Subtraction of fractions

Go down deep enough into anything and you will find mathematics.  ~Dean Schlicter

Fraction subtraction is similar to addition only. Every fraction simplification involves making denominator equal.

Let us try one example.

Ex1 : 1/2 - 1/4 = ?

           = (1x2)/(2x2) - 1/4 ( now both denominators are same i.e. 4)

           = 2/4 - 1/4 = 1/4

Ex2 : 1/3 - 1/4 - 1/6 = ?

           = (1x4)/(3x4) - (1x3)/(4x3) - (1x2)/(2x6) ( now all denominators are same)

           =      4/12 - 3/12 - 2/12 = -1/12

In the above example, how to conclude that we need to make all denominators to 12.

LCM of 3, 4 and 6 is 12. 

As I mentioned in LCM post, you can find this very easily. Please look into LCM post to know more details.

In next post we will do fraction simplification. We will try more examples...

 

Addition of fractions

Pure mathematics is, in its way, the poetry of logical ideas.  ~Albert Einstein

 

Fraction addition

Thumb rule in fractions: Simplification is easy if all denominators in fractions are equal. So try to make all denominators same. The purpose of finding LCM is making all denominators same.

Ex : 1/2 + 1/3

1/2 means 1 part out of 2 parts

1/3 means 1 part out of 3 parts

Total no of parts should be same to do addition or subtraction

so what we will do is

 1/2 = 1x3/2x3 = 3/6 means 3 parts out of 6 parts

 1/3 = 1x2/3x2 = 2/6 means 2 parts out of 6 parts

As total parts are same for both fractions, result is addition of two numerators 

result = 1/2 + 1/3 = 3/6 + 2/6 = 5/6

Conclusion is 1/a + 1/b = (a+b)/ axb

We can do this by simply memorizing above formula. But how many formulas you can remember. Try to learn simplification through mental calculation.

Let us try one more example.

Ex 2: 5/6 + 2/3 + 1/2

5/6 + 2/3 + 1/2 = 5/6 + (2x2)/(3x2) + (1x3)/(2x3)       -- making all denominators same

 = 5/6 + 4/6 + 3/6 = 12/6 = 2

Please remember if you multiply numerator and denominator with the same number, there is no change in value of fraction.

Try following examples: 

Ex 3 : 1/3 + 1/7 = ?

Ex 4 : 2/3 + 1/4 + 1/2 = ?

LCM of three numbers

Always substitute mentally the definitions in place of the defined.

                                                                                            --- Blaise Pascal

Ex 1: Find LCM of 2, 3 and 4

LCM of 2 and 4 : 4

LCM of 3 and 4 : 3x4= 12 (as no common factor for 3 and 4)

LCM of 2, 3 and 4 = 12

Ex2 : Find LCM of 3, 4, 5 and 6

LCM of 3, 4 and 5 : 3x4x5= 60 (as no common factor for 3, 4 and 5)

60 is divisible by  6.

LCM of 3, 4, 5 and 6 : 60

Ex3 : Find LCM of 12, 20, 25 and 30

LCM of 20 and 30 = 2x3x10= 60 ( no common factor for 2 and 3, 10 is common divisor for 20 and 30)
60 is divisible by 12 but not divisible by 25
LCM of 60 and 25 = 60x5 = 300 (as 300 is divisible by 12, 20, 25 and 30 )