Answer :

Sure! Let's solve the problem of multiplying the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{15}{16}\)[/tex] step-by-step.

1. Multiply the Numerators:
To multiply fractions, we start by multiplying the numerators (the top numbers) of each fraction together. For [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{15}{16}\)[/tex], we calculate:
[tex]\[
12 \times 15 = 180
\][/tex]

2. Multiply the Denominators:
Next, multiply the denominators (the bottom numbers) of each fraction together:
[tex]\[
25 \times 16 = 400
\][/tex]

3. Form the New Fraction:
The result of multiplying these two fractions is a new fraction with the product of the numerators over the product of the denominators:
[tex]\[
\frac{180}{400}
\][/tex]

4. Simplify the Fraction:
To simplify [tex]\(\frac{180}{400}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator, which is 20 in this case. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{180 \div 20}{400 \div 20} = \frac{9}{20}
\][/tex]

5. Convert to Decimal (Optional):
If needed, convert the simplified fraction into a decimal by dividing the numerator by the denominator:
[tex]\[
9 \div 20 = 0.45
\][/tex]

So, [tex]\(\frac{12}{25} \cdot \frac{15}{16} = \frac{9}{20} = 0.45\)[/tex].

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