Mixed Fraction - Definition, Formula and Examples

Mixed Fraction

Have you ever had one full object and just a part of another? Like one whole chocolate bar and a small piece from another? That situation is best shown using a mixed fraction.  A mixed fraction (also called a mixed number) is a way to represent quantities that are more than a whole but not yet two.

Mixed fractions are used in many everyday situations and are a simple way to show both whole and part together.  Also, we can perform different mathematical operations using mixed fractions, such as adding, subtracting, multiplying, and dividing. Learn about each of these operations with examples here.

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What is Mixed Fraction?

A mixed fraction is a number that has two parts. The first part is a whole number. The second part is a proper fraction. A proper fraction is a fraction where the top number (numerator) is smaller than the bottom number (denominator). 

For example, In the mixed fraction 4(1/3):

• 4 is the whole number. It means four complete parts.

• 1 is the numerator. It shows one part.

• 3 is the denominator. It tells that one whole is divided into three equal parts.

Therefore,  4(1/3) means 4 full items and 1 out of 3 parts of another item.

If someone asks what is mixed fraction, you can say it is a number that shows both whole parts and part of another whole.

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Mixed Fraction Examples in Real-Life

Here, we will look at a few examples of mixed fractions that show how they are used in everyday situations.

Example 1: You are baking a cake. You use 1(3/4) cups of sugar and 2(1/4) cups of flour.
1(3/4) = 7/4

2(1/4) = 9/4

Add: 7/4 + 9/4 = 16/4 = 4 cups

Example 2: You drink 1(1/2) bottles of water in the morning and 2(1/2) bottles in the afternoon.
1(1/2) = 3/2

2(1/2) = 5/2

Add: 3/2 + 5/2 = 8/2 = 4 bottles

Mixed Fraction Formula

A mixed fraction formula is used to convert a mixed fraction into an improper fraction.

The formula is:

Improper Fraction = (Whole Number × Denominator + Numerator) / Denominator

This means you multiply the whole number by the denominator, then add the numerator. The result becomes the new numerator, and the denominator stays the same.

Note:  Only improper fractions can be turned into mixed fractions. Proper fractions like 2/5 cannot be written this way because they are less than one whole.

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Steps to convert improper fraction into mixed fraction

A fraction where the numerator is larger than the denominator is called an improper fraction. Some examples of improper fractions are: 19/4, 14/3, 21/8, and 26/5. 

We can change an improper fraction into a mixed fraction by following these steps:

Step 1: Divide the numerator by the denominator.

Step 2: Find the quotient and remainder.

Step 3: Write the result in mixed fraction form as Quotient(Remainder/Divisor)

Here,
Q = Quotient

R = Remainder

D = Denominator of the original improper fraction

For example, 

1. Convert improper fraction 19/4 into a mixed fraction.

Solution

We have 19/4

Now divide 19 by 4

Quotient = 4

Remainder = 3

Then the mixed fraction is 4(3/4)

So, 19/4 = 4(3/4) as a mixed fraction

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Steps to Convert Mixed Fraction into Improper Fraction

To convert a mixed fraction into an improper fraction, follow these simple steps:

Step 1: Multiply the denominator by the whole number.

Step 2: Add the numerator to the result.

Step 3: Write the sum as the new numerator, and keep the same denominator.

For example, 

Convert the mixed fraction 5(2/3) into an improper fraction.

Solution

We have 5(2/3)

Step 1: Multiply 5 × 3 = 15

Step 2: Add 15 + 2 = 17

Step 3: Write the result as 17/3

So, 5(2/3) = 17/3 as an improper fraction.

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Operations on Mixed Fraction Various operations can be performed on mixed fractions. These include addition, subtraction, multiplication, and division.  Let's understand these operations step by step with examples

Addition of Mixed Fraction

Addition of mixed fractions is done using the steps below:

Step 1: Convert the given mixed fractions into improper fractions.

Step 2: Add the fractions using the standard method.

Step 3: If needed, convert the answer back into a mixed fraction.

Example: Add 3(1/4) and 2(2/3)

Solution

Convert to improper fractions:

3(1/4) = (4 × 3 + 1)/4 = 13/4

2(2/3) = (3 × 2 + 2)/3 = 8/3

Now find the common denominator.

The least common denominator of 4 and 3 is 12.

Convert the fractions
13/4 = 39/12

8/3 = 32/12

Add them
39/12 + 32/12 = 71/12

Now convert back to mixed fraction:

71 ÷ 12 = 5 remainder 11

So, 71/12 = 5(11/12)

Therefore, 3(1/4) + 2(2/3) = 5(11/12)

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Subtraction of Mixed Fraction

Subtraction of mixed fractions is done in the same way:

Step 1: Convert the mixed fractions into improper fractions.

Step 2: Subtract the fractions.

Step 3: Convert the result back into a mixed fraction.

Example: Subtract 5(3/5) − 2(1/2)

Solution
5(3/5) = (5 × 5 + 3)/5 = 28/5

2(1/2) = (2 × 2 + 1)/2 = 5/2

Find a common denominator for 5 and 2, which is 10.

Convert the fractions

28/5 = 56/10

5/2 = 25/10

Now subtract

56/10 − 25/10 = 31/10

Convert to a mixed fraction:

31 ÷ 10 = 3 remainder 1

So, 31/10 = 3(1/10)

Therefore,  5(3/5) − 2(1/2) = 3(1/10)

Multiplication of Mixed Fraction

To multiply mixed fractions:

Step 1: Convert the mixed fractions to improper fractions.

Step 2: Multiply the numerators and the denominators.

Step 3: Convert the result back to a mixed fraction if needed.

Example: Multiply 1(1/2) × 2(3/4)

Solution
1(1/2) = (2 × 1 + 1)/2 = 3/2

2(3/4) = (4 × 2 + 3)/4 = 11/4

Now multiply:

(3 × 11)/(2 × 4) = 33/8

Convert to a mixed fraction:

33 ÷ 8 = 4 remainder 1

So, 33/8 = 4(1/8)

Therefore,  1(1/2) × 2(3/4) = 4(1/8)

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Division of Mixed Fraction

To divide mixed fractions:

Step 1: Convert the mixed fractions to improper fractions.

Step 2: Keep the first fraction the same. Flip the second one (use its reciprocal).

Step 3: Multiply the first by the reciprocal of the second.

Step 4: Convert the answer into a mixed fraction.

Example: Divide 3(1/3) ÷ 1(2/5)

Solution
3(1/3) = (3 × 3 + 1)/3 = 10/3

1(2/5) = (5 × 1 + 2)/5 = 7/5

Now divide
10/3 ÷ 7/5 = 10/3 × 5/7 = 50/21

Convert to mixed fraction
50 ÷ 21 = 2 remainder 8

So, 50/21 = 2(8/21)

Therefore,  3(1/3) ÷ 1(2/5) = 2(8/21)

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