Improper Fraction to Mixed Number –  Conversion, Example, Facts, FAQs

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What Is Improper Fraction to Mixed Number Conversion?

Improper fraction to mixed number conversion helps us express any given improper fraction in the form of a mixed number (or mixed fraction). 

Note that an improper fraction and mixed number basically mean the same thing, but the way of representation is different. Let’s see how. 

Improper fraction and mixed number visual model

An improper fraction is a fraction whose numerator is greater than the denominator. Since the numerator > denominator, the value of an improper fraction is always greater than 1. 

Examples: $\frac{3}{2}, \frac{9}{4}, \frac{47}{12}$ 

A mixed fraction is a fraction which consists of a whole number and a proper fraction. Thus, a mixed number is always greater than 1. 

Examples: $1\frac{1}{2}, 2\frac{1}{4}, 3\frac{11}{12}$ 

Visualizing improper fraction to mixed number conversion

So, how do we turn an improper fraction into a mixed number? Let’s find out!

How to Convert an Improper Fraction to a Mixed Number

Let’s understand the steps with an example. Suppose we have to convert an improper fraction $\frac{7}{4}$ to a mixed number. If we visualize $\frac{7}{4}$, we get 

Step 1: Divide the numerator by the denominator. In this case, we get

Division of 7 by 4

Step 2: Note down the quotient and remainder. The quotient acts as the whole number part of the mixed number. The remainder is the new numerator. The denominator stays the same.

In simple words, write the mixed number in the form

 $Quotient\frac{Remainder}{Divisor}$. 

In this case, we get $\frac{7}{4} = 1 R 3$

It means that quotient $= 1$ and remainder $= 3$

Thus, $\frac{7}{4} = 1\frac{3}{4}$

Visual representation of an improper fraction and a mixed number

Converting an Improper Fraction To Mixed Number: Examples

Let’s discuss a few examples.

Example 1:$\frac{7}{3} = 2\frac{1}{3}$

Conversion of an improper fraction 7/3 to mixed number

Example 2: $\frac{14}{3} = 4\frac{2}{3}$

Converting improper fraction 14/3 to mixed number

Addition of Improper Fraction and Mixed Number

Addition of an improper fraction and a mixed number is quite easy. It can be done easily by converting the mixed number into an improper fraction. We will discuss two cases here.

Same Denominators

If the denominators of two fractions are the same, they are called the like fractions. In case the denominators are the same, then the numerators can be added while the denominator remains the same. 

Suppose we have to add $2\frac{1}{4}$ to $\frac{11}{4}$. 

$2\frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{9}{4}$

$\frac{9}{4} + \frac{11}{4} = \frac{20}{4} = 5$

Different Denominators

If the denominators of two fractions are different, they are called unlike fractions. Here, we first change them to a common denominator using the LCM method.

Suppose we have to add $2\frac{1}{2}$ to $\frac{7}{3}$.

$2\frac{1}{2} = \frac{5}{2}$

LCM $(2, 3) = 6$

$\frac{5 \times 3}{2 \times 3} = \frac{15}{6}$

$\frac{7 \times 2}{3 \times 2} = \frac{14}{6}$

$2\frac{1}{2} + \frac{7}{3} = \frac{15}{6} + \frac{14}{6}$

    $= \frac{15 + 14}{6}$

    $= \frac{29}{6}$

    $= 4\frac{5}{6}$

Facts on Improper Fraction to Mixed Number Conversion

  • The value of an improper fraction is always greater than or equal to 1.
  • To convert an improper fraction to a mixed number, we divide the numerator by the denominator. The whole number part of the mixed number is the quotient of the division.

Conclusion

In this article, we learned how to convert improper fractions into mixed numbers. Let’s solve a few examples and practice problems for revision.

Solved Examples on Improper Fraction to Mixed Number Conversion

1. Convert improper fraction into a mixed number: 175 

Solution:

Divide 17 by 5.

17 divided by 5

Note down the quotient and remainder. 

Quotient $= 3$

Remainder $= 2$

The quotient becomes the whole number part of the mixed number. The remainder acts as the new numerator. The denominator stays the same. 

$\frac{17}{5} = 3\frac{2}{5}$

2. Convert improper fraction into a mixed number: $\frac{121}{10}$

Solution: 

121 divided by 10

Quotient $= 12$ is to be written the new whole part of the mixed number.

Remainder $= 1$ is the new numerator. 

Denominator $= 10$ stays the same.

Thus, $\frac{121}{10} = 12\frac{1}{10}$

3. Convert improper fraction into a mixed number: $\frac{10}{3}$.

Solution: 

10 divided by 3

Quotient $= 3$

Remainder $= 1$

$\frac{10}{3} = 3\frac{1}{3}$

4. Add a mixed number and an improper fraction: $2\frac{3}{5} + \frac{21}{5}$. 

Solution:

To add $2\frac{3}{5}$ and $\frac{21}{5}$, we first need to convert improper fraction into a mixed number.

$2\frac{3}{5} = \frac{(5 \times 2) + 3}{5} = \frac{13}{5}$ 

$2\frac{3}{5} + \frac{22}{5} = \frac{13}{5} + \frac{21}{5} = \frac{13 + 21}{5} = \frac{34}{5}$

34 divided by 5

Quotient $= 6$

Remainder $= 4$

Thus, $\frac{34}{5} = 6\frac{4}{5}$

5. Convert improper fraction into a mixed number: $\frac{15}{7}$ 

Solution:

Improper Fraction to Mixed Number –  Conversion, Example, Facts, FAQs

Quotient $= 2$

Remainder $= 1$

$\frac{15}{7} = 2\frac{1}{6}$

Practice Problems on Improper Fraction to Mixed Number Conversion

Improper Fraction to Mixed Number -  Conversion, Example, Facts, FAQs

Attend this quiz & Test your knowledge.

1

Convert $\frac{80}{9}$ into a mixed fraction.

$6\frac{8}{9}$
$8\frac{8}{9}$
$8\frac{7}{9}$
$9\frac{1}{9}$
CorrectIncorrect
Correct answer is: $8\frac{8}{9}$
$80\div 9 = 8\; R \;8$
Quotient $= 8$
Remainder $= 8$
$\frac{80}{9} = 8\frac{8}{9}$
2

What will you get when you convert $\frac{138}{11}$ into a mixed fraction?

$11\frac{5}{11}$
$10\frac{11}{6}$
$12\frac{6}{11}$
$11\frac{6}{11}$
CorrectIncorrect
Correct answer is: $12\frac{6}{11}$
Dividend $= 138$
Divisor $= 11$
Quotient $= 12$
Remainder $= 6$
$\frac{138}{11} = 12\frac{6}{11}$
3

On converting $\frac{99}{8}$ into a mixed fraction, we get ____.

$12\frac{1}{8}$
$11\frac{3}{8}$
$10\frac{3}{8}$
$12\frac{3}{8}$
CorrectIncorrect
Correct answer is: $12\frac{3}{8}$
Dividend = 99
Divisor = 8
Quotient = 12
Remainder = 3
$\frac{99}{8} = 12\frac{3}{8}$
4

Add $4\frac{1}{2}$ and \frac{13}{2}$.

11
$11\frac{1}{2}$
$12\frac{1}{2}$
12
CorrectIncorrect
Correct answer is: 11
$4\frac{1}{2} + \frac{13}{2} = \frac{9}{2} + \frac{13}{2} = \frac{22}{2} = 11$
5

An improper fraction and a mixed number is always greater than or equal to ____.

0
1
$\;-\;1$
2
CorrectIncorrect
Correct answer is: 1
The value of any improper fraction or a mixed number is always greater than or equal to 1.

Frequently Asked Questions on Improper Fraction to Mixed Number Conversion

For converting a mixed fraction to an improper fraction, we multiply the denominator by the whole number and add the product to the numerator. This value represents the numerator. The denominator stays the same.If $a\frac{b}{c}$ is the mixed fraction, then improper fraction $= \frac{(a \times c) + b}{c}$

A proper fraction is a fraction where the numerator is less than the denominator, such as $\frac{1}{5},\;\frac{4}{9},\;\frac{16}{21}$ etc. An improper fraction is a fraction where the numerator is greater than the denominator, such as $\frac{3}{2},\; \frac{7}{4},\; \frac{131}{12}$ etc.

No, we can only convert an improper fraction to a mixed fraction.

No, the numerator of the fractional part of a mixed number is always greater than 0. It shows that the remainder is 0, which in turn means we get the whole number as the answer.

A proper fraction is a fraction where the numerator is less than the denominator, such as $\frac{1}{5}$, $\frac{4}{9}$, $\frac{16}{21}$, etc. A mixed fraction is a fraction which consists of a whole number and a proper fraction, such as $1\frac{1}{2}$, $2\frac{1}{4}$, $3\frac{11}{12}$, etc.