Mixed Fraction Definition, Conversion, Operations, and FAQ

Mixed Fraction Definition

We already know about proper and improper fractions. A mixed fraction is another type of fraction in which we have a whole number as well as a fraction.

For example, 5 (¼) is a mixed fraction where 5 is a whole number and \frac{1}{4}is a proper fraction.

Generally, we write the improper fractions in the form of mixed fractions. Let us learn how we can convert improper fractions to mixed fractions.

Conversion: Improper Fraction to a Mixed Fraction

An improper fraction can not be simplified further, and the value of the numerator is greater than the denominator, 

For example, 29/7 is an improper fraction. Let us convert this into a mixed fraction.

• Divide the fraction’s numerator(29) with the denominator (7).

• Upon dividing, we get 4 as the quotient and 1 as the remainder. 
• The quotient (4) will be the whole number for the mixed fraction, and the remainder (1) will be the numerator of the mixed fraction.
• The denominator of the mixed fraction will be the same as the improper fraction, i.e. 7.
• So, this way, improper fraction \frac{29}{7} is changed to a mixed fraction as 4(1 / 7)

Conversion: Mixed Fraction to an Improper Fraction

Let us convert the mixed fraction 3(1/4) into an improper fraction. 

Here 3 is the whole number, 1 is the numerator, and 4 is the denominator.

• Start by multiplying the denominator of the improper fraction (4) with the whole number (3). We will get 12.
• Add the numerator (1) to the product obtained (12). We will get 12+1 = 13.
• The denominator will be the same as it was in the mixed fraction, i.e. 4.
• Now we have numerator = 13 and denominator = 4.
• So, the mixed fraction 3(1/4) is equivalent to the improper fraction (13/4).

Operations on Mixed Fractions

We can perform addition, subtraction, multiplication and division on these fractions.

Addition of Mixed Fractions

To add mixed fractions, convert them to improper fractions.

Now check whether the denominators are the same or not? 

If denominators are the same – 

Simply, add the numerators of both the fractions and keep the same denominator.

For example – we want to add 1(⅖) and 1(⅕). 

Converting both the mixed fractions into improper fractions, we get 

1(⅖) = 7/5 and 1(⅕) = 6/5

Now, 7/5 and 6/5 have the same denominator. 

So, 7/5 + 6/5

= (7+6)/5

= 13/5 = 2(⅗)

If denominators are different

Now we will have to make both the denominators equal. For doing this, we follow the below process – 

• Calculate the LCM of the denominators.
• Multiply the denominators and numerators of both the fractions with such a number that they have the LCM as their new denominator.
• Add the numerators and keep the denominator as it is.

For example – After converting the mixed fractions, we have two fractions, 7/6 and 11/8. 

Now the denominators are different.

• Calculate the LCM of denominators (6 and 8) which is equal to 24.
• Now we have to make both the denominators equal to 24.
• To make the first denominator (6) equal to 24, we will have to multiply it by 4. Similarly, the second denominator (8) should be multiplied by 3.
• The multiplication is done in the numerator and denominator both so that the value of the fraction doesn’t change.
• So, we will multiply the numerators and denominators of (7/6) by 4 and (11/8) by 3, respectively.
• Now the new fractions are 28/24 and 33/24. 
• Now denominators are equal. So the sum of the fractions will be(28+33)/24 = (61/24) = 2(13/24)

Subtraction of Mixed Fractions

It is similar to the addition of mixed fractions. While we were adding the numerators in addition, here we will subtract them. All other procedures and rules are the same.

Multiplying Mixed Fractions

Multiplication of fractions is very easy. We just need to multiply both the numerators and denominators together and write them in fraction form. If the resultant fraction can be simplified, we simplify it otherwise, convert it into a mixed fraction (if required).

Suppose we have two mixed fractions, 2(¾) and 3(⅚), and we want to multiply them. Then follow the steps given below.

• The first step is to convert the mixed fractions to improper fractions. 2(¾) will convert to 11/4, and 3(⅚) will convert to 23/6.
• Now multiply the numerators and denominators of both the fractions and write the result in the fraction form. 

           It means (11/4) × (23/6) = (11 × 23)/(4×6) = 253/24

• Now simplify the fraction or convert it to a mixed fraction. So, 253/24 will be converted to 10(13/24)

Division of Mixed Fractions

It is the opposite process of multiplication. Now, suppose we divide the last two mixed fractions 2(¾) and 3(⅚).

• After converting both the fractions into improper fractions, multiply the first fraction with the multiplicative inverse of the second.  

           It means (11/4) ÷ (23/6) = (11/4) × (6/23) (11 × 6)/(4×23) = 66/92

• Now simplify the fraction or convert it to a mixed fraction. So, 66/92 will be simplified to 33/46.

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Example

 1. Convert 17/5 to mixed fractions.

Follow these steps for converting an improper fraction to a mixed fraction.

• Divide the numerator (17) with the denominator (5).
• The quotient part of the answer (3) will be the whole number for the mixed fraction.
• The denominator of the fraction part will be the same as the improper fraction, i.e. 5.
• The remainder (2) will be the numerator of the fraction part.
• So, the improper fraction 17/5 is changed to a Mixed fraction as 3(2/5).

2. Add the mixed fractions 1(⅔) and 2(¾).

Converting them into improper fractions – 

1(⅔) = 5/3 and 2(¾) = 11/4

We have to add (5/3) + (11/4)

Denominators are different. So LCM of denominators 3 and 4 = 12

To make the denominators 12, multiply the numerator and denominator of (5/3) by 4 and (11/4) by 3. 

We get, (20/12) + (33/12) 

Add both the numerators and keep the denominator the same. We get 53/12 

Converting 53/12 into a mixed fraction, we get 4(5/12) as our final answer.