Question

find the product.
\\(\frac{7}{9} \times \frac{3}{21}\\)
enter your simplified answer.
?

Explanation:

Step1: Multiply numerators and denominators

To find the product of two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), we use the rule \(\frac{a}{b} \times \frac{c}{d}=\frac{a\times c}{b\times d}\). So for \(\frac{7}{9} \times \frac{3}{21}\), we multiply the numerators \(7\times3 = 21\) and the denominators \(9\times21=189\). So we get \(\frac{21}{189}\).

Step2: Simplify the fraction

We can simplify \(\frac{21}{189}\) by finding the greatest common divisor (GCD) of 21 and 189. The GCD of 21 and 189 is 21. Divide both the numerator and the denominator by 21: \(\frac{21\div21}{189\div21}=\frac{1}{9}\). Alternatively, we can simplify before multiplying. Notice that 7 and 21 have a common factor of 7, and 3 and 9 have a common factor of 3. So \(\frac{7\div7}{9\div3}\times\frac{3\div3}{21\div7}=\frac{1}{3}\times\frac{1}{3}=\frac{1\times1}{3\times3}=\frac{1}{9}\).

Answer:

\(\frac{1}{9}\)