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 \( \frac{\frac{1}{2}}{\frac{3}{4}} \)?

Back

Multiply the numerator by the reciprocal of the denominator: \( \frac{1}{2} \times \frac{4}{3} = \frac{4}{6} \).

Front

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

Back

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

Front

What does it mean to divide fractions?

Back

Dividing fractions means multiplying by the reciprocal of the divisor.

Front

How do you divide the complex fraction \( \frac{\frac{1}{2}}{\frac{3}{4}} \)?

Back

Convert to multiplication: \( \frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{2}{3} \).

Front

What is the reciprocal of \( \frac{3}{4} \)?

Back

The reciprocal of \( \frac{3}{4} \) is \( \frac{4}{3} \).

Front

What is the result of simplifying \( \frac{\frac{5}{6}}{\frac{1}{2}} \)?

Back

The result is \( \frac{5}{3} \).

Front

What is a common mistake when simplifying complex fractions?

Back

A common mistake is failing to find a common denominator for the fractions in the numerator and denominator.

Front

What is the formula for simplifying a complex fraction?

Back

The formula is: \( \text{Complex Fraction} = \frac{\text{Numerator}}{\text{Denominator}} = \frac{\text{Numerator's Common Denominator}}{\text{Denominator's Common Denominator}} \).