FUNDAMENTAL OPERATIONS ON INTEGERS

In Math, The whole numbers and negative numbers together are called integers. The set of all integers is denoted by Z.

Z = {... - 2, - 1,0,1,2, ...}, is the set of all integers

Here, we are going to see, how the four fundamental operations in math (Addition, Subtraction, Multiplication and Division) work on integers.

Addition of Integers

Sum of two integers is again an integer.

Examples :

i) 8 + 4 = 12

ii) 10 + (-4) = 10 - 4 = 6

iii) 6 + 0 = 6

iv) 6 + 5 = 11

v) 4 + 0 = 4

Note :

(i) The addition of two positive integers is always a positive integer.

3 + 5 = 8

(ii) The addition of two negative integers is always a negative integer.

(-2) + (-3) = -5

When adding two negative integers, add them as usual and take negative sign to the answer.

(iii) The addition of a positive integer and a negative integer can either be a positive integer or negative integer, depending on the sign of the larger one.

8 + (-2) = 5

-5 + 3 = -2

When adding a positive integer and a negative integer, find the difference of them and take sign of the larger integer to the answer.

Subtraction of Integers

To subtract an integer from another integer, add the additive inverse of the second number to the first number.

Examples :

i) 5 – 3 = 5 + (additive inverse of 3) = 5 + (–3) = 2.

ii) 6 – (–2) = 6 + (additive inverse of –2) = 6 + 2 = 8.

iii) (–8) – (5) = (–8) + (–5) = – 13.

iv) (–20) – (–6) = –20 + 6 = –14.

Multiplication of Integers

We know that multiplication is repeated addition in the set of whole numbers. Let us learn about it now in the set of integers.

Rules :

1. The product of two positive integers is a positive integer.

2. The product of two negative integers is a positive integer.

3. The product of a positive integer and a negative integer is a negative integer.

Examples :

5 x 8 = 40

(-5) x (-9) = 45

(-15) x 3 = -(15 x 3) = -45

12 x (-4) = -(12 x 4) = -48

Division of Integers

We know that division is the inverse operation of multiplication.

Positive integer/Positive integer = Positive number

Negative integer/Negative integer =  Positive number

Negative integer/Positive integer  =  Negative number

Positive integer/Negative integer  =  Negative number

Examples :

250/50 = 5

(-144)/(-12) = 12

(-120)/20 = -6

100/(-25) = -4

Division by Zero

Division of any number (except 0) by zero  is meaningless because division by zero is not defined.

Remarks

1. Addition of any integer and zero or zero and any integer will result the same integer.

3 + 0 = 3

0 + 5 = 5

2. Subtract zero from any integer will result the same integer.

5 - 0 = 5

3. Subtract any integer from zero will result the same integer with opposite sign.

Subtracting 5 from zero :

0 - 5 = -5

Subtracting -3 from zero :

0 - (-3) = 0 + 3 = 3

4. Multiplication of any integer and a or 1 and any integer will result the same integer.

3 x 1 = 3

1 x 5 = 5

5. Dividing any integer by 1 will result the same integer.

7/1 = 7

6. Dividing zero by any integer will result zero.

0/5 = 0

7. Dividing any integer by zero is undefined.

7/0 = Undefined.

Problem 1 :

The temperature is −3°F at 7 a.m. During the next four hours, the temperature increases 21°F. What is the temperature at 11 a.m.?

Solution :

Temperature at 7 am = -3°F

Next four hours, the temperature increases to 21°F

Temperature at 11 am = -3 + 21

= 17°F

Problem 2 :

Your bank account has a balance of −$12. You deposit $60. What is your new balance?

Solution :

Your balance = −$12

Amount depositing = $60

New balance = -12 + 60

= $48

So, the new balance is $48.

Problem 3 :

In football, a team must gain 10 yards to get a first down. The team gains 6 yards on the first play, loses 3 yards on the second play, and gains 8 yards on the third play. Which expression can be used to decide whether the team gets a first down?

a)   10 + 6 − 3 + 8            b)  6 + (−3) + 8

c)  6 + (−3) + (−8)

Solution :

Gains 6 yards on the first play

Loses 3 yards in the second play

Gains 8 yards in the third play

+6 - 3 + 8

So, option b is correct.

Problem 4 :

Julia is planning a four-day trip to visit her cousin Kristy. She has figured out that she’ll need $10 the first day, $15 the second day, $25 the third day, and $15 the last day. How much money will Julia need to take on her trip?

Solution :

Amount spent by Julia = 10 + 15 + 25 + 15

= $65

So, the total amount spent by Julia is $65.

Problem 5 :

Melissa’s friends are soliciting contributions to help homeless people in their community. They will donate all of the money to an organization called Help the Homeless. Melissa gave $22, Jill contributed $15, Joe gave $12, Sam’s Used Cars donated $75, and Hill Street Church donated $125. How much money did Melissa and her friends collect?

Solution :

Amount donated by Melisa and her friend :

= 22 + 15 + 12 + 75 + 125

= $249

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.