Question

Can someone explain to me in simple terms how to add fractions with different denominators?

Answer 1

adding fractions with different denominators requires finding a common denominator

e.g.

`(1)/(2) +(5)/(7)`

an easy way to find a common denominator is to simplify multiply the denominators together

in this case it'd be 14

next, in order to add the fractions, we need to make both of them have denominator 14

for
`(1)/(2)`, we multiply it by
`(7)/(7)`. note that this is essentially multiplying it by 1, but we don't simplify now, we do it later

`(1*7)/(2*7)=(7)/(14)`

we have to multiply 5/7 by 2/2

`(5*2)/(7*2) = (10)/(14)`

now we can add the numerators

`(10)/(14) + (7)/(14) = (17)/(14)`

also, you can use a formula derived from using common denominators

`(a)/(b) +(c)/(d)=(ad + bc)/(bd)`