Simplifying Complex Fractions

Front

What is a complex fraction?

Back

A complex fraction is a fraction where the numerator, the denominator, or both contain fractions.

Front

How do you simplify a complex fraction?

Back

To simplify a complex fraction, find a common denominator for the fractions in the numerator and denominator, combine them, and then simplify the resulting fraction.

Front

What is the first step in simplifying the complex fraction \( \frac{\frac{a}{b}}{\frac{c}{d}} \)?

Back

The first step is to multiply the numerator by the reciprocal of the denominator: \( \frac{a}{b} \times \frac{d}{c} \).

Front

Simplify the complex fraction \( \frac{\frac{2}{3}}{\frac{4}{5}} \).

Back

The simplified form is \( \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6} \).

Front

What is the role of the least common denominator (LCD) in simplifying complex fractions?

Back

The least common denominator helps to combine fractions in the numerator and denominator before simplifying the complex fraction.

Front

Simplify the complex fraction \( \frac{\frac{x+1}{x}}{\frac{x-1}{x+2}} \).

Back

The simplified form is \( \frac{(x+1)(x+2)}{x(x-1)} \).

Front

What is the simplified form of \( \frac{\frac{3}{4}}{\frac{1}{2}} \)?

Back

The simplified form is \( \frac{3}{4} \times 2 = \frac{3}{2} \).

Front

Define 'reciprocal' in the context of fractions.

Back

The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \).

Front

What is the simplified form of \( \frac{\frac{5}{6}}{\frac{2}{3}} \)?

Back

The simplified form is \( \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} \).

Front

How do you handle complex fractions with variables?

Back

Follow the same steps as with numerical fractions: find a common denominator, combine, and simplify.