Compound fraction
A compound fraction (also called a complex fraction) is a fraction in which the numerator, denominator, or both are also fractions. For example, (3/4) ÷ (9/10) can be written as a compound fraction. To simplify it, you multiply by the reciprocal of the denominator fraction: (3/4) × (10/9) = 30/36 = 5/6. Compound fractions are essentially division problems in fraction form. This 7th grade math skill is taught in Saxon Math, Course 2, and reinforces understanding of fraction division and rational number operations.
Key Concepts
Property A compound fraction is a fraction where the numerator, denominator, or both are also fractions. It looks complicated, but it is just another way to write a division problem, like this: $\frac{\frac{3}{4}}{\frac{9}{10}}$.
Examples $\frac{\frac{2}{5}}{\frac{3}{7}} = \frac{2}{5} \div \frac{3}{7} = \frac{2}{5} \times \frac{7}{3} = \frac{14}{15}$ $\frac{6}{\frac{2}{3}} = 6 \div \frac{2}{3} = 6 \times \frac{3}{2} = 9$.
Explanation Don't be intimidated by these giant fractions! The main fraction bar is just a secret division sign. To solve it, rewrite the expression as a standard division problem, then use the 'flip and multiply' rule you already know.
Common Questions
What is a compound fraction?
A compound fraction (or complex fraction) is a fraction where the numerator, denominator, or both contain fractions. For example, (3/4) / (9/10) is a compound fraction.
How do you simplify a compound fraction?
Multiply the top fraction by the reciprocal of the bottom fraction. For (3/4) / (9/10), flip 9/10 to get 10/9, then multiply: (3/4) × (10/9) = 30/36 = 5/6.
What is the difference between a compound fraction and a regular fraction?
A regular fraction has whole numbers in the numerator and denominator. A compound fraction has one or more fractions in the numerator and/or denominator.
Why do compound fractions appear in math?
Compound fractions arise naturally in problems involving ratios of rates, unit conversions, and algebraic expressions. Knowing how to simplify them is an important pre-algebra skill.
What is a reciprocal in fractions?
The reciprocal of a fraction is made by flipping the numerator and denominator. The reciprocal of 3/4 is 4/3. Multiplying any fraction by its reciprocal always gives 1.
When do students learn compound fractions?
Compound fractions are typically covered in 7th grade math as part of rational number operations and fraction division.
Which textbook covers compound fractions?
Saxon Math, Course 2 covers compound fractions as part of its 7th grade curriculum.