Improper Fractions: An Improper fraction has a top number larger than the bottom number, It is “top-heavy”. Improper fractions can be written as a number plus a fraction. Improper fraction convert to a mixed number is to divide the fraction’s numerator by its denominator.

- One way Improper fraction convert to a mixed number is to divide the fraction’s numerator by its denominator. The integer part of the answer of division is the integer part of the mixed number. The denominator is the same as the original denominator.
- Another way divide the numerator of fractions by its denominator and then convert the decimal portion of the answer to a fraction.

Improper fractions having the numerator (top number) greater than the denominator (bottom number).

Example: 3/2, 15/9, 6/5 etc.

## Table of Contents

- Fractions
- Simplify Fractions
- Adding Fractions
- Multiplying Fractions
- Subtracting Fractions
- Dividing Fractions
- Proper Fractions
- Improper Fractions
- Mixed Fractions
- Like Fractions
- Unlike Fractions
- Fraction Calculator
- Fraction Simplifier
- Mixed Fraction Calculator
- Convert Fraction to Decimal
- Convert Decimal to Fraction

## Improper Fraction Definition

In a fraction if the numerator value is more than the denominator value, we call that fraction as improper fraction. So to change a fraction to improper fraction means, then it should be a mixed fraction.

Example :

(i) 10/7 , 11/5 , 13/12 , …… are improper fractions

(ii) 5 3/5 , 3 1/2, 4 7/9 are mixed fractions.

**Practice Improper Fractions**

(iii) Which of the following are improper fractions?

5/7, 2/5, 8/5, 13/17, 21/25, 29/49

(iv) Find the missing improper fraction of the following series

11/2, 13/2, 15/2, _____, 19/2, 21/2

## Convert Improper Fraction to Mixed Fraction

**Steps to convert an improper fraction to mixed fraction:**

- By Dividing the numerator with the denominator and then
- Write down the whole number answer
- Write down any remainder which we got above the denominator.

Note: All improper fractions can be converted to mixed fraction.

**Below you could see the Improper Fraction to Mixed Fraction example:**

Question: Convert the improper fraction 5/3 into mixed fraction.

Solution:

5/3 is a fraction where 5 is on the numerator and 3 is on the denominator

Since the numerator is greater than the denominator it is known as improper fraction.

To convert this improper fraction to mixed fraction we divide the numerator by the denominator

So, divide 5 by 3 [3 goes 1 times in 5 and the remainder we have 2]

So, here 1 is the whole number and the remainder 2 is the numerator and 3 will be the denominators

5/3 = 1 2/3

## Convert Mixed Fraction to Improper Fraction

All mixed fraction can be converted to improper fraction. The inverse process of improper to mixed is the process of mixed to improper

**Following are the steps to convert mixed fraction to improper fraction:**

- The denominator of the mixed number is multiplied with the whole number of the mixed fraction.
- After the first step completed the numerator part is added with the multiplied value.
- The sum will become the improper fraction of numerator and the denominator is placed as it is given.
- The denominator of the mixed number will be same as the denominator of the improper fraction.

**Mixed Fraction to Improper Fraction Example:**

Question: Convert the mixed fraction 2 1/3 into improper fraction.

Solution:

Here 2 is the whole number 1 is on the numerator and 3 is on the denominator

To convert this mixed fraction to improper fraction there are certain steps

Step 1: Multiply the denominator with the whole number

So 2 × 3 = 6

Step 2: Now add the numerator with that and place the same denominator as it is

So 6 + 1 = 7

7/3 is the improper fraction of 2 1/3.

## Adding Improper Fractions

In fraction the numerator is greater than the denominator means, such a fraction is called improper fraction.

**Steps for adding improper fraction:**

- Step 1: Initial step is the check whether the denominator is same or different.
- Step 2: If the denominators are same add the numerators
- Step 3: If the denominators are different then we have to make the common denominator by taking the Least common denominator
- Step 4: Convert the denominator as a least common denominator
- Step 5: Finally add the numerators

Note: When we add two improper fractions the result is also an improper fraction

**Adding improper fractions examples**

Question 1: Add given improper fraction 7/5 + 11/7

Solution:

Step 1: Here the denominators are different

Step 2: Take the LCD for 5,7

LCD of 5, 7 = 35

Step 3: To make the common denominator as 35

Multiply and divide by 7 for the first term and 5 for the second term

7/5 × 7/7 + 11/7 × 5/5

49/35 + 55/35

Step 4: Add the numerator,

49+55/35 = 104/35

Hence the answer for 7/5 + 11/7 = 104/35

Question 2: Add given improper fraction 9/7 + 14/11

Solution:

Step 1: Here the denominators are different

Step 2: Take the LCD for 7, 11

LCD of 7, 11 = 77

Step 3: To make the common denominator as 77

Multiply and divide by 11 for the first term and 7 for the second term

9/7 × 11/11 + 14/11 × 7/7

99/77 + 98/77

Step 4: Add the numerator,

98+99/77 = 197/77

Hence the answer for 9/7 + 14/11 = 197/77

## Multiplying Improper Fractions

The improper fraction is also the one form of mixed numbers. Because if we multiplying the mixed numbers means first convert the mixed numbers as improper fractions. Sometimes, this improper fractions have equal value in both numerator and denominator.

**The rules for multiplying the improper fractions with other types of numbers:**

- If we multiplying the improper fractions with whole number means that whole number is multiplied with numerator value of improper fraction.
- If we multiplying the improper fractions with mixed numbers means first convert the mixed number into improper fraction. Then multiply both improper fraction.
- If we multiplying two improper fractions means we perform normal multiplication.

Below you could see how to multiply improper fractions

**Multiplying Improper Fractions Examples:**

Question 1: Multiplying given two improper fractions. A = 6/5 and B = 7/2 .

Solution:

The given two improper fractions are 6/5 and 7/2 .

The multiplication of improper fractions are 6/5 x 7/2 = 42/10 .

Here we can simplify the resultant fraction. So we get the answer as 21/5 .

Question 2: Multiplying the 1 10/3 and 7/2 improper fractions.

Solution:

The given improper fractions are 1 10/3 and 7/2 .

First the given mixed number is converted into improper fraction as 13/3 .

Multiplication of two improper fraction as 13/3 x 7/2 = 91/6

## Subtracting Improper Fractions

**Steps for adding improper fraction:**

- check whether the denominator is same or different.
- If the denominators are same subtract the numerators
- If the denominators are different then we have to make the common denominator by taking the Least common denominator
- convert the denominator as a least common denominator
- Finally subtract the numerators

**Below you could see examples for subtracting improper fractions**

Question 1: Subtracting improper fractions: 9/7 – 5/2

Solution:

Numerator of the both fraction is larger than the denominator and both fraction denominators are different so we need to take LCM, then only we make the both the fraction has same denominator, it will be shown below,

LCM of 7 and 2 is 14

9×2/7×2 – 5×7/2×7

Simplify the above equation then we do the subtraction operation

18/14 – 35/14

−17/14

Question 2: Subtracting improper fractions: 11/9 – 9/4

Solution:

Numerator of the both fraction is larger than the denominator and both fraction denominators are different so we need to take LCM, then only we make the both the fraction has same denominator, it will be shown below,

LCM of 9 and 4 is 36

11×4/9×4 – 9×9/9×4

Simplify the above equation then we do the subtraction operation

44/36 – 81/36

−37/26

## Dividing Improper Fractions

**Steps for dividing improper fractions:**

- Interchange numerator and denominator of that second improper fraction.
- Next, multiply improper fractions using the formula a∗c/b∗d.
- Now ,Simplify fraction to get answer.

**Below you could see dividing improper fractions examples:**

Question 1: Solve 14/12 ÷ 16/12

Solution:

Dividing improper fractions 14/12 ÷ 161/2

The given two improper fractions 14/12 and 16/12

Interchange numerator and denominator of that second improper fraction 16/12 = 12/16

We need to multiply the improper fractions

14/12 × 12/16

Using this formula

a∗c/b∗d

a = 14, b = 12, c = 12 and d = 16.

we get

= 14×12/12×16

= 14/16

This can be simplified has

= 7/8

Answers for the improper fraction 14/12 ÷ 16/12 = 7/8

Question 2: Solve 18/12 ÷ 16/12

Solution:

Dividing improper fractions 18/12 ÷ 16/12

The given two improper fractions 18/12 and 16/12

Interchange numerator and denominator of that second improper fraction 16/12 = 12/16

We need to multiply the improper fractions

18/12 × 12/16

Using this formula

a∗c/b∗d

a = 18, b = 12, c = 12 and d = 16

we get

= 18×12/12×16

= 18/16

This can be simplified as= 9/8

Answers the improper fraction 18/12 ÷ 16/12 = 9/8

## Improper Fraction Examples

Solution:

Denominators are same so we can add numerators directly

8/5 + 9/5 = 8+9/5 = 17/5

Solution:

Denominators are same so we can subtract numerators directly

15/2 – 21/2 = 15−2/12 = −6/2 = -3

Solution:

Denominators are not same so we have to make it same

Multiply first fraction by 5 and second fraction by 2

7/2 + 9/5 = 35/10 + 18/10

= 35+18/10

= 53/10

Solution:

Denominators are not same so we have to make it same.

Multiply first fraction by 5

5/3 – 13/15 = 25/15 – 13/15

= 25−13/15 = 12/15 = 4/5

Solution:

Reducing the improper fraction 60/24

First change the value 60

6 x 10 = 60

To change the value 24

6 x 4 = 24

We get

6×10/6×4 = 10/4

We can reducing the improper fraction we get 104

To change the value 10

2 x 5 = 10

To change the value 4

2 x 2 = 4

We get

5×2/2×2 = 5/2

Finally to reducing the improper fraction 60/24 = 5/2