# Solution of Class 6th Integers Mathematics (2023-24)

- Posted by doubtout
- Categories Class 6th Math
- Date July 7, 2020
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### Integers Class 6 Ex 6.1

**Question 1.****Write opposites of the following:****(a) Increase in weight****(b) 30 km North****(c) 326 BC****(d) Loss of ₹700****(e) 100 m above sea level.**

Solution:

(a) Decrease in weight

(b) 30 km South

(c) 326 AD

(d) Profit of ₹700

(e)100 m below sea level.

**Question 2.****Represent the following numbers as integers with appropriate signs.****(a) An aeroplane is flying at a height two thousand metre above the ground.****(b) A submarine is moving at a depth, eight hundred metre below the sea level.****(c) A deposit of rupees two hundred.****(d) Withdrawal of rupees seven hundred.**

Solution:

(a) +2000 m

(b) -800 m

(c) + ₹200

(d) – ₹700

**Question 3.****Represent the following numbers on a number line: ,****(a) +5****(b) -10****(c) ±8****(d) -1****(e) -6**

Solution:

**Question 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.**

Solution:

(a) F represents -8

(b) G is a negative integer.

(c) B represents +4 and E represents – 10

(d) E has the least value of -10.

(e) Decreasing order of all the points are: D, C, B, A, 0, H, G, F and E.

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

Solution:

(c) Siachin is the coolest place with -10°C temperature.

(d) (i) Delhi → 20°C

(ii) Ahemedabad → 30°C

**Question 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**

Solution:

(a) 9 is to the right of 2

(b) -3 is to the right of -8

(c) 0 is to the right of – 1

(d) 10 is to the right of -11

(e) 6 is to the right of -6

(f) 1 is to the right of -100.

**Question 7.****Write all the integers between the given pairs (write them in the increasing order):****(a) 0 and -7****(b) -4 and 4****(c) -8 and -15****(d) -30 and -23**

Solution:

(a) Integers between 0 and -7 are:

– 6, – 5, – 4, -3,-2,- 1.

(b) Integers between -4 and 4 are:

– 3, – 2, -1, .0, 1, 2, 3.

(c) Integers between -8 and -15 are:

-14,-13, -12,-11,-10,-9.

(d) Integers between -30 and -23 are:

– 29, – 28, – 27, – 26, – 25, – 24.

**Question 8.****(a) Write four negative integers greater than -20.****(b) Write four negative integers less than – 10.**

Solution:

(a) Four negative integers greater than – 20 are: – 19, – 18, – 17, – 16.

(b) Four negative integers less than – 10 are: – 11, – 12, – 13, – 14.

**Question 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.**

Solution:

(a) True (T)

(b) False (F); Correction: -100 is to the left of -50 on a number line.

(c) False (F); Correction: There is no smallest negative integer.

(d) False (F); Correction: -26 is smaller than -25.

**Question 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?**

Solution:

### ============================================

### Integers Class 6 Ex 6.2

**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**

Solution:

(a) 3 more than 5

Moving right 3 steps from 5, we reach at 8. Hence, 3 more than 5 = 8.

(b) 5 more than -5

Moving right 5 steps from -5 we reach at 0. Hence, 5 more than -5 = 0

(c) 6 less than 2

Moving left 6 steps from 2, we reach at -4. Hence, 6 less than 2 = -4

(d) 3 less than -2

Moving left 3 steps from -2, we reach at -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)**

Solution:

(a) 9 + (- 6)

**Question 3.****Add without using number line:****(а) 11 + (-7)****(b) (-13) + (+18)****(c) (-10) + (+19)****(d) (-250) + (+150)****(e) (-380) + (-270)****(f) (-217) + (-100).**

Solution:

(a) 11 + (-7) = 4 + (+7) + (-7)

[∵ (+7) + (-7) = 0]

= 4 + 0 = 4

Hence, 11 + (-7) = 4.

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

[∵ (-13) + (+13) = 0]

= 0 + (+ 5) = 5

Hence, (- 13) + (+ 18) = 5.

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

[∵ (-10) + (10) = 0] = 0 + (+9) = 9

Hence, (-10) + (19) = 9.

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

= (-100) + 0 = -100 [∵(-150) + (+150) = 0]

Hence, (-250) + (+150) = – 100.

(e) (-380) + (-270) = – [380 + 270] = (-650)

Hence, (-380) + (-270) = (-650).

(f) (-217) + (-100) = – [217 + 100] = -317

**Question 4.****Find the sum of:****(a) 137 and -354****(b) -52 and 52 .****(d) -312, 39 and 192****(d) -50, -200 and 300**

Solution:

(a) 137 and -354

(137) + ( -354) = (137) + (-137) + (-217) [∵ (137) + (-137) = 0]

= 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)

[∵ (-a) + (a) = 0]

= 0 + (- 81) = – 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) = 50 [ ∵ (-a) + (+ a) = 0]

**Question 5.****Find the sum of:****(a) (- 7) + (-9) + 4 + 16****(b) (37) + (-2) + (-65) + (-18)**

Solution:

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

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

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

= 0 + 0 + 4 = 4 [∵ (-a) + (a) = 0]

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

= (+37) + (-75)

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

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

### ============================================ Integers Class 6 Ex 6.3

**Question 1.****Find:****(a) 35 – (20)****(b) 72 – (90)****(c) (-15) – (-18)****(d) (- 20) – (13)****(e) 23 – (-12)****(f) (-32) – (-40)**

Solution:

(a) 35 – (20) = 15 + (20) – (20)

= 15 + 0 = 15 [(+a) + (-a) = 0]

(b) 72 – 90

72 – (72 + 18) = 72 – 72 – 18

= 0 – 18 = – 18 [a + (- a) = 0]

(c) (- 15) – (- 18)

= (- 15) + (additive inverse of – 18)

= (-15) + (18) = 3

(d) (- 20) – (13)

(- 20) – (13) = – [20 + 13] = – 33

(e) 23 – (- 12)

23 – (- 12) = 23 + (additive inverse of – 12)

= 23 + 12 = 35

(f) (- 32) – (- 40)

(- 32) + (additive inverse of – 40)

= (- 32) + 40 = 8

**Question 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)**

Solution:

(a) (-3) + (-6) = – [3 + 6] = – 9 and (-3) – (-6) = (-3) + 6 = 3

Here, – 9 < 3

∴ (- 3) + (- 6) < (- 3) – (- 6)

(b) (-21) – (-10) = (-21) + 10 = -11 and (-31) + (-11) = – (31 + 11) = – 42

Here, -42 < -11 or -11 > -42 ∴ (-21) , -(-10) >(-31)+ (-11)

(c) 45 – (-11) = 45 + 11 = 56 and 57 + (-4) = 57 -4 = 53

Here, 56 >53

∴ 45 – (-11) > 57 + ( -4)

(d) (-25) – (-42) = -25 + 42 = 17

and (-42) – (-25) = -42 + 25 = -17

Here, 17 > -17

∴ (-25) – (-42) > (-42) – (-25).

**Question 3.****Fill in the blanks.****(a) (-8) + …. = 0****(b) 13 + …. = 0****(c) 12 + (-12) = ….****(d) (-4) + …. = – 12****(e) …. -15 = – 10.**

Solution:

(a) (-8) + (additive inverse of -8) = 0

= (-8) + (8) = 0

∴ Value of blank is 8

(b) 13 + (additive inverse of 13) = 0

= 13 + (-13) = 0

∴ Value of blank is – 13

(c) 12 + (-12) = 0 [∵ -12 is additive inverse of 12]

∴ The Value of blank is 0

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

∴ Value of blank is -8.

(e) (+5) – 15 = -10

∴ Value of blank is +5.

**Question 4.****Find :****(a) (-7) – 8 – (-25)****(b) (-13) + 32 – 8 – 1****(c) (-7) + (-8) + (-90)****(d) 50 – (-40) – (-2)**

Solution:

(a) (-7) – 8 – (-25)

= (-7) – 8 + 25

[ ∵ Additive inverse of – 25 is 25]

= -7 + 17 = -7 + 7 +10

[∵ (-a) + (+a) = 0]

= 0 + 10 = 10.

(b) (-13) + 32 – 8 – 1

= (-13) + (13) + 19 – (8 + 1)

= 0 + 19 – 9

= 19 – 9 [∵ (-13) + (13) = 0]

= 10 + 9 – 9 = 10 + 0 = 10.

[(+9) – (+9) = 0]

(c) (-7) + (-8) + (-90) = – (7 + 8) + (-90)

= -15 + (-90)

= -(15 + 90)

= -105.

(d) 50 – (-40) – (-2)

= 50 – [- 40 – 2]

= 50 – (-42)

= 50 + 42

= 92.