**3.1.1 Introduction**: We can use the number line to explain the addition of signed numbers.

**3.2 Arithmetic Operations **

**3.2.1 Addition**

**3.2.1.1 Addition of integer with like signs: **Find the sum of the absolute values and write the answer along with the common number sign.

Take two** positive integers** like 2 and 4 are to be added.

(+2) + (+4) = (+6)

The “+“sign inside the parentheses shows the number sign and the one outside the parenthesis is sign of addition.

Draw the number line

Find 2 on the number line, and go four units more in the positive direction. The number you get is (+6)

To add **two negative integers**, such as -2 and -4, find -2 on the number line and then go four units more in the negative direction. The number you get is -6

To add a positive and a negative integer find the difference between their absolute value and place sign of the greater of the two numbers

Take two numbers -3 and +2. The difference between their absolute value is 1, and on comparing the absolute numbers we find that 3 > 2 therefore (-) sign will be taken along with the result

And can be showed as

(-3) + (+2) = (-1)

-3 + 2 = -1

Draw the number line

Place -3 and +2 in a number line. Start from -3, move 2 units towards positive direction.

The number we get is -1

**3.2.1.1 Subtraction of integer with like signs: **Find the difference of the absolute values and write the answer along with the common number sign.

Take two positive integers like +2and+ 4 are to be subtracted and can be showed as

(+4) - (+2) = (+2)

Draw the number line

Find +4 on the number line, and go two units in the negative direction. The number you get is +2

To subtract **two negative integers**, such as -2 and -4, Negative integers like (-2) and (-4) are to be subtracted and can be showed as

(-2) - (-4) = (-6)

find -2 on the number line and then go four units more in the negative direction. The number you get is (-6)

**3.2.1.2 Subtraction of integer with unlike signs: **To subtract a positive and a negative integer find the sum of their absolute value and place sign of the greater of the two numbers

Take a positive integer and a negative integer like +3 and - 4 respectively, to be subtracted. The sum of their absolute values is 7 and since 4> 3 answer will be -7

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

Draw the number line

Find -4 on the number line, and go three units in the negative direction. The number is -7

**3.2.3.1 ****Multiplication of integers with like signs:** Multiplication of two integers with like signs (either negative or positive) gives a **positive **product

**(+) x (+) = (+)**

**(-) x (-) = (+)**

Example: (+4) x (+5) = +20

(-4) x (-5) = +20

**3.2.3.2 ****Multiplication of integers with unlike signs:** Multiplication of two integers with unlike signs (one negative and other positive) gives a **negative** product.

**(+) x (-) = (-)**

Example: (+7) x (-5) = -35

**3.2.4 Division**

**3.2.4.1 Divis****ion of integers with like signs:** Division of two integers with like signs (either negative or positive) gives a **positive **quotient

**(+) / (+) = (+)**

**(-) x (-) = (+)**

Example: (+10) **/** (+5) = +2

(-10) **/ **(-5) = +2

**3.2.4.2 Divis****ion of integers with unlike signs:** Division of two integers with unlike signs (one negative and other positive) gives a **negative** quotient.

**(+) / (-) = (-)**

Example: (+42) / (-7) = -6

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