Video: Simplifying One-Variable Equations with Fractions of Different Denominators

Write an equation equivalent to ((8/9)𝑥) + 2/5 = 13/15.

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Video Transcript

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 multiple.

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 equals 39.

So this would be an equivalent equation to our eight-ninths 𝑥 plus two-fifths equals 13 15ths.

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