Multiplying Fractions

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In this section, we continue to learn about fractions. Our next step is to learn about multiplying fractions. How do we multiply two or more fractions together?
Multiplying Fractions:
  1. Simplify each fraction involved in the multiplication
  2. Setup the multiplication and look to cross cancel any common factors
  3. Multiply the numerators together, this gives us the numerator of the product
  4. Multiply the denominators together, this gives us the denominator of the product
What do we mean by cross canceling? This process eliminates the need to simplify after multiplication. We always want to start with fractions that are simplified. When we perform our multiplication, we can cancel common factors from one numerator across to the other fraction's denominator.
Example 1: Find each product $$\frac{2}{3}\cdot \frac{9}{11}$$ -Each fraction is simplified
-Can we cross cancel anything? Yes a common factor of 3 between the first fraction's numerator and the second fraction's denominator $$\require{cancel}\frac{2}{\cancel{3}}\cdot \frac{\cancel{3}\cdot 3}{11}$$ $$\frac{2}{1}\cdot \frac{3}{11}$$ -Multiply the numerators together
$$2 \cdot 3=6$$ -Multiply the denominators together
$$1 \cdot 11=11$$ Result: $$\frac{6}{11}$$ $$\frac{2}{3}\cdot \frac{9}{11}=\frac{6}{11}$$
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