**Integers**

Points to remember:

(a) Every positive integer is larger than every negative integer.

(b) Zero is less than every positive integer.

(c) Zero is larger than every negative integer.

(d) Zero is neither a negative integer nor a positive integer.

(e) Farther a number from zero on the right, larger is its value.

(f) Farther a number from zero on the left, smaller is its value.

## 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

Answer:

(a) Increase in weight

Ans: Decrease in weight

(b) 30 km north

Ans: 30 km south

(c) 80 m east

Ans: 80m west

(d) Loss of Rs 700

Ans: Profit of Rs 700

(e) 100 m above sea level

Ans: 100m below sea level

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

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

Ans: +2000m.

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

Ans: -800m.

(c) A deposit of rupees two hundred.

Ans: +200 rupees.

(d) Withdrawal of rupees seven hundred.

Ans: -700 rupees.

3). Represent the following numbers on a number line:

(a) + 5 (b) – 10 (c) + 8

(d) – 1 (e) – 6

Answer:

(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?

Ans: F.

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

Ans: negative integer

(c) Write integers for points B and E.

Ans: B is +4

E is -10.

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

Ans: E

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

Ans: Points in decreasing order of value:

D, C, B, A, 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.

Answer:

**Place Temperature**

Siachin 10°C below 0°C __-10 ^{0}C__

Shimla 2°C below 0°C __-2 ^{0}C__

Ahmedabad 30°C above 0°C __+30 ^{0}C__

Delhi 20°C above 0°C __ +20 ^{0}C__

Srinagar 5°C below 0°C __-5 ^{0}C.__

(b) Following is the number line representing the temperature in degrees Celsius. Plot the name of the city against its temperature.

(c) Which is the coolest place?

Ans: Siachin.

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

Ans: Ahmedabad and Delhi.

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

Answer:

(a) 2, 9

Ans: 9 is to the right of 2.

(b) – 3, – 8

Ans: -3 is to the right of -8.

(c) 0, – 1

Ans: 0 is to the right of -1.

(d) – 11, 10

Ans: 10 is to the right of -11.

(e) – 6, 6

Ans: 6 is to the right of -6.

(f) 1, – 100

Ans: 1 is to the right of -100.

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

Answer:

(a) 0 and – 7

Ans: -7, -6, -5, -4, -3, -2, -1, 0.

(b) – 4 and 4

Ans: -4, -3, -2, -1, 0, 1, 2, 3, 4.

(c) – 8 and – 15

Ans: -15, -14, -13, -12, -11, -10, -9, -8.

(d) – 30 and – 23

Ans: -30, -29, -28, -27, -26, -25, -24, -23.

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

Ans: Four negative integers greater than -20 are -19, -18, -17 and -16.

(b) Write four integers less than – 10.

Ans: Four integers less than -10 are -11, -12, -13 and -14.

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.

True.

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

False.

– 100 is to the left of – 50 on a number line. (or)

– 50 is to the right of – 100 on a number line.

(c) Smallest negative integer is – 1.

False.

The greatest negative integer is – 1.

(d) – 26 is greater than – 25.

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?

To the left.

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

To the right.

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