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Mixed Fractions

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Mixed Fractions also called Mixed Numbers are a group of fractions that are represented in a special form in which the whole number part of a fraction is written alongside the fraction. We write mixed fractions of only improper fractions, i.e. only improper fractions can be converted into mixed fractions and proper fractions can not.

Suppose 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.

In this article, we will learn about Mixed Fractions, Converting improper fractions into mixed fractions, examples, and others in detail.

Definition of Mixed Fractions

Mixed fraction is defined as a fraction that has both a whole number and a fractional part. It can be formed by combining a whole number and a fraction. We expressed a mixed fraction as a fraction using the quotient and remainder of the division of the fraction.

Example: 5{\Large\frac{2}{4}}     is a mixed fraction in which 5 is the quotient and 2 is the remainder. Therefore, A mixed fraction is the product of a whole number and a proper fraction.

Now, let’s learn about How to Convert Improper Fraction into Mixed Fraction and vice-versa in detail.

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

Divinding 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: Obseve 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:

= 2(2/5)

= (5×2 + 2)/5

= 12/5

Operations on Mixed Fractions

Various operations performed on mixed fractions are,

  • Addition of Mixed Fraction
  • Subtraction of Mixed Fraction
  • Multiplication of Mixed Fraction
  • Division of Mixed Fraction

Let’s learn about the same in detail.

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.

Learn more about, Adding Fractions

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

Solution:

= 2(1/7) + 4(5/7)

= 15/7 + 33/7

= (15 + 33)/7

= 48/7

Subtraction 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: Subtract fractions using the subtraction of fractions method.

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

Solution:

= 4(5/7) – 2(1/7)

= 33/7 – 15/7

= (33 – 15)/7

= 18/7

Multiplication 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: Multiply fractions using the multiplication of fractions method.

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

Solution:

= 2(1/7) × 4(5/7)

= 15/7 × 33/7

= (15 × 33)/(7 × 7)

= 495/49

Division 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: Divide fractions using the division of fractions method.

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

Solution:

= 2(1/7) ÷ 4(5/7)

= 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 (b ????). 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.

Read More,

Mixed Fraction Examples

Example 1: Convert Improper Fractions to Mixed Fractions.

  • a) 16/5
  • b) 17/7

Solution:

  • a) 16/5

We have 16/5

Dividing 16 by 5

  • Quotient = 3
  • Remainder = 1

= 3(1/5)

  • b) 17/7

We have 17/7

Dividing 17 by 7

  • Quotient = 2
  • Remainder = 3

= 2(3/5)

Example 2: Add 3(2/3) and 5(1/3)

Solution:

= 3(2/3) + 5(1/3)

= 3 + 5 + 2/3 + 1/3

= 8 + (2+1)/3

= 8 + 3/3

= 8 + 1 = 9

Example 3: Subtract 5(2/3) and 3(1/3)

Solution:

= 5(2/3) – 3(1/3)

= (5 – 3) + (2/3 – 1/3)

= 2 + (2-1)/3

= 2 + 1/3

= 2(1/3)

Example 4: Multiply 5(2/3) and 3(1/3)

Solution:

= 5(2/3) × 3(1/3)

= 17/3 × 10/3

= (17 × 10)/(3 × 3)

= 170/9

Example 5: Divide 5(2/3) and 3(1/3)

Solution:

= 5(2/3) ÷ 3(1/3)

= 17/3 ÷ 10/3

= 17/3 × 3/10

= 17/10

Practice Questions on Mixed Fractions

Q1: Add 5(1/3) and 3(2/3)

Q2: Subtract 7(2/5) from 11(9/5)

Q3: Multiply 8(3/4) and 4(2/3)

Q4: Divide 5(2/3) by 4(1/2)

FAQs on Mixed Fractions

1. What are Mixed Fractions?

Mixed fractionas are the fractions that are represented using a whole number and the proper fraction. Only improper fraction can be converted to mixed fraction. Suppose we have an improper fraction 5/2 then in form of the mixed fraction it is written as, 2(1/2).

2. How to Add Mixed Fractions?

To add mixed fraction, we first convert the mixed fraction into improper fraction and then add them using general methods of addition of fractions.

3. How to Subtract Mixed Fractions?

To subtract mixed fraction, we first convert the mixed fraction into improper fraction and then subtract them using general methods of subtaraction of fractions.

4. How to Convert an Improper Fraction into a Mixed Fraction?

Improper fractions are converted into mixed fraction by simply dividing the numerator of the improper fraction with the denominator and then writing the value of division in the format,

Q(R/D)

where,

  • Q is the Quotient
  • R is the Remainder
  • D is the Denominator

5. How to Convert a Mixed Fraction into an Improper Fraction?

To convert a mixed fraction into improper fraction study the example added below, suppose we are given a mixed fraction as a(b/c) then it is converted into improper fraction as,

(a×c + b)/c



Last Updated : 03 Jan, 2024
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