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# Fractions and Equivalent Decimals

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 Sub Topics The decimal number and the fraction are almost similar. Decimal numbers are derived from fractions only. So there exist a equivalent decimals for every fraction. Decimals are numbers whose denominator is power of ten, the basic difference between the fractions and the decimals are that the fractions have the denominator and numerator whereas the decimal number only is a number that is separated by (.) decimal separator or period. Example of some fractions are: $\frac{1}{2}$ = 0.5, $\frac{3}{2}$ = 1.5, $\frac{4}{2}$ = 2 (which is also a decimal with value 2. 0) If we want to find a decimal from a fraction, we can do it in a very simple method by making the denominator in the multiple of 10 and with which the numerator will also get simplified: Example: $\frac{3}{4}$ = $\frac{3*25}{4*25}$ = $\frac{75}{100}$ = 0.75 There are certain fraction and equivalent decimals whose exact values are difficult to find. For example we want to divide $\frac{8}{9}$ we will get the equivalent decimal as 0.88888888....... This gives a recurring value which does not get the exact answer in such case we can take an approximate value for the given fraction. In this case $\frac{8}{9}$ = 0.89

## Fractions and Decimals Definition

Fractions describes how many parts a certain size can be where as a decimal has ten at its base. Fractions and decimals are equivalent representations of the part of a whole. It is easy to express any proper fraction or improper fraction in terms of decimals. Decimals are the representation of number in combination of whole and decimal part.A decimal is a way of representing a fraction.

## Convert Fractions into Decimals

A number with base 10 is known as a decimal number. A decimal is a fraction with the denominator of 10.
If we want to convert a fraction to a decimal, the simple method is by making the denominator of the fraction a multiple of 10 with which the numerator will also get altered and changing the place value of the decimal.
Given below are the steps to convert fraction into decimals.
1. Multiply the denominator of the fraction in such a way that it becomes 10, 100, 1000 or 1 followed by zeroes.
2. Multiply that number to numerator also by which help we got 10, 100 or 1000.
3. Place decimal in numerator in such a way that its place is just equivalent to number of zeroes of denominators counted from the right most digit of numerator.
Example: Express $\frac{35}{25}$ as a decimal

Solution:
Given: $\frac{35}{25}$

To make the denominator 100 we multiply 25 by 4.
Multiply numerator and denominator by 4

$\frac{35 * 4}{25*4}$ = $\frac{140}{100}$

= $\frac{14}{10}$

Since 10 is having one zero shift one place from the right.

Therefore $\frac{35}{25}$  = 1.4

## Decimal Equivalents of Fractions

Equivalent fractions are the fractions representing same part of an object. They are equal to each other and they look different. The fractions have a different numerator and a denominator. Equivalent Fractions is one of the important concepts within the study of fractions. To get an equivalent fraction you can multiply or divide but never add or subtract. Equivalent means equal in value. Fraction can look different but they can have same value and hence equivalent.
These fractions have the value same, $\frac{1}{8}$ = $\frac{3}{24}$ = $\frac{7}{56}$

Example: If an apple is cut into two pieces, each piece is also one-half of the apple. If an apple is cut into 6 pieces, then that three pieces denote the same amount of apple that $\frac{1}{2}$ did. We say that $\frac{1}{2}$ is equivalent to $\frac{3}{6}$

If a decimal number is given then it can easily be converted into an equivalent fraction. If two fractions are given then it can be found easily whether they are equivalent or not. Simplify both the fraction to lowest form. If both comes equal, then they are equivalent fractions else they are not.

## Examples of Equivalent Fractions

Example 1: Find the unknown value from the equation, $\frac{5}{9}$ =$\frac{30}{?}$

Solution:
Given: $\frac{5}{9}$ =$\frac{30}{?}$

We know the numerators of the two fractions. They are 5 and 30.

Relation between them 5 times 6 is 30. So, multiply the denominator also with 6.

So 9 x 6 = 54. $\frac{5}{9}$ is equivalent to $\frac{30}{54}$.

Therefore the unknown in the given fraction  is 54.

Hence $\frac{5}{9}$ = $\frac{30}{54}$

Example 2:  Convert $\frac{5}{4}$ to decimal.

Solution: In the given fraction $\frac{5}{4}$, 4 is the denominator. As the denominator should be in multiples of 10.
Multiply 4 with 25 = 100
As multiplication with 25 gave 100.

So, new fraction will be $\frac{5}{4}$ × $\frac{25}{25}$

= $\frac{125}{100}$

Since 100 is having two zeroes shift two places from the right.
On shifting, we get 1.25

Therefore, $\frac{5}{4}$ = 1.25