HOW TO ADD FRACTIONS - Why LCM, Explanations with insight

HOW TO ADD FRACTIONS

We know 2/3, 5/7, 3/7, 5/8, 4/9, 3/5, 7/3 are all fractions. It is of the form p/q

The upper part is called numerator and lower part is called as denominator.

In 3/7, 3 → numerator, 7 → denominator

Now, what is fraction? Where it comes in my life?

Take a paper and divide it into exactly four equal parts. Out of four equal parts made by one single paper, if we select exactly one part then here comes the fraction.

i.e. 1/4 Out of four equal parts, you have taken one part.

Now how much is 3/4 ? From four equal parts made by one single paper 3 parts is taken.

but we must Know , 3/4 itself is one single number(fraction)

We know, in 3/4 , 3 is numerator and 4 is denominator, because of our knowledge about number system our mind is conditioned to think 3 as one number and 4 as different number ,but it is wrong. The whole 3/4 itself is single number.

In 3/4 entire ( ¾) is one number, it is a single number

Now 3/4 is one fraction, 1/4 is one more fraction.

Then how to add these fractions?

Simple, 1/4 + 3/4 =

Here 4 is the common denominator Write 4 as denominator and just add numerator

i.e. 1/4 + 3/4 = ( 1 + 3 ) / 4 = 4/4

What is 4/4 ? Out of 4 equal parts, made by using 1 single paper, you have selected all 4, nothing but whole paper.

i.e. whole one paper you have taken i.e. 4/4 = 1

Rule NO 1. While adding fractions whenever denominator is same, just add/subtract numerator and keep common denominator as a denominator.

2/3 + 1/3 = 3/3 = 1

2/5 + 1/5 = 3/5

3/7 + 1/7 + 2/7 = 6/7

2/9 + 5/9 + 1/9 = 8/9

6/13 - 2/13 = 4/13

12/17 - 5/17 = 7/17

Is there any different rule whenever denominator is different?

Yes, what it is? Why it is so?

Take 2/3 and 5/6

2/3 + 5/6 = ?

What is 2/3 ? Take one paper divided it into 3 equal parts and keep 2 . i.e. 2/3

Remember the word ‘equal’

While adding fractions or subtracting fractions we must try to understand its real meaning.

What is 5/6 ?

Take one more paper divide it into six equal parts and keep 5 out of it i.e.

Then how much papers you keep now?

2/3 + 5/6 = ?

It is not so easy; think it again, 2 out of 3 and 5 out of 6 is how much?

It is difficult to say, how much it is;

Use different technique;

Dividing a paper in to 3 equal parts and taking 2 parts is 2/3

Dividing same paper into 6 equal parts and taking 4 parts is 4/6

Both are one and the same or not? 2/3= 4/6 (2/3 and 4/6 are same)

Dividing a paper in to 6 equal parts and taking 5 parts is 5/6

Rule NO2: is following Rule NO 1. (While adding fractions whenever denominator is same just add/subtract numerator and keep common denominator as a denominator.)

2/3 + 5/6 =

4/6 + 5/6 = (4 + 5)/6 = 9/6

So while adding fractions whenever denominators are different we must make same (common) denominator. Why?

To make equal number of divisions in each different events, so that it can be compared/added/subtracted. Instead of asking 2 out of 3 and 5 out of 6 is how much? It is better to ask 4 out of 6 and 5 out of 6 are how much?

But all the time it is difficult to apply this theory. So it is better to apply some technique to make equal denominator. Technique is

2/3 + 3/5 = ?

Denominators of given fractions are 3 and 5.

Find the product of denominators. (3 X 5 = 15)

2/3 x what /what = something / 15

2/3 x what /5 = something/15

2/3 x 5/5 = 10/15

similarly

3/5 x what/what = something/15

3/5 x what/3 = something /15

3/5 x 3/3 = 9/15

therefore

2/3 + 3/5 = 10/15 + 9/15 = 19/15

Add 3/5 and 4/7

Denominator product is (5 x 7=35)

3/5 + 7/7 = 21/35 , and 4/7 x 5/5 = 20/35 therefore

3/5 + 4/7 = 21/35 + 20/35 = 41/35

How to add three different fractions with three different denominators? And how to add mixed fractions?