Let's solve the given problem step-by-step.
We need to multiply two fractions:
[tex]\[
\frac{2}{3} \times \frac{5}{9}
\][/tex]
Step 1: Multiply the numerators.
The numerator of the first fraction is 2, and the numerator of the second fraction is 5. Multiplying these together:
[tex]\[
2 \times 5 = 10
\][/tex]
Step 2: Multiply the denominators.
The denominator of the first fraction is 3, and the denominator of the second fraction is 9. Multiplying these together:
[tex]\[
3 \times 9 = 27
\][/tex]
So, the result of the multiplication is:
[tex]\[
\frac{2}{3} \times \frac{5}{9} = \frac{10}{27}
\][/tex]
Step 3: Simplify the fraction if possible.
We check to see if the fraction [tex]\(\frac{10}{27}\)[/tex] can be simplified. This means finding the greatest common divisor (GCD) of the numerator and the denominator.
In this case, the numerator is 10 and the denominator is 27. The GCD of 10 and 27 is 1. Since 1 is the only common divisor, the fraction [tex]\(\frac{10}{27}\)[/tex] is already in its simplest form.
Therefore, the simplified result is:
[tex]\[
\frac{10}{27}
\][/tex]
So, the detailed solution is:
1. Multiply the numerators: [tex]\(2 \times 5 = 10\)[/tex].
2. Multiply the denominators: [tex]\(3 \times 9 = 27\)[/tex].
3. The product of the fractions is: [tex]\(\frac{10}{27}\)[/tex].
4. Since the GCD of 10 and 27 is 1, [tex]\(\frac{10}{27}\)[/tex] is already in its simplest form.
Thus, the answer is
[tex]\[
\frac{2}{3} \times \frac{5}{9} = \frac{10}{27}
\][/tex]
