-42) – (-25)

**3. Fill in the blanks.**

**(a) (–8) + _____ = 0**

**(b) 13 + _____ = 0**

**(c) 12 + (–12) = ____**

**(d) (–4) + ____ = –12**

**(e) ____ – 15 = – 10**

**Solutions:**

**(a) **(-8) + 8 = 0

(b) 13 + (-13) = 0

(c) 12 + (-12) = 0

(d) (-4) + (-8) = -12

(e) 5 – 15 = -10

**4. Find**

**(a) (–7) – 8 – (–25)**

**(b) (–13) + 32 – 8 – 1**

**(c) (–7) + (–8) + (–90)**

**(d) 50 – (–40) – (–2)**

**Solutions:**

**(a) **(-7) – 8 – (-25) = -7 -8 + 25

= -15 + 25

= 10

(b) (-13) + 32 – 8 – 1 = -13 + 32 – 8 – 1

= 32 – 22

= 10

(c) (-7) + (-8) + (-90) = -7 – 8 – 90

= – 105

(d) 50 – (-40) – (-2) = 50 + 40 + 2

= 92

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