# FRACTION

## Fraction - Introduction

Fraction :

fraction represents a part of a whole or, more generally, any number of equal parts.  a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

In fractions (for example 17/23), the number above the line (17) is called numerator and the number below the line (23) is called denominator.

The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole.

For example, in the fraction 3/4, the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole.

The picture given below illustrates the fraction 3/4.

## Different kinds of fractions

Now, let us look at some different kinds of fractions.

Proper fraction :

A fraction is called a proper fraction if its

Denominator > Numerator.

Example : 3/4, 1/2, 9/10, 5/6

Improper fraction :

A fraction is called an improper fraction if its

Numerator > Denominator.

Example : 5/4, 6/5, 41/30, 51/25

Mixed fraction :

A fraction consisting of a natural number and a proper fraction is called a mixed fractions.

Example : 2 3/4, 1 4/5, 5 1/7

Think it :

Mixed fraction  =  Natural number + Proper fraction

Let us look at next stuff on "Fractions in mathematics"

## Addition and subtraction of fractions with same denominator

Example 1 :

Simplify : 2/5 + 3/5

Solution :

Here, for both the fractions, we have the same denominator, we have to take only one denominator and add the numerators.

Then, we get

2/5 + 3/5  =  (2+3) / 5  =  5/5  =  1

Example 2 :

Simplify : 7/5 - 3/5

Solution :

Here, for both the fractions, we have the same denominator, we have to take only one denominator and subtract the numerators.

Then, we get

7/5 - 3/5  =  (7-3) / 5  =  4/5

## Addition and subtraction of fractions with different denominators

Here, we explain two methods to add two fractions with different denominators.

1)  Cross multiplication method

2)  L.C.M method

Cross multiplication method :

If the denominators of the fractions are co-prime or relatively prime, we have to apply this method.

Fro example, let us consider the two fractions 1/8,  1/3.

In the above two fractions, denominators are 8 and 3.

For 8 and 3, there is no common divisor other than 1. So 8 and 3 are co-prime.

Here we have to apply cross-multiplication method to add the two fractions 1/8 and 1/3 as given below.

L.C.M method :

If the denominators of the fractions are not co-prime (there is a common divisor other than 1), we have to apply this method.

Fro example, let us consider the two fractions 5/12,  1/20.

In the above two fractions, denominators are 12 and 20.

For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.

For 12 & 20, we have the following common divisors other than 1.

2 & 4

So 12 and 20 are not co-prime.

In the next step, we have to find the L.C.M (Least common multiple) of 12 and 20.

12 =  2² x 3

20 = 2² x 5

When we decompose 12 and 20 in to prime numbers, we find 2, 3 and 5 as prime factors for 12 and 20.

To get L.C.M of 12 and 20, we have to take 2, 3 and 5 with maximum powers found above.

So, L.C.M of 12 and 20 = 2² x 3 x 5

= 4 x 3 x 5

= 60

Now we have to make the denominators of both the fractions to be 60 and add the two fractions 5/12 and 1/20 as given below.

Note :

We have to do the same process for subtraction of two fractions with different denominators.

Let us look at next stuff on "Fractions in mathematics"

## Multiplication of a fraction by a whole number

To multiply a proper or improper fraction with the whole number,first, we have to multiply the whole number with the numerator of the fraction, keeping the denominator same.

For example,

2 x 3/5   =  6/5

3 x  7/11  =  21/11

To multiply a mixed fraction by a whole number, first convert the mixed fraction to an improper fraction and then multiply.

For example,

4 x 3 4/7   =  4 x 25/7  =  100/7  =  14 2/7

Let us look at next stuff on "Fractions in mathematics"

## Converting improper fractions to mixed numbers

The picture given below clearly illustrates, how to convert improper fractions in to mixed numbers

## Multiplication of a fraction by a fraction

To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators.

For example,

2/3 x 4/5   =  8/15

1/3 x  7/11  =  7/33

## The reciprocal of a fraction

If the product of two non-zero numbers is equal to one, then the two numbers are reciprocal to each other.

That is, the reciprocal of 3/5 is 5/3 and the reciprocal 5/3 is 3/5.

Moreover,

(5/3)x(3/5)  =  1

Note:

Reciprocal of 1 is 1 itself. 0 does not have a reciprocal.

## Division of a whole number by a fraction

To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.

For example,

÷  2/5  =  6 x 5/2  =  30/2  =  15

While dividing a whole number by a mixed fraction, first convert the mixed fraction into improper fraction and then solve it.

÷  3 4/5  =  6 ÷ 19/5  =  6 x 5/19  =  30/19  =  1 11/19

## Division of a fraction by another fraction

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction.

For example,

1/5 ÷  3/7  =  1/5 x 7/3  =  7/15

After having gone through the stuff given above, we hope that the students would have understood "Fractions in mathematics".

Apart from the stuff given above, if you want to know more about "Fractions in mathematics", please click here

Apart from "Fractions in mathematics", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6