## How to Convert between Fractions, Decimals and Mixed Numbers

#### What are Fractions?

Fractions are generally used to define any whole number into equal parts. While writing a fraction, there are two numbers involved. The number at the top is called the numerator, while that at the bottom is called a denominator. There are three types of fractions. They are:
Proper Fractions: In proper fractions, the denominator is greater than the numerator. For ex: $$\frac{3}{4}$$, $$\frac{1}{3}$$
Improper Fraction: As the name suggests, these fractions are “top-heavy” or the numerator is greater than the denominator. For ex: $$\frac{7}{3}$$, $$\frac{5}{2}$$
Mixed-Fraction: Mixed fractions are another type of improper fractions where there is a whole number as well as a fraction part. For ex: $$1\frac{1}{3}$$ ,$$2\frac{3}{7}$$

#### What are Decimals?

In mathematics, a decimal can be defined as a number which has two parts: a whole part and a fractional part, and these two parts are separated by a decimal point. The whole part always represents a number greater than one, while the fractional part, i.e., the part after the decimal, always represents a number less than one.

For example, let’s take the number $$15.74$$. Now here the whole part is represented by $$15$$, whereas the fractional part $$( \frac{74}{100} \ )$$ is represented by $$74$$. Here $$74$$ can also be denoted as the decimal part, as it lies after the decimal point.

#### What are Mixed Numbers?

A mixed number is a combination of two numbers: a whole number and a proper fraction (A proper fraction is a fraction which has a denominator which is greater than the numerator, i.e., $$\frac{2}{3}$$, $$\frac{4}{7}$$, $$\frac{5}{6}$$, etc.). Moreover, a mixed number can be converted into a fraction and it always lies between two whole numbers.

For ex: Let’s take the mixed number $$1\frac{3}{4}$$. So, this mixed number comprises of two parts, a whole number which is $$1$$ and a proper fraction $$\frac{3}{4}$$. Now, if we convert this mixed number into an improper fraction which is $$\frac{7}{4}$$ we find that it lies between the two whole numbers $$1$$ and $$2$$.
Some other examples of a mixed number are $$2\frac{1}{2}$$, $$3\frac{1}{2}$$, $$4\frac{1}{5}$$, etc.

#### How to convert Fraction to Decimal

To convert a decimal to fraction, follow these steps:

• First, write the given decimal over $$1$$ (i.e., write the denominator of the decimal as $$1$$ ).
• Next multiply both numerator and denominator by $$10$$ for every digit on the right side of the decimal. For example, a decimal number $$12.3947$$ should be multiplied by $$10000$$.
• Next simplify the numerator and denominator to get your desired fractional number.

#### How to convert Mixed Number to Decimal

To convert a mixed number to a fraction, follow these steps:

• First, convert the mixed number into a fraction. To do this just multiply the denominator with the whole part and add to the numerator. Now just write this answer over the denominator.
• After conversion, just apply common division rule to get the desired decimal number.

### Exercises for Convert between Fractions, Decimals and Mixed Numbers

1) $$\frac{4}{5} =$$

2) $$0.15 =$$

3) $$1{2 \over 3}$$

4) $$\frac{6}{10}$$

5) $$\frac{5}{2} =$$

6) $$\frac{12}{5} =$$

7) $$\frac{27}{8} =$$

8) $$\frac{5}{11} =$$

9) $$0.71 =$$

10) $$0.37 =$$

1) $$\frac{4}{5} = \ 4 \ \div \ 5 = \ \color{red}{0.8}$$
Solution
Step 1:  Divide the top number by the bottom number: $$\ 4 \ \div \ 5 = \ 0.8$$
2) $$0.15 = \color{red}{0.15 \over 1} \color{red}{ = {0.15 \times 100 \over 1 \times 100}} \color{red}{ = {15 \over 100}= } \color{red}{\frac{15 \ \div \ 5}{100 \ \div \ 5} = } \color{red}{\frac{3}{20}}$$
Solution
Step 1:  Write decimal over 1. $${0.15 \over 1}$$
Step 2: Multiply both top and bottom by 10 for every digit on the right side of the decimal point. In this decimal, because we have two numbers after the decimal point, therefore we must multiply it by $$100$$ . So:  $${0.15 \over 1} ={0.15 \times 100 \ \over \ 1\times 100}$$
Step 3:  Simplify. $${15 \over 100} = { 3 \over 20}$$
3) $$1{2 \over3} = \color{red}{{5 \over 3 } = \ 5 \ \div \ 3 = \ {1.6...}}$$
Solution
Step 1: Convert the mixed number to a fraction $$1{2 \over3} = {5 \over 3 }$$
Step 2:
Divide the top number by the bottom number. $$\ 5 \ \div \ 3 = \ {1.6...}$$
4) $$\frac{6}{10} = \ 6 \ \div \ 10 = \ \color{red}{0.6}$$

5) $$\frac{5}{2} = \ 5 \ \div \ 2 = \ \color{red}{2.5}$$

6) $$\frac{12}{5} = \ 12 \ \div \ 5 = \ \color{red}{2.4}$$

7) $$\frac{27}{8} = \ 27 \ \div \ 8 = \ \color{red}{3.375}$$

8) $$\frac{5}{11} = \ 5 \ \div \ 11 = \ \color{red}{0.455...}$$

9) $$0.71 = \color{red}{0.71 \over 1} = \color{red}{ {0.71 \times 100 \over 1 \times 100} = } \color{red} {{71 \over 100}}$$

10) $$0.37 = \color{red}{0.37 \over 1} = \color{red} { {0.37 \times 100 \over 1 \times 100} = } \color{red}{ {37 \over 100}}$$

## Convert between Fractions, Decimals and Mixed Numbers Quiz

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