How do we multiply fractions?
Understand the Problem
The question is asking how to multiply fractions, specifically in the context of rational algebraic expressions. It indicates a need for understanding the process and rules involved in this mathematical operation.
Answer
The result of multiplying the fractions $\frac{a}{b}$ and $\frac{c}{d}$ is $\frac{a \cdot c}{b \cdot d}$.
Answer for screen readers
The resulting fraction from multiplying $\frac{a}{b}$ and $\frac{c}{d}$ is $$ \frac{a \cdot c}{b \cdot d} $$.
Steps to Solve
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Identify the fractions First, identify the rational algebraic expressions that you will be multiplying. For example, let's consider the fractions $\frac{a}{b}$ and $\frac{c}{d}$.
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Multiply the numerators Multiply the numerators of both fractions: $$ \text{Numerator} = a \cdot c $$
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Multiply the denominators Next, multiply the denominators of both fractions: $$ \text{Denominator} = b \cdot d $$
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Form the new fraction Combine the results to form a new fraction: $$ \text{Result} = \frac{a \cdot c}{b \cdot d} $$
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Simplify the fraction (if possible) If the resulting fraction can be simplified, factor both the numerator and denominator and cancel any common factors.
The resulting fraction from multiplying $\frac{a}{b}$ and $\frac{c}{d}$ is $$ \frac{a \cdot c}{b \cdot d} $$.
More Information
Multiplying fractions is straightforward: you simply multiply the numerators together and the denominators together. Simplifying the result can often make the expression more manageable and easier to understand.
Tips
- Forgetting to simplify the resulting fraction.
- Incorrectly multiplying either the numerators or the denominators.
- Confusing addition with multiplication; remember to only multiply when dealing with products.
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