Math Assignment Help With Inverse Operations And Reciprocals

Chapter 7. Inverse Operations And Reciprocals

7.1 Introduction: The operation that reverses the effect of another operation is said to be an inverse operation. In another words, two operations are said to be inverse of each other, if one of them undoes the effect of another.

  • Addition and Subtraction are inverse operation of each other.
  • Multiplication and Division are inverse operation of each other.
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7.2 Inverse relationship between Addition and Subtraction:

Subtraction is the inverse operation of addition and vice versa. While adding a certain amount to a given quantity, it increases by that amount, whereas subtracting the same amount to the new increased quantity you get the original one again.

It can be understood easily by the following example:

You are given 35 apples. You add 5 apples more to them. Now the total amounts of apples you have are

35+5 = 40 (addition)

Now take out five apples from the new amount of apples.

40 – 5 = 35 (subtraction)

This is the amount you originally had.

Few more examples:

i) 30 + 3 = 33

Can be reversed by

33 – 3 = 30

ii) 12 +12 = 24

Can be reversed by

24 – 12 = 12

Similarly, subtraction is reversed by addition

25 – 6 = 19

Can be reversed by

19 + 6 = 25

The reason behind is that we are dealing with an equation. An equation is balanced. If exactly the same thing is done to both sides of the equation, it will remain balanced.

7.3 Inverse relationship between Multiplication and Division:

Division is the inverse operation of multiplication and vice versa. While multiplying a amount x to a given quantity, it increases x times, whereas dividing the same amount to the new increased quantity you get the original one again.

For example: multiply 4 to 25

Can be reversed by

100/4 = 25

Similarly, division is reversed by multiplication

Example:

36/6 = 6

7.4 Reciprocals:

reciprocal is the multiplicative inverse. In simple words, it is 1 divided by the number.

Reciprocal = 1/number

We know that when a number is dived by 1, its value does not change. So turn it upside down and it becomes the reciprocal of that number.

Example: 5 = 5/1

Reciprocal = 1/5

A point of concern is on multiplying a number by its reciprocal you get 1

2 x ½ = 1

5 x 1/5 = 1

A point to be noted is that every number has a reciprocal except zero. Reciprocal of zero is not defined.

Reciprocal of a Variable: If you are given a variable "x", its reciprocal is "1/x".

Likewise, if you are given x/y, its reciprocal will be y/x.

Reciprocal of x is 1/x but it can also be shown as x-1.

Example: What is the reciprocal of (x – 1)/(y+1)

Reciprocal = (y + 1)/ (x – 1)

Reciprocal of a fraction:

Example: Fraction Reciprocal

5/4 4/5

6/7 7/6

Reciprocal of Mixed fractions

1. First convert it to an improper fraction:
2. Reverse the numerator and denominator

Example: find the reciprocal of 2 ¾

Solution: first convert it into proper fraction

¾ = 11/4

Find the reciprocal

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