**Proper and improper fraction :**

Students who are at the initial stage of learning math must be aware of the different types of fractions.

The picture given below clearly illustrates the different types of fractions.

The value of a proper fraction will always be less than 1 and for improper fraction, it will be greater than 1.

The picture given below clearly illustrates this.

A quantity which is expressed as a whole number and a proper fraction. Always its value will be greater than or equal to 1.

The picture given below clearly illustrates this.

1. Improper fraction can be converted into mixed numeral and vice versa.

2. Proper fraction can never be converted into mixed numeral.

3. When we convert a mixed numeral into a fraction, always we would an improper fraction.

The picture given below illustrates how to convert an improper fraction into mixed number.

The picture given below illustrates how to write a mixed number as an improper fraction.

**Example 1 :**

Write the following improper fraction as mixed numeral.

**275 / 3**

**Solution : **

When we divide 275 by 3 as explained in the above picture, 3 goes into 275 by 91 times and we will have 2 left in 275.

By using the method explained in the picture above, the mixed fraction or mixed numeral which is equal to 275/3 is

**91 ^{2}⁄_{3}**

**Example 2 :**

Write the following improper fraction as mixed numeral.

**155 / 7**

**Solution : **

When we divide 155 by 7 as explained in the above picture, 7 goes into 155 by 22 times and we will have 1 left in 155.

By using the method explained in the picture above, the mixed fraction or mixed numeral which is equal to 155/7 is

**22 ^{1}⁄_{7}**

**Example 3 :**

Write the following improper fraction as mixed number.

**782 / 13**

**Solution : **

When we divide 782 by 13 as explained in the above picture, 13 goes into 782 by 60 times and we will have 2 left in 782.

By using the method explained in the picture above, the mixed fraction or mixed numeral which is equal to 782/13 is

**60 ^{2}⁄_{13}**

**Example 4 :**

Write the following mixed numeral as improper fraction.

**9 ^{3}⁄_{8}**

**Solution : **

We have to do the following steps to write the given mixed numeral as improper fraction.

**Step 1 : **

Multiply the denominator 8 by the whole number 9.

Thus, we get 72

**Step 2 : **

Add this 72 to the numerator 3.

Thus, we get 75.

**Step 3 : **

Now, form a fraction with this 75 as numerator and 8 (denominator in the given mixed number) as denominator.

Therefore, the required improper fraction is 75/8.

**Example 5 :**

Write the following mixed numeral as improper fraction.

**11 ^{13}⁄_{15}**

**Solution : **

We have to do the following steps to write the given mixed numeral as improper fraction.

**Step 1 : **

Multiply the denominator 15 by the whole number 11.

Thus, we get 165

**Step 2 : **

Add this 165 to the numerator 13.

Thus, we get 178.

**Step 3 : **

Now, form a fraction with this 178 as numerator and 15 (denominator in the given mixed number) as denominator.

Therefore, the required improper fraction is 178/15.

After having gone through the stuff given above, we hope that the students would have understood "Proper and improper fraction".

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