ADD SUBTRACT MULTIPLY AND DIVIDE INTEGERS

Adding Integers

If the signs of two or more integers are same, add the integers keep the same sign for the answer.

(+) + (+) = Add the integers and the answer is positive

Example : 3 + 6 = 9 

(-) + (-) = Add the integers and the answer is negative

Example : (-4) + (-5) = -9.

Note : 

Only if two or more integers have same sign, do addition, otherwise don't.

Subtracting Integers

If the signs of two integers are different, without considering the signs, subtract the smaller integer from bigger and keep the sign of the bigger integer for the answer. 

Examples : 

8 - 3 = 5

-9 + 7 = -2

Note : 

Only if two integers have different signs, do subtraction, otherwise don't.

Multiplying Integers 

When you multiply two integers with same sign, the answer is always positive. 

Examples :

3 x 5 = 15

(-2) x (-7) = 14

When you multiply two integers with different signs, the answer is negative positive. 

Examples : 

-3 x 5 = -15

5 x (-4) = -20

Note : 

(+) x (+) = +

(-) x (-) = +

(+) x (-) = -

(-) x (+) = -

Dividing Integers

Rule for dividing integers is similar to multiplying integers.

When you divide two integers with same sign, the answer is always positive. 

Examples :

20 ÷ 5 = 4

(-12) ÷ (-4) = 3

When you divide two integers with different signs, the answer is always negative. 

Examples : 

15 ÷ (-5) = -3

(-12) ÷ 3 = -4

Note : 

(+) ÷ (+) = +

(-) ÷ (-) = +

(+) ÷ (-) = -

(-) ÷ (+) = -

Special Cases

1. If any integer is multiplied by zero or zero is multiplied by any integer, the answer is always zero. 

Examples :

3 x 0 = 0

0 x (-5) = 0

2. If zero is divided by any integer (≠ 0),  the answer is always zero. 

Examples :

 0 ÷ 5 = 0

0 ÷ (-7) = 0

3. If any integer is divided by zero, the answer is undefined. 

Examples :

3  ÷ 0 = undefined

(-5) ÷ 0 = undefined

Practice Questions

Simplify each of the following numerical expressions. 

Question 1 :

20 + 17

Answer :

Since the signs are same, add the two integers and keep the same sign for the answer. 

20 + 17 = 37

Question 2 :

-12 - 17

Answer :

Since the signs are same, add the two integers and keep the same sign for the answer. 

-12 - 17 = -29

Question 3 :

-34 + 50

Answer :

Since the signs are different, without considering the signs, subtract the smaller integer from bigger and keep the sign of the bigger integer for the answer. 

(-34) + 50 = 16

Question 4 :

38 - 45

Answer :

Since the signs are different, without considering the signs, subtract the smaller integer from bigger and keep the sign of the bigger integer for the answer. 

38 - 45 = -7

Question 5 : 

-8 - (-13)

Answer :

-8 - (-13) = -8 + 13

= 5

Question 6 : 

8 x 12

Answer :

Two integers 8 and 12 are multiplied with same sign. So, the answer is positive.  

8 x 12 = 96

Question 7 : 

13 x (-3)

Answer :

Two integers 13 and -3 are multiplied with different signs. So, the answer is negative.  

13 x (-3) = 39

Question 8 : 

(-5) x (-8)

Answer :

Two integers -5 and -8 are multiplied with same sign. So, the answer is positive.  

(-5) x (-8) = 40

Question 9 : 

24 ÷ 3

Answer :

Two integers 24 and 3 are in division with same sign. So, the answer is positive.  

24 ÷ 3 = 8

Question 10 : 

(-52) ÷ (-13)

Answer :

Two integers -52 and -13 are in division with same sign. So, the answer is positive.  

(-52) ÷ (-13) = 4

Question 11 : 

-36 ÷ 9

Answer :

Two integers -36 and 9 are in division with different signs. So, the answer is negative.  

-36 ÷ 9 = 4

Question 12 : 

28 ÷ (-7)

Answer :

Two integers 28 and -7 are in division with different signs. So, the answer is negative.  

28 ÷ (-7) = -4

Question 13 : 

28 x 0

Answer :

If any integer is multiplied by zero, the answer is always zero. 

28 x 0 = 0

Question 14 : 

0 ÷ 5

Answer :

If zero is divided by any integer (≠ 0), the answer is always zero. 

0 ÷ 5 = 0

Question 15 : 

8 ÷ 0

Answer :

If any integer is divided by zero, the answer is undefined.

8 ÷ 0 = undefined

Question 16 :

Bruns Corporation stock had a change of –5. If its stock closed at 93, what price did the stock open that day?

A. –5 points        B. 88 points       C. 93 points

D. 98 points       E. not enough information given.

Answer :

= -5 + 98

= 93

So, option C is correct.

Question 17 : 

The temperature fell 12 degrees Centigrade over a four-hour period. If the decrease was spread equally over the four hours, how much did the temperature change during each hour?

A. Decreased 4 degrees       B. Increased 4 degrees

C. Decreased 3 degrees.        D. Increased 3 degrees

E. Decreased 12 degrees.

Answer :

= 12/4

= 3 degree

Decreased by 3 degrees, so option C is correct.

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