Mixed Fractions

Mixed Fractions also called Mixed Numbers are a group of fraction that has both a whole number and a fractional part. It can be formed by combining a whole number and a fraction.

Mixed fraction, also known as a mixed number, is a numerical expression that combines a whole number and a proper fraction. This form of fraction is used to represent quantities that are more than a whole but less than the next whole number.

For Example - We are given an improper fraction as 11/3 then in mixed fraction form it is written as 3(2/3) and read as "3 whole 2 by 3". Here, 3 is the whole number part and 2/3 is the fraction part.

Structure of Mixed Fraction

A mixed fraction is written as:

\text{Whole Number} \; \frac{\text{Numerator}}{\text{Denominator}}

Where

• Whole Number: The integer part of the mixed fraction.
• Numerator: The top part of the fractional component, representing how many parts we have.
• Denominator: The bottom part of the fractional component, representing the total number of equal parts the whole is divided into.

Note: We can write mixed fractions of only improper fractions, i.e. only improper fractions can be converted into mixed fractions and proper fractions can not.

How to Convert Improper Fraction into Mixed Fraction?

A fraction in which the numerator of the fraction is greater than the denominator of the fraction is called the Improper Fraction. Various examples of improper fractions are, 12/5, 23/11, 7/2, etc. We can convert the improper fraction into mixed fractions by following the steps added below,

• Step 1: Divide the numerator of the given improper fraction with its numerator.
• Step 2: Find the Quotinet and Remainder of the division.
• Step 3: Write the number in Mixed Fraction format as,

Q(R/D)

Where,

• Q is Ouotient
• R is Remainder
• D is Denominator of the Improper Fraction

For Example, Change the improper fraction 12/5 into mixed fraction.

Solution:

We have 12/5
Dividing then,

• Quotient = 2
• Remainder = 2

Then in mixed fractions as,
= 2(2/5)

How to Convert Mixed Fraction into Improper Fraction?

Mixed Fraction can be converted into Improper Fraction by following the steps added below,

• Step 1: Observe the mixed fraction and multiply the denominator with the whole number and then add the numerator.
• Step 2: Simplify the step 1
• Step 3: Write the value obtained in step 1 as numerator and denominator is the same.

The same can be explained by the example as,

For Example, Change the mixed fraction 2(2/5) into improper fraction.

Solution:

We have 2(2/5)
= (5×2 + 2)/5
= 12/5, which is an improper fraction

Operations on Mixed Fractions

Various operations performed on mixed fractions are,

Addition of Mixed Fraction

Addition of mixed fraction is achieved by the steps added below,

• Step 1: Convert the given mixed fractions into improper fractions.
• Step 2: Add fractions using the addition of fractions method.

Example: Add 2(1/7) and 4(5/7)

Solution:

We have, 2(1/7) + 4(5/7)
Converting the above mixed fractions to improper fractions, we get
= 15/7 + 33/7
= (15 + 33)/7
= 48/7

Subtraction of Mixed Fraction

Subtraction of mixed fraction is achieved by the steps added below,

• Step 1: Convert the given mixed fractions into improper fractions.
• Step 2: Subtract fractions using the subtraction of fractions method.

Example: Subtract 4(5/7) and 2(1/7)

Solution:

Given, 4(5/7) - 2(1/7)
Converting the above mixed fractions to improper fractions, we get

= 33/7 - 15/7
= (33 - 15)/7
= 18/7

Multiplication of Mixed Fraction

Multiplication of mixed fraction is achieved by the steps added below,

• Step 1: Convert the given mixed fractions into improper fractions.
• Step 2: Multiply fractions using the multiplication of fractions method.

Example: Multiply 2(1/7) and 4(5/7)

Solution:

We have, 2(1/7) × 4(5/7)
Converting the above mixed fractions to improper fractions, we get
= 15/7 × 33/7
= (15 × 33)/(7 × 7)
= 495/49

Division of Mixed Fraction

Division of mixed fraction is achieved by the steps added below,

• Step 1: Convert the given mixed fractions into improper fractions.
• Step 2: Divide fractions using the division of fractions method.

Example: Divide 2(1/7) and 4(5/7)

Solution:

We have, 2(1/7) ÷ 4(5/7)
Converting the above mixed fractions to improper fractions, we get
= 15/7 ÷ 33/7
= 15/7 × 7/33
= 15/33

Are Mixed Numbers Rational Numbers?

A rational number is a type of real number with the formula a/b where b does not equal zero. When a rational number is divided, the result is a decimal number that can be terminated or repeated.

An Improper Fraction, which is a quotient of two integers, can be expressed as a Mixed Fraction with both Integer and Fractional Parts. Therefore , we can say that every Mixed Fraction can be expressed as a Rational Number.

For Example:

6{\Large\frac{4}{5}}    is a mixed fraction or mixed number and it can be re-written as 34/5. Here, 34/5 is in form of  improper fraction.  All decimals which are either terminating or showing repeating pattern after some point are rational numbers, therefore 34/5 is rational number.