Answer
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Step 1:: Recall that the product of two fractions can be found by multiplying the numerators and multiplying the denominators separately.
\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}
This gives us the formula:
Step 2:: In this case, we have a = \frac{1}{3} and b = \frac{4}{5}.
ac = \frac{1}{3} \times \frac{4}{5} = \frac{4}{15}
Multiply the numerators:
Step 3:: Multiply the denominators:
bd = \frac{3}{1} \times \frac{5}{4} = \frac{15}{4}
Step 4:: Combine the results from Steps 2 and 3 using the formula from Step 1:
\frac{1}{3} \times \frac{4}{5} = \frac{4}{15} \times \frac{15}{4} = \frac{60}{60}
Step 5:: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 60 in this case:
\frac{60}{60} = \frac{60 \div 60}{60 \div 60} = \frac{1}{1}
Final Answer
The product of \frac{1}{3} and \frac{4}{5} is equal to 1.
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