Conversion of Fractions: In mathematics, a fraction is used to represent a piece of something larger. It depicts the whole’s equal pieces. The numerator and denominator are the two elements of a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. The numerator specifies the number of equal parts taken, whereas the denominator specifies the total number of equal parts in the total.

Conversion means to change the expression from one form to another. Conversion of fraction includes the conversion of the fraction to decimals, conversion of fractions to per cent, Conversion of an improper fraction to mixed fraction and vice versa. Let us have a look at the article to understand the concept in a better way.

Definition of Fractions

A fraction can be defined as a part of a whole number.

The numbers of the form \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b \neq 0\), are called fractions.

Here, \(a \rightarrow\) Numerator and \(b \rightarrow\) Denominator.

Examples: \(\frac{2}{4}, \frac{5}{10}, \frac{1}{4}, \frac{3}{17} \ldots\)

In the above figure, the figure has been divided into \(7\) equal parts. Out of these \(7\) equal parts, \(4\) parts are shaded. The shaded portion represents \({\text{four}} – {\text{sevenths}}\).

Numerically, it is denoted as \(\frac{4}{7}\).

Here, \(\frac{4}{7}\) is a fraction, and \({\text{four}} – {\text{sevenths}}\) is a fractional number.

Types of Fractions 

There are \(3\) different types of fractions are,

1. Proper Fractions: A fraction whose numerator is less than its denominator is called a proper fraction.
Examples: \(\frac{2}{4}, \frac{5}{10}, \frac{1}{4}, \frac{3}{17}\) etc. are all proper fractions.

2. Improper Fractions: A fraction whose numerator is greater than its denominator is called an improper fraction.
Examples: \(\frac{5}{4}, \frac{13}{10}, \frac{11}{7}, \frac{23}{17}\), etc., are all improper fractions.

3. Mixed Fractions: A combination of a whole number and a proper fraction is called a mixed fraction.
Examples: \(1 \frac{2}{4}, 3 \frac{5}{10}, 5 \frac{1}{4}, \quad 6 \frac{3}{17}\), etc., are all mixed fractions.

4. Like Fractions: The group of two or more fractions with the same denominators is Like Fractions.
Examples: \(\frac{1}{2}, \frac{2}{2}, \frac{3}{2}, \frac{4}{2}, \frac{5}{2}\), etc., are all like fractions.

5. Unlike Fractions: The group of two or more fractions with different denominators is called Like Fractions.
Examples: \(\frac{1}{2}, \frac{2}{4}, \frac{3}{5}, \frac{4}{7}, \frac{5}{8}\), etc., are all unlike fractions.

6. Unit Fractions: A unit fraction is any fraction with 1 as its numerator and an integer for the denominator.
Examples: \(\frac{1}{2}, \frac{1}{4}, \frac{1}{5}, \frac{1}{7}, \frac{1}{8}\), etc., are all unit fractions.

Definition of Conversion of Fractions

Conversion of Fractions means to change the fraction from one form to another form. For example: like fractions to decimals and fractions to percents etc.

Conversion of Unlike Fractions to Like Fractions

To convert the unlike fractions to like fractions follow the below steps:

1. Find the LCM of the denominators of the given fractions.
2. Find the quotient by dividing the LCM by the denominator of the given fractions.
3. Multiply the numerator by the corresponding quotient.

Example: Convert \(\frac{4}{9}\) and \(\frac{5}{6}\) to like fractions.
First take the L.C.M for the denominators
L.C.M of \(9\) and \(6=18\)
\(\frac{4}{9}=\frac{4 \times 2}{9 \times 2}=\frac{8}{18}\)
\(\frac{5}{6}=\frac{5 \times 3}{6 \times 3}=\frac{15}{18}\)
So, \(\frac{8}{18}\) and \(\frac{15}{18}\) are with the same denominator and are like fractions.

Conversion of an Improper Fraction to a Mixed Fraction

To convert an Improper Fraction to a Mixed Fraction can follow these steps:

1. Divide the numerator of the fraction by the denominator of the fraction and note down the quotient and remainder.
2. Write down the quotient as the whole number part of the fraction.
3. The denominator remains the same as the denominator of the improper fraction.
4. Write down any remainder as the numerator.
5. Write the mixed fraction as \({\text{Quotient}}\frac{{{\text{Remainder}}}}{{{\text{Denominator}}}}\).

Example: Express the following improper fraction as a mixed fraction: \(\frac{15}{7}\)
If we divide \(15\) by \(7\) , we get \(2\) as the quotient and \(1\) as the remainder.
So, \(\frac{15}{7}\) can be written as \(2 \frac{1}{7}\).
\(\Rightarrow \frac{15}{7}=2 \frac{1}{7}\)

Conversion of a Mixed Fraction to an Improper Fraction

To convert a mixed fraction to an improper fraction, follow these steps:

1. Multiply the denominator of the fractional part by the whole number part.
2. Add the numerator with the product.
3. This sum becomes the numerator of the improper fraction. The denominator of the mixed fraction remains the denominator of the improper fraction.
4. Hence, the improper fraction is given by:

\({\text{Improper fraction}} = \frac{{\left({{\text{whole number}} \times {\text{Denominator}}} \right) + {\text{Numerator}}}}{{{\text{Deniminator}}}}\)

Example: Convert the mixed fraction \(12 \frac{1}{8}\) to an improper fraction.

Use the formula,

\({\text{Improper fraction}} = \frac{{\left({{\text{whole number}} \times {\text{Denominator}}} \right) + {\text{Numerator}}}}{{{\text{Deniminator}}}}\)

So, we have, \(2 \frac{1}{8}=\frac{(12 \times 8)+1}{8}=\frac{97}{8}\)

So, \(2 \frac{1}{7}\) can be written as \(\frac{15}{7}\) in improper fraction.

\(\Rightarrow \frac{15}{7}=2 \frac{1}{7}\)

Conversion of Fractions to Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

Example-1: Convert \(\frac{2}{{10}}\) to decimal form.

Divide the numerator by the denominator.
\(\frac{2}{10}=0.2\)

Example-2: Convert \(\frac{20}{50}\) to decimal form.

Divide the numerator by the denominator.
\(\frac{20}{50}=0.4\)

Example-3: Convert \(\frac{30}{100}\) to decimal form.

Divide the numerator by the denominator.

\(\frac{30}{100}=0.3\)

Convertion of Decimal to Fraction

We can convert a decimal to a fraction by using the following steps,  

In this case, we shall use the decimal \(0.25\) as an example.

1. Rewrite the decimal number as a fraction where the decimal number is the numerator and the denominator is one.
2. Multiply both the numerator and the denominator by \(10\) to the power of the number of digits after the decimal point. If there is one value after the decimal, multiply by \(10\) , if there are two, then multiply by \(100\), if there are three, then multiply by \(1,000\), etc.
3. In the case of converting \(0.25\) to a fraction, there are two digits after the decimal point. Since \(10\) to the \(2nd\) power is \(100\), we have to multiply both the numerator and denominator by \(100\) in step two.
4. Express the fraction in the simplest or reduced form.

So, we have, \(0.25=\frac{25}{100}=\frac{1}{4}\)

Conversion of Fractions to Percents

To convert a fraction to a per cent, first, divide the numerator by the denominator. Then multiply the decimal by \(100\) and write \(\% \) sign after that.

Example-1: Convert \(\frac{2}{8}\) into per cent.
So, \( \frac{2}{8}=0.25 \times 100=25 \%\)

Example-2: Convert \(\frac{4}{25}\) into per cent.
So, \(\frac{4}{25}=0.16 \times 100=16 \%\)

Example-3: Convert \(\frac{30}{100}\) to per cent.
To convert a fraction to a per cent, first, divide the numerator by the denominator. Then multiply the decimal by \(100\).
So, \(\frac{30}{100}=0.3 \times 100=30 \%\)

Solved Examples on Conversion of Fractions (Practice Problems)

Q.1. Convert \(\frac{7}{10}\) to decimal.
Ans: To convert \(\frac{7}{10}\) to a decimal, divide the numerator by the denominator.
So, \(\frac{7}{10}=0.7\)
Hence, the decimal form of \(\frac{7}{10}\) can be written as \(0.7\)

Q.2. Convert the mixed fraction \(11 \frac{1}{8}\) to an improper fraction.
Ans: Use the formula,
\({\text{Improper fraction}} = \frac{{\left({{\text{whole number}} \times {\text{Denominator}}} \right) + {\text{Numerator}}}}{{{\text{Deniminator}}}}\)
So, \(11 \frac{1}{8}=\frac{(1 \times 8)+1}{8}=\frac{80}{8}\)

Q.3. Convert \(\frac{2}{10}\) into percent.
Ans: To convert a fraction to a per cent, first divide the numerator by the denominator. Then multiply the decimal by \(100\).
So, \(\frac{2}{10}=0.2 \times 100=20 \%\)
Hence, the obtained per cent is \(20 \%\).

Q.4. Express the following improper fraction as a mixed fraction: \(\frac{17}{5}\)
Ans: If we divide \(17\) by \(5\), we get \(3\) as the quotient and \(2\) as the remainder.
So, \(\frac{17}{5}\) can be written as \(3 \frac{2}{5}\)
So, \(\frac{17}{5}=3 \frac{2}{5}\)
Hence, the obtained mixed fraction is \(3 \frac{2}{5}\).

Q.5. Heera got \(\frac{3}{4}\) of the questions correct on the school test. How is that fraction written as a percent?
Ans: To convert a fraction to a per cent, first divide the numerator by the denominator.
Then multiply the decimal by \(100\).
So, \(\frac{3}{4}=0.75=0.75 \times 100=75 \%\)
Hence, Heera got \(75 \%\) of the test result.

Q.6. Each part of a multipart question on a test is worth the same number of points. The whole question is worth \(37.5\) points. Daniel got \(\frac{1}{4}\) of the parts of a question correct. How many points did Daniel receive?
Ans: Convert the fraction \(\frac{1}{4}\) as the decimal \(0.25\).
So, \(\frac{1}{4} \times 37.5=0.25 \times 37.5\)
Multiply \(0.25 \times 37.5=9.375\)
Hence, Daniel received \(9.375\) points.

Q.7. Convert \(0.00093\) to a fraction.
Ans: Given decimal fraction is \(0.00093\).
To convert \(0.00093\) into a fractional number, first we need to write in the numerator \(93\), leaving out the decimal point and then write \(100000\) in the denominator since after the decimal point there are two numbers.
Therefore, \(0.00093=\frac{93}{100000}\)

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Summary 

Fractions are defined as pieces of a whole in mathematics. The whole might be a single object or a collection of things. When we cut a slice of cake from the entire cake in real life, the portion is the fraction of the cake. A fraction is a term that comes from the Latin language. “Fractus” means “broken” in Latin. Words were used to indicate the fraction in ancient times. It was afterwards reintroduced in a numerical format. A piece or sector of any quantity is also known as a fraction. It is represented by the ‘/’ sign, as in a/b. For example, 2/4 is a fraction with the numerator in the top section and the denominator in the bottom part.

Conversion of Fractions means to change the fraction from one form to another form like a fraction to decimals and fractions to percents etc. You must note that to convert a fraction to a decimal, you must divide the numerator by the denominator. Furthermore, to convert a fraction to a per cent, first, divide the numerator by the denominator. Then multiply the decimal by \(100\). Similarly, this article helps a lot to learn more about different forms of Conversion of Fractions.

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Frequently Asked Questions (FAQs) – Conversion of Fractions

Q.1. Explain Conversion of Fraction to percent with example?
Ans: To convert a fraction to a per cent, first divide the numerator by the denominator. Then multiply the decimal by \(100\) and write \(\%\) sign after that.
Example: \(\frac{4}{8}=0.5 \times 100=50 \%\)

Q.2. How do you convert a mixed fraction to an improper fraction?
Ans: We can convert a mixed fraction to an improper fraction by using the formula,
\({\text{Improper fraction}} = \frac{{\left({{\text{whole number}} \times {\text{Denominator}}} \right) + {\text{Numerator}}}}{{{\text{Deniminator}}}}\)

Q.3. How do you convert a fraction into a percentage?
Ans: To convert a fraction to a per cent, first divide the numerator by the denominator. Then multiply the decimal by \(100\) and write \(\% \) sign after that.

Q.4. What is \(\frac{1}{8}\) as a decimal?
Ans: To convert \(\frac{1}{8}\) to a decimal, divide the denominator into the numerator.
So, \(\frac{1}{8}=0.25\)

Q.5. How do I convert a fraction to a decimal?
Ans: To convert a fraction to a decimal, divide the numerator by the denominator.
Example: \(\frac{1}{10}=0.1\)

Q.6. What is \(0.5\) converted to a fraction?
Ans: In the decimal system, the first place after the decimal point represents tenths, so in \(0.5\) it shows that there are five-tenths.
\(0.5\) can be written as \(\frac{5}{10}=\frac{1}{2}\)

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