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Answer :
To multiply fractions and provide the answer as a reduced fraction, let's follow these steps:
1. Write the fractions to be multiplied:
The fractions given are [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{4}{13}\)[/tex].
2. Multiply the numerators:
Multiply the top numbers (numerators) of both fractions.
[tex]\[
13 \times 4 = 52
\][/tex]
3. Multiply the denominators:
Multiply the bottom numbers (denominators) of both fractions.
[tex]\[
15 \times 13 = 195
\][/tex]
4. Write the result as a fraction:
Combine the results from the above two steps to form a new fraction.
[tex]\[
\frac{52}{195}
\][/tex]
5. Simplify the fraction:
Check if the fraction can be reduced to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator, and dividing both by it.
The GCD of 52 and 195 is 13.
6. Divide by the GCD:
[tex]\[
\frac{52 \div 13}{195 \div 13} = \frac{4}{15}
\][/tex]
Therefore, the product of the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{4}{13}\)[/tex], reduced to its simplest form, is [tex]\(\frac{4}{15}\)[/tex].
1. Write the fractions to be multiplied:
The fractions given are [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{4}{13}\)[/tex].
2. Multiply the numerators:
Multiply the top numbers (numerators) of both fractions.
[tex]\[
13 \times 4 = 52
\][/tex]
3. Multiply the denominators:
Multiply the bottom numbers (denominators) of both fractions.
[tex]\[
15 \times 13 = 195
\][/tex]
4. Write the result as a fraction:
Combine the results from the above two steps to form a new fraction.
[tex]\[
\frac{52}{195}
\][/tex]
5. Simplify the fraction:
Check if the fraction can be reduced to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator, and dividing both by it.
The GCD of 52 and 195 is 13.
6. Divide by the GCD:
[tex]\[
\frac{52 \div 13}{195 \div 13} = \frac{4}{15}
\][/tex]
Therefore, the product of the fractions [tex]\(\frac{13}{15}\)[/tex] and [tex]\(\frac{4}{13}\)[/tex], reduced to its simplest form, is [tex]\(\frac{4}{15}\)[/tex].
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