Complex fraction represents a fraction where numerator, denominator or both numerator and denominator contains fraction. For example:
\(\displaystyle \frac{^1/_2}{3}\) (Numerator is a fraction)
\(\displaystyle \frac{2}{^1/_3}\) (Denominator is a fraction)
\(\displaystyle \frac{^1/_2}{^1/_3}\) (Numerator and Denominator are both fractions)
Operation with complex fractions should be handled in the same way as with simple fractions. First, convert complex fraction to its lowest term. Following are rules to convert complex fractions to simple fractions -
1) Write a fraction in division form
\(\displaystyle \frac{^1/_2}{3}\) can be expressed as \(\displaystyle \frac{1}{2} \div 3\)
\(\displaystyle\frac{2}{^1/_3}\) can be expressed as \(\displaystyle 2 \div \frac{1}{3}\)
\(\displaystyle \frac{^1/_2}{^1/_3}\) can be expressed as \(\displaystyle \frac{1}{2} \div \frac{1}{3} \)
2) Change the division sign to multiplication and invert the denominator. i.e. inverting the fraction that occurs on the right side of the division sign.
\(\displaystyle \frac{1}{2} \div 3\) \(\displaystyle = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\)
\(\displaystyle 2 \div \frac{1}{3} = 2\times3 = 6\)
\(\displaystyle \frac{1}{2} \div \frac{1}{3} =\frac{1}{2} \times 3 = \frac{3}{2}\)
Let’s perform a few arithmetic operations with complex fractions.
Addition:
\(\displaystyle \frac{^1/_2}{3} + \frac{2}{^1/_3} = \frac{1}{6} + \frac{6}{1}\)
Now complex fraction is reduced to simple fraction. Add two simple fractions by making the denominator of both the fractions equal.
\(\displaystyle \frac{1}{6} + \frac{6\times6}{1\times6} = \frac{1}{6} + \frac{36}{6} = \frac{37}{6}\)
Multiplication:
\(\displaystyle \frac{^1/_2}{3} \times \frac{2}{^1/_3} = \frac{1}{6} \times \frac{6}{1} = 1\)
Division:
\(\displaystyle \frac{^1/_2}{3} \div \frac{2}{^1/_3} = \frac{1}{6} \div \frac{6}{1} = \frac{1}{36}\)
Point to remember - Reduce complex fraction to simple fraction before performing any operation on it.
Applying Compound Fractions to Real Life
Complex fractions may seem abstract, but they are quite useful in real life. For example, in cooking, a recipe might require half of \( \frac{3}{4} \) cup of sugar, leading to a compound fraction. Understanding how to simplify these can quickly help you figure out that you need \( \frac{3}{8} \) cup of sugar.
Another practical application is in measurements and constructions where dimensions might be given in fractions, and calculations require further division or multiplication of these fractional measures. Being fluent in simplifying compound fractions can save time and reduce errors in such tasks.
