Simplifying Complex Fractions

Front

What is a complex fraction?

Back

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

Front

How do you simplify a complex fraction?

Back

To simplify a complex fraction, multiply the numerator and the denominator by the least common denominator (LCD) of the fractions involved.

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions.

Front

Simplify the complex fraction: \( \frac{\frac{1}{2}}{\frac{1}{3}} \)

Back

\( \frac{\frac{1}{2}}{\frac{1}{3}} = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2} \)

Front

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

Back

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

Front

If you have \( \frac{\frac{3}{4}}{\frac{5}{6}} \), what is the simplified form?

Back

\( \frac{\frac{3}{4}}{\frac{5}{6}} = \frac{3}{4} \times \frac{6}{5} = \frac{18}{20} = \frac{9}{10} \)

Front

What does it mean to 'multiply by the reciprocal'?

Back

To 'multiply by the reciprocal' means to multiply by the flipped version of a fraction, where the numerator and denominator are swapped.

Front

How can you check if your simplification is correct?

Back

You can check your simplification by cross-multiplying or substituting values to see if both sides of the equation are equal.

Front

What is an example of a complex fraction with variables?

Back

An example is \( \frac{\frac{x+1}{x}}{\frac{x-1}{x+2}} \).

Front

What is the simplified form of \( \frac{\frac{x+1}{x}}{\frac{x-1}{x+2}} \)?

Back

\( \frac{\frac{x+1}{x}}{\frac{x-1}{x+2}} = \frac{x+1}{x} \times \frac{x+2}{x-1} = \frac{(x+1)(x+2)}{x(x-1)} \)