2.6 As A Improper Fraction

In mathematics, when we dissever a complete function into some equal parts so each role shows the fraction of whole function. Like pizza, pizza is a circular in shape, if nosotros carve up it in viii equal parts and then each role 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 every bit 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 instance:

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

5/3, 8/five, 12/eleven, 4/iv 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 class of improper fraction.

For case:

iv can be written as 4/iv, where numerator and denominator both are equal and hence information technology is the improper fraction.
Also, seven can be written equally 7/seven, where numerator and denominator both are equal and hence it is the improper fraction.
In this way, nosotros can write the any whole number in the class 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 case:

2 2/iii, 4 5/6, three 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 manner that the quotient must be whole number and rest likewise we accept to write.

The quotient is written as whole number and the rest in the numerator and denominator will exist go along equally it is.

For example:

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

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

Hence, nosotros write 13/iv equally 13/four = whole number as caliber *rest/ denominator

Thus, 13/4 = 3 ¼

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

When we dissever 7 by 5 then caliber is 1 and the remainder is 2.

Hence, 7/5 = 1 two/5 is the mixed fraction class.

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 nosotros will become it is the improper fraction form.

For example:

ii three/5 is the mixed fraction, it tin can exist written in the grade of improper fraction every bit follows.

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

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

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

Also, we can write the mixed fraction 3 5/half dozen in the grade of improper fraction as follows.

three v/6 = (whole number*denominator + numerator) / denominator

iii v/6 = (3*half-dozen + v) / 6 = (xviii + 5)/ half dozen= 23/ vi

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

Conversion of improper fraction into the decimal form:

To convert the improper fraction into the decimal form, we accept to start split the numerator by denominator every bit numerator is less than denominator. And nosotros take to split up the numerator till we will get the rest as zero.

For example:

13/five is the improper fraction every bit numerator is less than denominator.

Kickoff we separate the numerator 13 past denominator 5 till we volition become the remainder equally zero.

And so we got the respond as, 13/5 = 2.half-dozen

And hence, ii.six is the decimal form of improper fraction 13/v.

Likewise, we tin convert the improper fraction seven/5 into the decimal form past dividing numerator 7 by the denominator five till we will become the respond as cypher.

Hence we got, 7/5 = 1.4 and i.4 is the decimal form of 7/5.