OPERATIONS WITH FRACTIONS

About "Operations with fractions"

Operations with fractions :

We can not imagine the subject Math without the term "Fraction". Because, we solve many problems with it. So, we must be aware of the operations which we often do in fractions.

Let us explore the following operations with fractions.

(i) Addition

(ii) Subtraction

(iii) Multiplication

(iv) Division

(v) Reciprocal

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"