Solution of Chapter 6. Integers (NCERT - Mathematics Book)

Write opposites of the following:

(a) Increase in weight

(b) 30 km north

(c) 326 BC

(d) Loss of Rs 700

(e) 100 m above sea level

Represent the following numbers as integers with appropriate signs.

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

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

(c) A deposit of rupees two hundred.

(d) Withdrawal of rupees seven hundred.

Represent the following numbers on a number line:

(a) +5

(b) -10

(c) + 8

(d) -1

(e) -6

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 their values.

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 temperatures 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.

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

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

Write four negative integers greater than -20

Write four negative integers less than -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?

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

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)

Add without using number line:

(a) 11 + (-7)

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

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

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

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

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

Find the sum of:

(a) 137 and – 354

(b) -52 and 52

(c) -312, 39 and 192

(d) -50, -200 and 300

Find the sum:

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

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

Find:

(a) 35 – (20)

(b) 72 – (90)

(c) (-15) – (-18)

(d) (-20) – (13)

(e) 23 – (-12)

(f) (-32) – (-40)

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)

Fill in the blanks:

(a) (-8) + ….. = 0

(b) 13 + ……. = 0

(c) 12 + (-12) = ……..

(d) (-4) + …… = -12

(e) …… - 15 = -10

Find:

(a) (-7) – 8 – (-25)

(b) (-13) + 32 – 8 -1

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

(d) 50 – (-40) – (-2)