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: 32,94,4712 

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: 112,214,31112 

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 74 to a mixed number. If we visualize 74, 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

 QuotientRemainderDivisor

In this case, we get 74=1R3

It means that quotient =1 and remainder =3

Thus, 74=134

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 1:73=213

Conversion of an improper fraction 7/3 to mixed number

Example 2: 143=423

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 214 to 114

214=(2×4)+14=94

94+114=204=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 212 to 73.

212=52

LCM (2,3)=6

5×32×3=156

7×23×2=146

212+73=156+146

    =15+146

    =296

    =456

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. 

175=325

2. Convert improper fraction into a mixed number: 12110

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, 12110=12110

3. Convert improper fraction into a mixed number: 103.

Solution: 

10 divided by 3

Quotient =3

Remainder =1

103=313

4. Add a mixed number and an improper fraction: 235+215. 

Solution:

To add 235 and 215, we first need to convert improper fraction into a mixed number.

235=(5×2)+35=135 

235+225=135+215=13+215=345

34 divided by 5

Quotient =6

Remainder =4

Thus, 345=645

5. Convert improper fraction into a mixed number: 157 

Solution:

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

Quotient =2

Remainder =1

157=216

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 809 into a mixed fraction.

689
889
879
919
CorrectIncorrect
Correct answer is: 889
80÷9=8R8
Quotient =8
Remainder =8
809=889
2

What will you get when you convert 13811 into a mixed fraction?

11511
10116
12611
11611
CorrectIncorrect
Correct answer is: 12611
Dividend =138
Divisor =11
Quotient =12
Remainder =6
13811=12611
3

On converting 998 into a mixed fraction, we get ____.

1218
1138
1038
1238
CorrectIncorrect
Correct answer is: 1238
Dividend = 99
Divisor = 8
Quotient = 12
Remainder = 3
998=1238
4

Add 412 and \frac{13}{2}$.

11
1112
1212
12
CorrectIncorrect
Correct answer is: 11
412+132=92+132=222=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 abc is the mixed fraction, then improper fraction =(a×c)+bc

A proper fraction is a fraction where the numerator is less than the denominator, such as 15,49,1621 etc. An improper fraction is a fraction where the numerator is greater than the denominator, such as 32,74,13112 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 15, 49, 1621, etc. A mixed fraction is a fraction which consists of a whole number and a proper fraction, such as 112, 214, 31112, etc.