QuestionSimplify the expression: $\frac{1}{5} x + \frac{1}{11}(x + 16)$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $\frac{1}{5} x+\frac{1}{11}(x+16)$ . We need to simplify this expression

STEP 2

First, we need to distribute the $\frac{1}{11}$ to both terms inside the parentheses.
$\frac{1}{5} x+\frac{1}{11}x+\frac{1}{11}*16$

STEP 3

Now, we need to calculate the multiplication of $\frac{1}{11}$ and $16$ .
$\frac{1}{5} x+\frac{1}{11}x+\frac{16}{11}$

STEP 4

Next, we need to add the two terms with $x$ together. Since they have the same variable, they are like terms and can be combined.
$\frac{1}{}x + \frac{1}{11}x = \left(\frac{1}{} + \frac{1}{11}\right)x$

STEP 5

Now, we need to add the fractions $\frac{1}{5}$ and $\frac{1}{11}$ together. In order to do this, we need to find a common denominator. The least common multiple of $5$ and $11$ is $55$ , so that will be our common denominator.
$\left(\frac{1}{5} + \frac{1}{11}\right)x = \left(\frac{11}{55} + \frac{5}{55}\right)x$

STEP 6

Next, we add the fractions together.
$\left(\frac{11}{55} + \frac{5}{55}\right)x = \frac{16}{55}x$

STEP 7

Finally, we combine the two terms to get the simplified expression.
$\frac{16}{55}x + \frac{16}{11}$ So, the simplified expression is $\frac{16}{55}x + \frac{16}{11}$ .

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