Finding Common Denominators

U02_l3_t1_we7 Finding Common Denominators

We have to rewrite the following fractions

with fraction with least common denominator

So LCD of the 2 fractions is going to be the LCM

of both of these denominators over here.

and if we can make this as common denominators

we can add the two fractions

First let us find the LCM,

let me write it out LCD of 8 & 6

is going to be the LCM of 8 & 6

and a couple of ways to think about the LCM

you could really take the multiples of 8 & 6

and see what their smallest common multiple is.

Multiples of 6 - 6,12,18,24,30... i can keep going

and the multiples of 8 are 8,16,24,. looks like

we are done. I have found a common multiple

it is the smallest multiple they have other

common multiples like 48,72 and we can go on

but this is their smallest common multiple

So it is 24. Another way to find the LCM is

take the prime factorization of 6 - 2x3

and the LCM of 6 must have one 2 & one 3

what is the prime factorization of 8 is 2x2x2.

Inorder to be divisible by 8 we need to have three 2's

in the prime factorization. To be divisible by 6

we need to have 2,3 and to be divisible by 8 we need

three 2's, we have only one 2 so we add a couple more

so thsi is now divisible by 6 & 8

So 2x2x2x3 = 24. So LCM of 8 & 6

which is the LCD also is 24

So we want to write each of this fractions as

24 as their denominator.

So lets start with 2/8, i want to write that as / 24

so get the denominator as 24,

we need to multiply the denominator by 3

inorder not to change the fraction, we need to

multiply the numerator also by the same number

so we will multiply numerator by 3 ; 2x3=6

so 2/8 = 6/24

2/8 x 3/3 = 6/24

and lets do the same things with 5/6

5/6 = / 24, i will do it in a different colour, blue

to get the denominator from 6 to 24, we need

to multiply by 4, so we need to multiply

numerator also by 4 so 5x4 = 20

5/6 = 20/24

so we have written both the fractions with common denominator

So we are done