# Which number has no reciprocal value

## Reciprocal

### Reciprocal of whole numbers

Whole numbers can also be written as fractions,

\ [5 \ text {is the same as} \ frac {5} {1} \]

because the division by \ (1 \) does not change the result. Therefore:

\ [\ text {The reciprocal of} \ frac {{\ colorbox {yellow} {\ (5 \)}}} {{\ colorbox {orange} {\ (1 \)}}} \ text {is} \ frac {{\ colorbox {orange} {\ (1 \)}}} {{\ colorbox {yellow} {\ (5 \)}}}. \]

**Further examples**

\ [\ text {The reciprocal of} 2 \ text {is} \ frac {1} {2}. \]

\ [\ text {The reciprocal of} 3 \ text {is} \ frac {1} {3}. \]

\ [\ text {The reciprocal of} 4 \ text {is} \ frac {1} {4}. \]

We can hold on to:

The **Reciprocal of an integer** \ (x \) is \ (\ frac {1} {x} \).

According to the power laws, \ (\ frac {1} {x} = x ^ {- 1} \), which is why the reciprocal of a number \ (x \) can generally be expressed with as well as with \ (x ^ {- 1} \).

### Property of a reciprocal

If you multiply a number by its reciprocal, you get 1.

**Examples**

\ [\ frac {{\ colorbox {yellow} {\ (2 \)}}} {{\ colorbox {orange} {\ (3 \)}}} \ cdot \ frac {{\ colorbox {orange} {\ ( 3 \)}}} {{\ colorbox {yellow} {\ (2 \)}}} = 1 \]

\ [\ frac {{\ colorbox {yellow} {\ (2 \)}}} {{\ colorbox {orange} {\ (1 \)}}} \ cdot \ frac {{\ colorbox {orange} {\ ( 1 \)}}} {{\ colorbox {yellow} {\ (2 \)}}} = 1 \]

\ [\ frac {{\ colorbox {yellow} {\ (5 \)}}} {{\ colorbox {orange} {\ (4 \)}}} \ cdot \ frac {{\ colorbox {orange} {\ ( 4 \)}}} {{\ colorbox {yellow} {\ (5 \)}}} = 1 \]

In this chapter we learned how to find the reciprocal of fractions and integers. We also now know that multiplying a number by its reciprocal is 1.

### Fractional calculation from A to Z

In the following chapters you will find everything you need to know about fractions:

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