**Integers**

Integers are whole numbers, both positive and negative, along with zero. They are represented on the number line. In this exercise, we will explore various concepts related to integers.

**Exercise 6.1**

Exercise 6.1 of NCERT Solutions for Class 6 Integers covers multiple questions related to integers. Let's discuss the questions and their solutions in detail.

**Question 1**

The first question asks to represent the following numbers on the number line: -1, -3, 4, -2, 0, -5, 6, and -8.

To represent these numbers on the number line, we can follow these steps:
1. Draw a horizontal line and mark a point representing zero.
2. For negative numbers, move to the left of zero and mark the respective points.
3. For positive numbers, move to the right of zero and mark the respective points.

**Question 2**

In the second question, we need to fill in the blank spaces with the appropriate signs (+ or -):
a) -15 + (-3) = -18
b) (-22) + 15 = -7
c) 12 + (-5) = 7
d) (-9) + (-12) = -21
e) (-6) + 7 = 1

To solve these equations, we need to follow the rules of addition and the concept of integers. Adding two negative numbers gives a negative sum, adding two positive numbers gives a positive sum, and adding a positive and a negative number depends on the magnitude of the numbers.

**Question 3**

The third question deals with the concept of subtraction of integers. We need to find the value of the following subtractions:
a) (-12) - (-8) = -12 + 8 = -4
b) 15 - (-20) = 15 + 20 = 35
c) (-7) - 10 = -7 + (-10) = -17
d) 9 - (-6) = 9 + 6 = 15
e) (-5) - 15 = -5 + (-15) = -20

Subtraction of integers can be done by converting it into addition. Subtracting a negative number is equivalent to adding its positive counterpart.

**Question 4**

The fourth question involves the concept of multiplication of integers. We need to find the value of the following multiplications:
a) (-6) × (-2) = 12
b) (-8) × 4 = -32
c) (-2) × 10 = -20
d) (-5) × (-3) = 15
e) (-12) × (-1) = 12

The rules for multiplication of integers are that the product of two positive numbers or two negative numbers is positive, and the product of a positive and a negative number is negative.

**Question 5**

The fifth question focuses on division of integers. We need to find the value of the following divisions:
a) (-24) ÷ (-6) = 4
b) (-16) ÷ 8 = -2
c) (-14) ÷ (-7) = 2
d) 20 ÷ (-4) = -5
e) (-30) ÷ (-2) = 15

The rules for division of