UPSKILL MATH PLUS
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Learn moreConnection between the Area of a rectangle and fraction multiplication:
To find the length and breadth of the above shaded rectangle:
We should always start with a unit square (of side \(1\) unit).
\(\implies\) Length \(= \frac{1}{2}\)
\(\implies\) Breadth \(= \frac{1}{3}\)
From the above picture, we get,
Area of each rectangle \(= \frac{1}{6}\) sq. units
Because there are \(6\) such rectangles, they give a square of area \(1\) square unit.
What is the relation between the area and the product of length and breadth?
The area of a rectangle with fractional sides equals the product of its sides.
(i.e) Area of rectangle \(=\) Length \(\times\) Breadth
For the above example,
Area of rectangle \(= \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\) sq.units
Thus, if we want to find the product of two fractions, we can find the area of the rectangle formed with the two fractions as its sides.
Brahmagupta's Formula for multiplication of fractions:
If there are two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), multiplying those two fractions refers to multiplying the numerators together and the denominators together.
\(\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\)
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 \(\frac{3}{5} \times \frac{4}{5}\)
Solution:
\(\frac{3}{5} \times \frac{4}{5}\)
Using the above formula, we get,
\(\frac{3}{5} \times \frac{4}{5}\)
\(=\frac{3 \times 4}{5 \times 5}\)
\(=\frac{12}{25}\)
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