Multiplying mixed numbers involves converting them into improper fractions first. An improper fraction has a numerator larger than its denominator. Once you've converted the mixed numbers, you simply multiply the numerators and the denominators. Finally, simplify the resulting fraction if possible, or convert it back into a mixed number.
For example, to multiply $2\frac{1}{2}$ by $1\frac{1}{3}$, first convert them to improper fractions: $2\frac{1}{2} = \frac{5}{2}$ and $1\frac{1}{3} = \frac{4}{3}$. Then, multiply the fractions: $\frac{5}{2} \times \frac{4}{3} = \frac{20}{6}$. Finally, simplify $\frac{20}{6}$ to $3\frac{1}{3}$.
Match the term with its correct definition:
| Term | Definition |
|---|---|
| 1. Mixed Number | A. The top number in a fraction. |
| 2. Improper Fraction | B. A fraction where the numerator is greater than or equal to the denominator. |
| 3. Numerator | C. A whole number and a fraction combined. |
| 4. Denominator | D. The bottom number in a fraction. |
| 5. Simplify | E. To reduce a fraction to its lowest terms. |
Answers: 1-C, 2-B, 3-A, 4-D, 5-E
Complete the following paragraph with the correct words.
To multiply mixed numbers, first convert them into _______ fractions. Then, multiply the _______ and the _______. Finally, _______ the fraction if possible.
Answers: improper, numerators, denominators, simplify
Explain, in your own words, why it's necessary to convert mixed numbers to improper fractions before multiplying. Provide an example to support your explanation.
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