**Chapter 6 Integers**

### Very Short Answer Type

Question 1.

Represent the following on number line:

(a) -5

(b) 4

Solution:

(a) – 5

(b) 4

Question 2.

Identify the negative integers from the given numbers.

– 5, 3, 0, 5, – 6, 7, 3, 4, – 4, – 7

Solution:

Negative integers are – 5, – 6, – 4 and – 7 .

Question 3.

What is the additive identity of – 20?

Solution:

Additive identity of – 20 is 20.

Question 4.

What is negative of 0?

Solution:

The negative of 0 is 0 it self.

Question 5.

What is the absolute value of |- 6| ?

Solution:

Absolute value of |- 6| is 6.

Question 6.

What is the absolute value of |0| ?

Solution:

Absolute value of |0| is 0.

Question 7.

What is the negative of – 13?

Solution:

Negative of (- 13) is – (- 13) = 13.

Question 8.

What is the successor of – 7?

Solution:

The successor of -7 = -7 + 1 = -6

Question 9.

What is the predecessor of – 5?

Solution:

The predecessor of -5 is – 5 – 1 = -6.

Question 10.

Write the opposite of 50 km towards north?

Solution:

Opposite of 50 km towards north is 50 km towards south.

### Short Answer Type

Question 11.

Write the following integers in their increasing order.

– 3, 0, – 6, 5, – 4, 6, 3, – 8

Solution:

The required increasing order is:

– 8, – 6, – 4, – 3, 0, 3, 5, 6

Question 12.

Comparing the following pairs of number use > or < .

Solution:

(a) 0 > – 6

(b) – 10 < – 2

(c) – 100 < 100

(d) 2 > – 2

Question 13.

Write all the integers between the following pair of integers:

(а) 0 and – 4

(B) – 5 and 5

(c) – 8 and – 13

(d) 3 and 6

Solution:

(a) Integers between 0 and – 4 are: -3, -2, -1

(B) Integers between – 5 and 5 are: -4, -3, -2, -1, 0, 1, 2, 3, 4.

(c) Integers between – 8 and – 13 are: -12, -11, -10, -9

(d) Integers between 3 and 6 are: 4 and 5

Question 14.

Find the solution of the following additions using number line:

(a)(- 3) + 5

(B) (- 5) + (-2)

Solution:

(a)(- 3) + 5

∴ (-3) + 5 = 2

(B) (- 5) + (-2)

∴ (-5) + (-2) = (-7)

Question 15.

Find the sum of the following integers:

(a) (- 8) + (+ 5) + (- 3) + (- 2)

(B) (- 7) + (- 9) + (+ 4) + (+ 3)

Solution:

(a) (- 8) + (+ 5) + (- 3) + (- 2)

= (- 8) + (+ 5) – (3 + 2)

= (- 8) + (+ 5) – (5)

= (- 8) + 0 = – 8 [ ∵ (+ a) + (- a) = 0]

(b) (- 7) + (- 9) + (+ 4) + (+ 3)

= (- 7) + (- 9) + (4 + 3)

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

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

= 0 + (- 9) = – 9 [ ∵ (- a) + (+ a) = 0]

### Long Answer Type

Question 16.

Ramesh thinks of an integer. He subtracts 12 from it and gets the result as – 6. What was the integer he thought of?

Solution:

The given sum can be written as under.

(___) – (12) = – 6

The required integer is 12 – 6 = 6.

Question 17.

Fill in the blanks:

(a) To subtract (- 8) from 13, we add ……… to 13.

(b) To subtract 5 from (- 12), we add ……… to (-13)

(c) The negative of a negative integer is a ……… integer.

(d) An integer when added to its opposite gives ……… as the sum.

(e) -4 + …….. = 1

(f) 4 – (- 3) = ………

(g) ……… + (- 79) = 19

Solution:

(a) 8

(b) – 4

(c) positive

(d) 0

(e) 5

(f) 7

(g) 98

Question 18.

Determines:

(a) | 5 | – |- 3 |

(b) | 5 – 6|+ | -1 |

(c) – 7 + | – 3 |

(d) | 5 | + | – 12 |

Solution:

(a) | 5 | – | – 3 | = 5 – 3 = 2 [∵ |a| = a and |- a| = a]

(b) |5 – 6 | + |- 1| = |- 1| + |-1| = 1 + 1 = 2

(c) – 7 + | – 3 | = -7 + 3 = -4

(d) | 5 | + | – 12 | = 5 + 12 = 17

### Higher Order Thinking Skills (HOTS)

Question 19.

If * is an operation such that for two integers p and q, p * q = p + q – 2, then find:

(a) 6 * 2

(b) (- 2) * (- 3)

(c) (- 2) * (4)

(d) (+ 3) * (- 1)

Solution:

(a) Given that: p * q = p + q – 2

⇒ 6 * 2 = 6 + 2 – 2 = 6 + 0 = 6

Thus, 6 * 2 = 6.

(b) Given that: p * q = p + q – 2

⇒ (- 2) * (- 3) = (- 2) + (- 3) – 2

= -5 – 2 = -7.

Thus, (- 2) * (- 3) = – 7.

(c) Given that: p * q = p + q – 2

⇒ (- 2) * (4) = (- 2) + (4) – 2 = 2 – 2 = 0.

Thus, (- 2) * (4) = 0.

(d) Given that p*q – p + q – 2

⇒ (+ 3) * (- 1) = (+ 3) + (- 1) – 2 = 2 – 2 = 0

Thus, (+ 3) * (- 1) = 0.

Question 20.

Complete the table:

Solution:

The required table can be completed as under: