Question

What is a common denominator for 5/6 and 2/9?

Answer 1

18

Explanation:

We have `5/6` and `2/9` and we're looking for the common denominator. Another way of saying this is to say we're looking for the Lowest Common Multiple of the two denominators. To find a LCM, I like to start with a prime factorization:

`6=2xx3`
`9=3xx3`

And now we gather up the largest groups of primes we can.

We have a group of 2s (just one of them, but that is a group), so we need a single 2.

We also have a group of 3s (there's two of them in the 9, so we need two 3s).

Therefore:

`LCM=2xx3xx3=18`

We can now convert the fractions:

`5/6(1),2/9(1)`

`5/6(3/3),2/9(2/2)`

`15/18,4/18`

Answer 2

`18`

Explanation:

To start with lets just think about the bottom numbers of 6 and 9.

Notice that 9 can be written as `6+3`.

So each 9 contains a 'spare' 3
Adding 9's means we accumulate the 'spare' 3's
Get 2 lots of 'spare' 3's and we have another 6. Which means we can exactly divide 6 into it with no remainder.

1st 9 `->6+color(red)(3)`
2nd 9`->ul(6+color(red)(3) larr" Add - counting in 9's"`
`color(white)("dddddd") 12 +color(red)(6 )= 18`

Every time you get another 6 you have found a common multiple.

So 18 is the first common multiple of both 6 and 9