## What Is A Mixed Fraction?

A fraction represented with its quotient and remainder is a mixed fraction. For example, 3 1/7 is a mixed fraction, where 3 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

A mixed fraction is defined as a fraction formed by combining a whole number and a fraction. For example, if 8 is a whole number and ½ is a fraction, then 8 ½ is a mixed fraction.

## How to Convert Mixed Fraction to an Improper Fraction?

A mixed fraction can also be converted to an improper fraction. To do that, follow the steps given below. Let us understand this by taking an example of a mixed fraction 2 ¼. Here 2 is the whole number, 1 is the numerator and 4 is the denominator.

**Step 1:** Multiply the denominator of the mixed fraction with the whole number part.

**Step 2:** Add the numerator to the product obtained from step 1.

**Step 3:** Write the improper fraction with the sum obtained from step 2 in the numerator/denominator form.

A mixed number is a whole number plus a fractional part. An improper fraction is a fraction where the numerator (top number) is larger than the denominator (bottom number). You can convert between mixed numbers and improper fractions without changing the value of the figure.

**Example**

**Example:** Convert the following mixed number to an improper fraction. **2 4/5**

**Step 1: **Multiply the denominator (the bottom number in the fraction) and the whole number.

Solution: 2×5= 10

**Step 2:** Add the answer from Step 1 to the numerator (the top number in the fraction)

Solution: 10+4=14

**Step 3: **Write answer from Step 2 over the denominator = 14/5

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

An improper fraction is a fraction that has a numerator greater than or equal to the denominator and cannot be simplified further. For example, 7/3 is an improper fraction. Let us learn how to convert this improper fraction to a mixed fraction.

You can go the other direction, too! To change an improper fraction to a mixed number, follow these steps:

- Divide the numerator by the denominator.
- Write down the whole number part of the quotient.
- Take the remainder and write it over the original denominator.

Let’s try it with 9/4. First, divide.

**9/4 =9÷4 =2 R1**

Write down the whole number part, **2.** Then take the remainder and write it over the original denominator. That’s your answer!

**2 ¼ **So, 9/4 is the same as 2 ¼.

## How to Add Mixed Fraction?

To add mixed fractions:

- Convert them to Improper Fractions
- Then add them (using Addition of Fractions)
- Then convert back to Mixed Fractions

**Example: What is 2 ¾ + 3 ½ =?**

**Convert to Improper Fractions:**

2 ¾ = 11/4

3 ½ = 7/2

**Common denominator of 4:**

11/4 stays as 11/4.

7/2 becomes 14/4.

(by multiplying top and bottom by 2)

Now Add: 11/4 + 14/4 = 25/4

**Convert back to Mixed Fractions: **25/4 = 6 ¼

## How to Subtract a Mixed Fraction?

Just follow the same method, but subtract instead of add:

**Example: What is 3 ¾ – 2 ½ =?**

**Convert to Improper Fractions:**

3 ¾ = 15/4

2 ½ = 5/2

**Common denominator of 4:**

15/4 stays as 15/4.

5/2 becomes 10/4.

(by multiplying top and bottom by 2)

Now subtract: 15/4 – 10/4 = 5/4

## How to Multiply Mixed Fraction?

Multiplying Mixed Numbers using the Multiplying Fractions Formula

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for multiplying of fractions: a/b * c/d = ac / bd
- Reduce fractions and simplify if possible

**Example: What is **1 (2/6) x 2 ¼ =?

1 2/6 * 2 1/4 = 8/6 * 9/4 = 8*9 / 6*4 = 72 / 24

Reduce the fraction to get 3/1 and simplify to **3**.

## How to Divide Mixed Fraction?

Dividing Mixed Numbers using the Dividing Fractions Formula:

- Convert the mixed numbers to improper fractions
- Use the algebraic formula for division of fractions: a/b ÷ c/d = ad / bc
- Reduce fractions and simplify if possible

**Example: What is** 1 2/6 ÷ 2 1/4 =?

1 2/6 ÷ 2 1/4 = 8/6 ÷ 9/4 = 8*4 / 9*6 = 32 / 54

Reduce the fraction to get **16/27.**