Question

evaluate.
\frac{2}{3} - \frac{1}{6} \cdot \frac{1}{4}
write your answer in simplest form.

Explanation:

Step1: Perform the multiplication

First, we calculate the multiplication part \(\frac{1}{6} \cdot \frac{1}{4}\). When multiplying fractions, we multiply the numerators together and the denominators together. So, \(\frac{1}{6} \cdot \frac{1}{4}=\frac{1\times1}{6\times4}=\frac{1}{24}\).

Step2: Perform the subtraction

Now we have the expression \(\frac{2}{3}-\frac{1}{24}\). To subtract these fractions, we need a common denominator. The least common denominator of 3 and 24 is 24. We convert \(\frac{2}{3}\) to a fraction with denominator 24: \(\frac{2}{3}=\frac{2\times8}{3\times8}=\frac{16}{24}\). Now we subtract: \(\frac{16}{24}-\frac{1}{24}=\frac{16 - 1}{24}=\frac{15}{24}\). We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So, \(\frac{15\div3}{24\div3}=\frac{5}{8}\).

Answer:

\(\frac{5}{8}\)