General Rule for multiplying two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\)
\(\frac{a}{b} \times \frac{c}{d} = \frac {a \times c}{b \times d}\)
This formula was first stated in the general form by \(\text{Brahmagupta}\) in his \(\text{Brahmasphutasiddhanta}\) in \(\text{628 CE}\).
The formula above works even when the multiplier or multiplicand is a whole number.
We can simply rewrite the whole number as a fraction with denominator \(1\).
Example:
1. Solve \(3 \times \frac{3}{4}\)
Solution:
\(3 \times \frac{3}{4}\) can be rewritten as \(\frac{3}{1} \times \frac{3}{4}\)
Using the above formula we get,
\(\frac{3}{1} \times \frac{3}{4}\)
\(=\frac{3 \times 3}{1 \times 4}\)
\(=\frac{9}{4}\)
Example:
2. Solve \(\frac{3}{5} \times 4\)
Solution:
\(\frac{3}{5} \times 4\) can be rewritten as \(\frac{3}{5} \times \frac{4}{1}\)
Using the above formula we get,
\(\frac{3}{5} \times \frac{4}{1}\)
\(=\frac{3 \times 4}{5 \times 1}\)
\(=\frac{12}{5}\)