Mixed Fractions

Mixed fractions (or mixed numbers) are fractions that have both a whole number and a fractional part. Its value is always greater than one.

For example, we are given an improper fraction as 11/3 and 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.

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.

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 an improper fraction. 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 by its denominator.
• Step 2: Find the quotient and remainder of the division.
• Step 3: Write the number in mixed fraction format.

Q(R/D)

• 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)

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

To perform arithmetic operations on mixed fractions, first convert them into improper fractions. Then apply the corresponding rules of fraction arithmetic.

1. Addition of Mixed Fraction

Example: Add 2\frac{1}{7} \ and \ 4\frac{5}{7}.

Solution:

2\frac{1}{7}+4\frac{5}{7}

=\frac{15}{7}+\frac{33}{7}

=\frac{48}{7}=6\frac{6}{7}

2. Subtraction of Mixed Fraction

Example: Subtract (2\frac{1}{7}) \ from \ (4\frac{5}{7}).

Solution:

Given, 4\frac{5}{7}-2\frac{1}{7}
Converting the above mixed fractions to improper fractions, we get

=\frac{33}{7}-\frac{15}{7}

=\frac{33-15}{7}

=\frac{18}{7}=2\frac{4}{7}

3. Multiplication of Mixed Fraction

Example: Multiply (2\frac{1}{7}) \ and \ (4\frac{5}{7}).

Solution:

We have, 2\frac{1}{7}\times4\frac{5}{7}
Converting the above mixed fractions to improper fractions, we get

=\frac{15}{7}\times\frac{33}{7}

=\frac{15\times33}{7\times7}

=\frac{495}{49}=10\frac{5}{49}

4. Division of Mixed Fraction

Example: Divide (2\frac{1}{7}) \ by \ (4\frac{5}{7}).

Solution:

We have, 2\frac{1}{7}\div4\frac{5}{7}
Converting the above mixed fractions to improper fractions, we get

=\frac{15}{7}\div\frac{33}{7}

Taking the reciprocal of the second fraction:

=\frac{15}{7}\times\frac{7}{33}

=\frac{15}{33}=\frac{5}{11}