## Integers

## Exercise – 6.1

**Ex 6.1 Question 1.**

**Write the 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.

**Ex 6.1 Question 2.**

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

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

**(b) A submarine is moving at a depth, eight hundred meters 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

**Ex 6.1 Question 3.**

**Represent the following numbers on a number line: ,**

**(a) +5**

**(b) -10**

**(c) ±8**

**(d) -1**

**(e) -6**

**Solution:**

**Ex 6.1 Question 4.**

**The 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 = D, C, B, A, 0, H, G, F, and E.

**Ex 6.1 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 =10°C temperature.

(d) (i) Delhi = 20°C

(ii) Ahmedabad = 30°C

**Ex 6.1 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 on the number line.

(b) -3 is to the right of -8 on the number line.

(c) 0 is to the right of – 1 on the number line.

(d) 10 is to the right of -11 on the number line.

(e) 6 is to the right of -6 on the number line.

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

**Ex 6.1 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 = – 6, – 5, – 4, -3,-2,- 1.

(b) Integers between -4 and 4 = – 3, – 2, -1, .0, 1, 2, 3.

(c) Integers between -8 and -15 = -14,-13, -12,-11,-10,-9.

(d) Integers between -30 and -23 = – 29, – 28, – 27, – 26, – 25, – 24.

**Ex 6.1 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 = – 19, – 18, – 17, – 16.

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

**Ex 6.1 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) A smallest negative integer is – 1**

**(d) – 26 is greater than – 25.**

**Solution:**

(a) True (T)

(b) False (F);

Correction: -100 lies to the left of -50 on a number line.

(c) False (F);

Correction: -1 is the greater negative integer.

(d) False (F);

Correction: -26 is smaller than -25.

**Ex 6.1 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:**