BASIC MATHEMATICS-1

ADDITION , MULTIPLICATION AND 

SUBTRACTION 

A). ADDITION 

RULE

Type of Numbers	Operation	Result	Example
Positive + Positive	Add	Positive (+)	10 + 15 = 25
Negative + Negative	Add	Negative (-)	(-10) + (-15) = -25
Positive + Negative*	Subtract	Positive (+)	(-10) + 15 =5
Negative + Positive*	Subtract	Negative (-)	10 + (-15)= -5

v    Whenever a positive number and a negative number are added, the sign of the greater number will decide the operation and sign of the result. In the above example 10 + (-15) = -5 and (-10) + 15 =5; here, without sign 15 is greater than 10 hence, numbers will be subtracted and the answer will give the sign of the greater number.

v    Also, since we know the multiplication of negative sign and a positive sign will result in negative sign, therefore if we write 10 + (-5), it means the ‘+’ sign here is multiplied by ‘-’ inside the bracket. Therefore, the result becomes 10 – 5 = 5.

v    Alternatively, to find the sum of a positive and a negative integer, take the absolute value (“absolute value” means to remove any negative sign of a number, and make the number positive) of each integer and then subtract these values. Take above example, 10 + (-15); absolute value of 10 is 10 and -15 is 15.

⇒ 10 – 15 = -5

Thus, we can conclude the above table as follow:

Adding two positive integers results in positive integer Adding two negative integers results in sum of integers with a negative sign. Addition of a positive and a negative integer gives either a positive or negative-sum depending on the value of the given numbers.

B). SUBTRACTION OF INTEGERS

RULE

Like in addition, the subtraction of integers also has three possibilities. They are:

• Subtraction between two positive numbers
• Subtraction between two negative numbers
• Subtraction between a positive number and a negative number

For ease of calculation, we need to renovate subtraction problems into addition problems. There are two steps to this:

1. Convert the subtraction sign into an addition sign.

2. After converting the sign, take the inverse of the number which comes after the sign.

Once the transformation is done, follow the rules of addition given above.

For example, find the value of: (-5) – (7)

Step 1: Change the subtraction sign into an addition sign

⇒ (-5) + (7)

Step 2: Take the inverse of the number which comes after the sign

⇒ –5 + (-7)                                  (opposite of 7 is -7)

⇒ –5 + (-7) = -12      [Add and put the sign of greater number]

C). MULTIPLICATION

RULE

In addition and subtraction, the sign of the resulted integer depends on the sign of the largest value. For example, -7+4 = -3 but in the case of multiplication of integers, two signs are multiplied together. 

(+) × (+) = +	Plus x Plus = Plus
(+) x (-) = –	Plus x Minus = Minus
(-) × (+) = –	Minus x Plus = Minus
(-) × (-) = +	Minus x Minus = Plus

Rules: 

• When two positive integers are multiplied then the result is positive.
• When two negative integers are multiplied then also the result is positive.
• But when one positive and one negative integer is multiplied, then the result is negative.
• When there is no symbol, then the integer is positive.

Solved Examples

Example 1: Evaluate the following:

1. (-5 )+  9
2. (-1) – ( -2)

Solution:

1. (-5 )+ 9 = 4  [Subtract and put the sign of greater number]
2. (-1) – ( -2)

⇒ (-1) + (-2)   [Transform subtraction problems into addition problems]

⇒ (-1) + (2)    [Subtract and put the sign of greater number]

Hence,

(-1) – ( -2) = 1

Example 2: Add -10 and -19.

Solution: -10 and -19 are both negative numbers. So if we add them, we get the sum in negative, such as;

(-10)+(-19) = -10-19 = -29

Example 3: Subtract -10 and -19.

Solution: (-10) – (-19)

Here, the two minus symbol will become plus. So,

-10 + 19 = 19 -10 = 9

Example 4: Evaluate 9 – 10 +(-5) + 6

Solution: First open the brackets.

9 – 10 -5 + 6

Add the positive and negative integers separately.

= 9 + 6 – 10 -5

= 15 – 15

= 0

Calculate the following:
TRY YOURSELF

1 + 5  = 

20 + 25= 

10 + 16  = 

20 – 8  = 

40 – 10  = 

6 – 4 ÷ = 

9 × 5  = 

4 × 3  = 

8 × 3  = 

7 × 3 = 

20 ÷ 2  = 

9 ÷ 3  = 

18 ÷ 3  = 

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