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A Mixed Fraction is a type of fraction that consists of two parts: an integer and a fractional component. It represents a value greater than a whole number but not entirely a whole number. For example, the Mixed Fraction ^{9}⁄_{12} combines the whole number 9 with the fraction ^{1}⁄_{2}. Another term often used for Mixed Fractions is mixed numbers.

Mixed Fractions are commonly used to represent values in a clear and simple way when dealing with quantities that include both whole numbers and parts of a whole.

## What are Mixed Fractions?

**Definition of Mixed Fraction:** A mixed fraction is a type of fraction that combines a whole number and a proper fraction. The proper fraction represents a part of a whole, while the whole number gives the full units. For example, in the mixed fraction ^{2}⁄_{3}, 2 is the whole number and ^{3}⁄_{4} is the proper fraction.

Mixed fractions are useful for expressing values that fall between whole numbers and fractional parts.

## Conversion of an Improper Fraction to Mixed Fractions

An improper fraction is one where the numerator is greater than or equal to the denominator. For example, ^{13}⁄_{5} is an improper fraction because 13 is greater than 5. To convert an improper fraction into a mixed number, follow these steps:

- Divide the numerator by the denominator.
- Identify the quotient (whole number) and the remainder.
- Mixed number = Quotient +
^{Remainder}⁄_{Denominator}.

**For example, converting ^{13}⁄_{5} into a mixed fraction:**

- Divide 13 by 5, which gives a quotient of 2 and a remainder of 3.
- The mixed number is: 2*3/5.

This process is called the **Mixed Fraction Formula** in mathematics. By converting improper fractions into mixed numbers, we can represent fractions in a more understandable format, combining whole numbers and fractional parts.

## Mixed Directions Formula

The mixed fraction formula is a way to express an improper fraction as a combination of a whole number and a proper fraction.

The formula for a mixed fraction is:

Mixed fraction = Quotient × ^{Remainder}⁄_{Divisor}

Let’s break down the process of using a mixed fraction formula by the example of converting 135 into a mixed fraction:

- Divide the numerator (13) by the denominator (5) which gives us 2 as a quotient with a remainder of 3.
- Now, the quotient becomes the whole number. In this case, 2 is the quotient, so the whole number part of the mixed fraction is 2.
- Furthermore, the remainder becomes the numerator of the proper fraction. Therefore, the remainder is 3, so the numerator of the fraction part is 3.
- The divisor remains the denominator of the fraction part. The divisor here is 5, so the denominator of the fraction part is 5.

Thus, the improper fraction 13/5 is written as the mixed fraction 2*3/5.

## Conversion of Mixed Fractions to an Improper Fraction

To convert a mixed fraction into an improper fraction, follow these steps using the example 2*4/5 (where 2 is the whole number, and 4/5 is the fractional part):

- Multiply the denominator by the whole number. Take the denominator of the fraction (5) and multiply it by the whole number (2).

5×2=10

- Add the numerator to the result. Add the numerator (4) to the product from step 1:

10+4=14

Now, write the result as an improper fraction. The improper fraction will have the sum from step 2 (14) as the numerator and the original denominator (5) as the denominator. Thus, the mixed fraction 2*4/5 is converted to the improper fraction 14/5.

## Operation on Mixed Fractions

Just like with whole numbers, mixed fractions can undergo the four basic arithmetic operations: addition, subtraction, multiplication, and division. However, when performing operations on mixed fractions, it’s often easier to first convert them into improper fractions and then apply the operation.

### Addition of Mixed Fractions

Adding mixed fractions requires a few systematic steps to ensure accuracy. Follow the steps below to perform the addition operation on mixed fractions.

- First, change each mixed number into an improper fraction by multiplying the whole number by the denominator and adding the numerator.
- If the denominators of both fractions are already the same, you can move on to the next step. If not, proceed to the next step to align the fractions.
- If the denominators are different, find the LCM of the two denominators. Convert the fractions to have the same denominator by multiplying both the numerator and denominator of each fraction by appropriate factors.
- Once the denominators are the same, add the numerators together, keeping the denominator the same.
- If the result is an improper fraction, you can convert it back into a mixed fraction by dividing the numerator by the denominator.

By following these stages, you can accurately add two mixed fractions.

### Subtraction of Mixed Fractions

Mixed fractions can be subtracted easily by following these steps.

- Improper fractions should be adopted from mixed fractions.
- It is crucial to look for similarity between the denominators.
- If such fractions are similar, then the numerator of one should be deducted from that of the other and recorded.
- However, when they differ, find out their common LCM in order to make them equal.
- Now just subtract the numerators and you have your answer.

### Multiplying Mixed Fractions

In order to multiply mixed fractions we follow these steps elaborated below:

- First convert your mixed fraction into improper fraction.
- Next, multiply across by multiplying numerators and denominators together respectively.
- Finally, reduce this resultant to simplest or improper form or even rewrite it in the form of mixed fractions.

### Division of Mixed Fractions

Sequentially, the mixed fractions are divided in this manner:

- A mixed fraction should be converted to an improper one.
- Then, the first fraction is multiplied by the reciprocal of the second.
- At last, the result may either be simplified or left as an improper or mixed fraction.

## Improper Fractions and Mixed Fractions

An improper fraction is when the numerator is greater than or equal to the denominator, while a mixed fraction combines a whole number and a proper fraction. For example, ^{9}⁄_{4} is an improper fraction and ^{2}⁄_{3} is a mixed fraction.

## Mixed Fractions Practice Questions

^{2}⁄_{14}+^{1}⁄_{5}^{6}⁄_{17}+^{1}⁄_{2}^{12}⁄_{12}+^{1}⁄_{4}

## FAQs on Mixed Fractions

**Q1. What is a mixed fraction?**

A mixed fraction combines a whole number and a proper fraction.

**Q2. How do you convert an improper fraction to a mixed fraction?**

Divide the numerator by the denominator, and use the quotient and remainder to form the mixed fraction.

**Q3. What is the formula to convert a mixed fraction to an improper fraction?**

Improper fraction = ^{(Whole number × Denominator) + Numerator}⁄_{Denominator}