Write an equation equivalent to
eight-ninths 𝑥 plus two-fifths equals 13 15ths.
So there will be multiple equations
that we could write that would be equivalent to this. However, let’s go ahead and write
one where there are no denominators.
We could choose to just divide each
fraction out and make them decimals. We could choose to multiply all
three pieces by the same number. And we could just pick whatever one
that we would want.
However, let’s go ahead and choose
a number that would get rid of all the denominators. So what would be the smallest
number that nine, five, and 15 are going to. It’s called the least common
Five goes into 15 evenly. But five does not go into nine. So we can’t use 15. So is there a number that nine and
15 both go into? That number would be 45.
So what we need to do to write an
equivalent equation is to multiply every single term by 45. And what should happen is that all
of our denominators will cancel into the 45.
Nine goes into itself once and goes
into 45 five times. Five goes into itself once and goes
into 45 nine times. 15 goes into itself once and into
45 three times.
So we have five times eight 𝑥 plus
nine times two equals three times 13, which gives us the equation 40𝑥 plus 18
So this would be an equivalent
equation to our eight-ninths 𝑥 plus two-fifths equals 13 15ths.