To find the product of the fractions [tex]\(\frac{5}{2}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex], follow these steps:
### Step 1: Multiply the Numerators
The numerator of the product is found by multiplying the numerators of the given fractions:
[tex]\[
\text{Numerator} = 5 \times 3 = 15
\][/tex]
### Step 2: Multiply the Denominators
The denominator of the product is found by multiplying the denominators of the given fractions:
[tex]\[
\text{Denominator} = 2 \times 10 = 20
\][/tex]
So, the product of the fractions before simplification is:
[tex]\[
\frac{15}{20}
\][/tex]
### Step 3: Simplify the Fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 15 and 20 is 5.
Now simplify the fraction by dividing both the numerator and the denominator by their GCD:
[tex]\[
\frac{15 \div 5}{20 \div 5} = \frac{3}{4}
\][/tex]
Thus, the simplified product of the fractions [tex]\(\frac{5}{2}\)[/tex] and [tex]\(\frac{3}{10}\)[/tex] is:
[tex]\[
\frac{3}{4}
\][/tex]
### Answer
The correct option is:
A. [tex]\(\frac{3}{4}\)[/tex]
