Simplify the expression one-sixth 𝑥 plus two-sixths 𝑥 plus five sixths 𝑥.
First, we ask the question, can we add these terms together? In order to add them together, they must be like terms. Like terms have the same variable taken to the same power. All three of these terms have 𝑥 as their variable. And all of the 𝑥 variables are taken to the first power. But we commonly write 𝑥 to the first power as 𝑥.
We’ve just shown how all three of these terms are like terms. And we combine like terms by combining their coefficients. We combine one-sixth plus two-sixths plus five-sixths. And we keep that 𝑥-variable.
To add fractions, you need common denominators, which we already have. And that means we add the numerators, one plus two plus five. The denominator doesn’t change. And our variable will still be 𝑥. One plus two plus five equals eight. The denominator doesn’t change. So we have eight over six 𝑥.
In order to simplify this expression fully, we need to consider if the coefficient eight over six can be simplified. Eight and six are both even numbers. They’re both divisible by two. If we divide the numerator and the denominator by two, eight divided by two equals four. Six divided by two equals three. Eight-sixths 𝑥 can be simplified to four-thirds 𝑥.
The simplified form of this expression is four-thirds 𝑥.