# Improper Fractions

In mathematics, when we divide a complete part into some equal parts then each part shows the fraction of whole part. Like pizza, pizza is a circular in shape, if we divide it in 8 equal parts then each part is the fraction of whole part.

Fractions are written in the form of ratio of two numbers. The upper number is called as numerator and the number below is called as denominator.

For example: a/b is the fraction, in which a is numerator and b is the denominator. ## Improper fractions:

Improper fractions are those fractions in which numerator is greater than or equal to the denominator.

For example:

a/b is the proper fraction only if a > b.

5/3, 8/5, 12/11, 4/4 all are the improper fractions, because numerator is greater or equal than denominator. Here, 8 > 5, hence it is the improper fraction.

Note:

Each whole number is written in the form of improper fraction.

For example:

• 4 can be written as 4/4, where numerator and denominator both are equal and hence it is the improper fraction.
• Also, 7 can be written as 7/7, where numerator and denominator both are equal and hence it is the improper fraction.
• In this way, we can write the any whole number in the form of improper fraction.

### Mixed fractions:

Mixed fractions are those which are written in the form of whole number and the proper fraction both together.

For example:

2 2/3, 4 5/6, 3 6/7 all are the mixed fractions and then can simplified to improper fractions.

### Conversion of improper fractions into the proper fractions:

To convert the improper fraction into the mixed fraction we have to first divide the numerator by denominator in such way that the quotient must be whole number and remainder also we have to write.

The quotient is written as whole number and the remainder in the numerator and denominator will be keep as it is.

For example:

• 13/4 is the improper fraction which can be written in the form of mixed fraction as follows.

When we divide 13 by 4 then quotient is 3 which is a whole number and the remainder is 1.

Hence, we write 13/4 as 13/4 = whole number as quotient *remainder/ denominator

Thus, 13/4 = 3 ¼

• Also, we can write 7/5 in the mixed fraction form as follows.

When we divide 7 by 5 then quotient is 1 and the remainder is 2.

Hence, 7/5 = 1 2/5 is the mixed fraction form.

### Conversion of mixed fraction into the improper fraction:

While converting the mixed fraction into the improper fraction, we have to first multiply the whole number by denominator and then we have to add it to the numerator and the form we will get it is the improper fraction form.

For example:

• 2 3/5 is the mixed fraction, it can be written in the form of improper fraction as follows.

2 3/5 = (whole number*denominator + numerator) / denominator

2 3/5 = (2*5 + 3)/ 5 = (10+3)/5 = 13/5

And hence, 13/5 is the improper fraction as it has numerator greater than denominator.

• Also, we can write the mixed fraction 3 5/6 in the form of improper fraction as follows.

3 5/6 = (whole number*denominator + numerator) / denominator

3 5/6 = (3*6 + 5) / 6 = (18 + 5)/ 6= 23/ 6

Thus, 23/6 is the improper fraction since here numerator is greater than the denominator.

### Conversion of improper fraction into the decimal form:

To convert the improper fraction into the decimal form, we have to first divide the numerator by denominator as numerator is less than denominator. And we have to divide the numerator till we will get the remainder as zero.

For example:

• 13/5 is the improper fraction as numerator is less than denominator.

First we divide the numerator 13 by denominator 5 till we will get the remainder as zero.

So we got the answer as, 13/5 = 2.6

And hence, 2.6 is the decimal form of improper fraction 13/5.

• Also, we can convert the improper fraction 7/5 into the decimal form by dividing numerator 7 by the denominator 5 till we will get the answer as zero.

Hence we got, 7/5 = 1.4 and 1.4 is the decimal form of 7/5.

Updated: July 14, 2021 — 10:55 pm