## Definition of Fraction:

The ratio of a whole number is called as a** Fraction**. A fraction can represent part of a whole.

*For Example*: \(\frac{15}{7}\) is a fraction, where 15 is a numerator and 7 is a denominator. 7 is the number of parts into which the whole number divides.

## Definition of a Mixed Fraction:

It is a form of a fraction which is defined as the ones having a fraction and a whole number.

**Example**: 2\(\frac{1}{7}\), where 2 is a whole number and \(\frac{1}{7}\) is a fraction.

## Types of Fractions:

There are three types of fractions.

Types of Fractions |
Explanation |

Proper Fraction | When the numerator is less than Denominator |

Improper Fraction | When the numerator is greater than or equal to the Denominator. |

Mixed Fraction | It is an improper function, which is written as a combination of a whole number and a fraction. |

### How to convert Improper fraction to a Mixed fraction?

- Step 1: Divide the Fraction’s numerator with the denominator i.e 15\(\div\)7.

- Step 2: The integer part of the answer will be the integer part for a mixed fraction. I.e 2 is an integer.

- Step 3: The Denominator will be the same as original, i.e 7.

- Step 4: So, the improper function \(\frac{15}{7}\) is changed to a Mixedfraction – 2\(\frac{1}{7}\).

Some more examples of mixed fractions are 3\(\frac{1}{4}\), 1\(\frac{2}{9}\), 7\(\frac{6}{7}\)… |

### How to convert a Mixed fraction to an Improper Fraction?

- Step 1: Multiply the denominator with the whole number integer. I.e Multiply 7with 2 in the given example, 2\(\frac{1}{7}\).

- Step 2: Add the numerator of the Fraction to the result in step 1. I.e Add 1+ 14

=15.

- Step 3: Keep the Denominator the same i.e 7.

- Step 4: The Improper fraction obtained is : \(\frac{15}{7}\).

## How to Add Mixed Fractions?

When it comes to adding Improper or mixed fractions, we can have either the same denominators for both the fractions to be added or the denominators can differ too.

Here’s a stepwise difference to **Add the improper fraction** with Same or Different Denominators.

**Note**: Change Mixed Fractions to Improper Fractions as shown above before applying any operations. (Addition, Subtraction, Multiplication).

Adding Mixed fractions with the same Denominators. Example: \(\frac{6}{4}+\frac{5}{4}\) |
Adding Mixed fractions with the different Denominators. Example: \(\frac{8}{6}+\frac{12}{8}\) |

Step 1: Keep the denominator ‘4’ same. |
Step 1: Find the LCM between the denominators i.e The LCM of 6 and 8 is 24 |

Step 2: Add the numerators ‘6’ +’5’ =11. |
Step 2: Multiply both Denominators and Numerators of both fractions with a number such that they have the LCM as their new Denominator. Multiply the numerator and Denominator of \(\frac{8}{6}\) with 4 and \(\frac{12}{8}\) with 3. |

Step 3: If the answer is in improper form, Convert it into a mixed fraction. I.e \(\frac{11}{4}\) = \(2\frac{3}{4}\) |
Step 3: Add the Numerator and keep the Denominators same. \(\frac{32}{24}+\frac{36}{24}=\frac{68}{24}\) |

So, We have \(2\frac{3}{4}\) wholes. | Step 4: If the answer is in Improper form, convert it into Mixed Fraction: \(2\frac{5}{6}\) |

Here’s a stepwise explanation on how to **Subtract the improper fraction** with Same or different Denominators.

Subtracting mixed fractions with the same Denominators. Example: \(\frac{6}{4}+\frac{5}{4}\) |
Subtracting Mixed fractions with the different Denominators. \(\frac{12}{8}+\frac{8}{6}\) |

Step 1: Keep the denominator ‘4’ same. |
Step 1: Find the LCM between the denominators i.e The LCM of 8 and 6 is 24 |

Step 2: Subtract the numerators ‘6’ -’5’ =1. |
Step 2: Multiply both Denominators and Numerators of both fractions with a number such that they have the LCM as their new Denominator. Multiply the numerator and Denominator of \(\frac{8}{6}\) with 4 and \(\frac{12}{8}\) with 3. |

Step 3: If the answer is in improper form, Convert it into a mixed fraction. I.e \(\frac{1}{4}\) |
Step 3: Subtract the Numerator and keep the Denominators same. \(\frac{36}{24}+\frac{32}{24}=\frac{4}{24}\) |

So, We have \( \frac{1}{4}\) wholes. | Step 4:If the answer is in Improper form, convert it into Mixed Fraction. \( \frac{4}{24}\) = \( \frac{1}{6}\) |

**How to Multiply Mixed Fractions?**

**Example**: \(2\frac{5}{6} \times 3\frac{1}{2}\)

**Solution: **

**Step 1**: Convert the mixed fraction into an improper fraction. \(\frac{17}{6} \times \frac{7}{2}\)

**Step 2**: Multiply the numerators of both the fractions together and denominators of both the fractions together. \(\frac{17\times 7}{6\times 2}\)

**Step 3**: You can convert the fraction into the simplest form or Mixed fraction. \(\frac{119}{12}\) or \(9\frac{11}{12}\)

Learn More Mathematical Concepts | |
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Surface Areas and Volume | Continuity and Differentiability |

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