Question

multiply the fractions. express your answer in its simplest form
(a) $\frac{2}{3} \times \frac{1}{3} =$
(b) $\frac{3}{7} \times \frac{2}{3} =$

Explanation:

Part (a)

Step1: Multiply numerators

To multiply fractions, we first multiply the numerators. For \(\frac{2}{5} \times \frac{1}{3}\), the numerators are \(2\) and \(1\). So, \(2\times1 = 2\).

Step2: Multiply denominators

Next, we multiply the denominators. The denominators are \(5\) and \(3\). So, \(5\times3=15\).

Step3: Form the fraction

Combining the results from Step 1 and Step 2, we get the fraction \(\frac{2}{15}\). Since \(2\) and \(15\) have no common factors other than \(1\), this is the simplest form.

Step1: Multiply numerators

For \(\frac{3}{7} \times \frac{2}{3}\), multiply the numerators \(3\) and \(2\). So, \(3\times2 = 6\).

Step2: Multiply denominators

Multiply the denominators \(7\) and \(3\). So, \(7\times3 = 21\).

Step3: Simplify the fraction

We get the fraction \(\frac{6}{21}\). Now, we simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is \(3\). \(\frac{6\div3}{21\div3}=\frac{2}{7}\).

Answer:

\(\frac{2}{15}\)

Part (b)