Mixed Fractions – Definition, Conversions, Examples

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:

  1. Divide the numerator by the denominator.
  2. Write down the whole number part of the quotient.
  3. 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.