Question

perform the operations and, if possible, simplify. \\(\frac{2}{3} - \frac{1}{6} + \frac{5}{18}\\) enter a reduced fraction or integer.

Explanation:

Step1: Find a common denominator

The denominators are 3, 6, and 18. The least common denominator (LCD) of 3, 6, and 18 is 18. Rewrite each fraction with the denominator 18:

• For $\frac{2}{3}$, multiply numerator and denominator by 6: $\frac{2\times6}{3\times6}=\frac{12}{18}$
• For $\frac{1}{6}$, multiply numerator and denominator by 3: $\frac{1\times3}{6\times3}=\frac{3}{18}$
• $\frac{5}{18}$ remains as it is.

Step2: Perform the operations

Now, substitute the rewritten fractions into the expression:
$\frac{12}{18}-\frac{3}{18}+\frac{5}{18}$
First, subtract $\frac{3}{18}$ from $\frac{12}{18}$: $\frac{12 - 3}{18}=\frac{9}{18}$
Then, add $\frac{5}{18}$ to $\frac{9}{18}$: $\frac{9+5}{18}=\frac{14}{18}$

Step3: Simplify the fraction

Simplify $\frac{14}{18}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
$\frac{14\div2}{18\div2}=\frac{7}{9}$

Answer:

$\frac{7}{9}$