Sure, let's evaluate the given expression step by step. The expression given is:
[tex]\[
\frac{2}{3} - \frac{4}{5} \cdot \frac{1}{6}
\][/tex]
### Step 1: Handle the multiplication within the expression
First, we need to multiply the fractions [tex]\(\frac{4}{5}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
\frac{4}{5} \cdot \frac{1}{6} = \frac{4 \cdot 1}{5 \cdot 6} = \frac{4}{30}
\][/tex]
Next, we need to simplify [tex]\(\frac{4}{30}\)[/tex]. The greatest common divisor (GCD) of 4 and 30 is 2, so we divide both the numerator and the denominator by 2:
[tex]\[
\frac{4}{30} = \frac{4 \div 2}{30 \div 2} = \frac{2}{15}
\][/tex]
So, we have:
[tex]\[
\frac{4}{5} \cdot \frac{1}{6} = \frac{2}{15}
\][/tex]
### Step 2: Perform the subtraction
Now, we subtract [tex]\(\frac{2}{15}\)[/tex] from [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{2}{3} - \frac{2}{15}
\][/tex]
### Step 3: Find a common denominator
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 15 is 15. Therefore, we convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{2}{3} = \frac{2 \cdot 5}{3 \cdot 5} = \frac{10}{15}
\][/tex]
So, the expression now is:
[tex]\[
\frac{10}{15} - \frac{2}{15}
\][/tex]
### Step 4: Perform the subtraction
Since the denominators are the same, we can subtract the numerators directly:
[tex]\[
\frac{10}{15} - \frac{2}{15} = \frac{10 - 2}{15} = \frac{8}{15}
\][/tex]
### Conclusion
Therefore, the result of the expression [tex]\(\frac{2}{3} - \frac{4}{5} \cdot \frac{1}{6}\)[/tex] is:
[tex]\[
\frac{8}{15}
\][/tex]
