Question

How do I get a common denominator

Answer 1

Common denominator

We want to find a number that is multiple of all the denominators of the fractions we have. For example, in the cases:

`\begin{gathered} (2)/(5)+(1)/(3) \\ \end{gathered}`

we have two denominators: 5 and 3

And for

`(1)/(3)+(3)/(12)`

we have 3 and 12

First method

2/5 + 1/3:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

5 x 3 = 15

then,

`(2)/(5)=(2*3)/(5*3)=(6)/(15)`

and

`(1)/(3)=(1*5)/(3*5)=(5)/(15)`

then we have that

`(2)/(5)+(1)/(3)=(6)/(15)+(5)/(15)`

1/3 + 3/12:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

3 x 12 = 36

then

`(1)/(3)+(3)/(12)=(1*12)/(3*12)+(3*3)/(12*3)=(12)/(36)+(9)/(36)`

Second method

1/3 + 3/12:

We can find the denominator by finding the multiples of both denominators:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We find some the numbers that both multiples share:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We choose the first common multiple, and this is the common denominator. In this case it is 12. Since

3 x 4 = 12, then

`(1)/(3)+(3)/(12)=(1*4)/(3*4)+(3)/(12)=(4)/(12)+(3)/(12)`