To multiply fractions with mixed numbers, you must first convert the mixed number(s) to improper fractions, then multiply the numerators and denominators, and finally simplify the result if necessary.
Here's a step-by-step guide:
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Convert Mixed Numbers to Improper Fractions:
- A mixed number has a whole number part and a fractional part (e.g., 2 1/2).
- To convert to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. Keep the same denominator.
- Example: 2 1/2 = (2 * 2 + 1) / 2 = 5/2
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Multiply the Numerators:
- Multiply the top numbers (numerators) of the fractions together.
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Multiply the Denominators:
- Multiply the bottom numbers (denominators) of the fractions together.
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Simplify:
- Reduce the resulting fraction to its simplest form.
- If the result is an improper fraction (numerator is greater than the denominator), you may want to convert it back to a mixed number.
Example:
Let's multiply 1/4 by 2 1/2.
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Convert Mixed Number to Improper Fraction: 2 1/2 = (2 * 2 + 1) / 2 = 5/2
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Multiply Numerators: 1 * 5 = 5
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Multiply Denominators: 4 * 2 = 8
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Simplify: The resulting fraction is 5/8, which is already in its simplest form.
Therefore, 1/4 * 2 1/2 = 5/8
Another Example (with simplification):
Multiply 1 1/3 by 3/4
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Convert to Improper Fraction: 1 1/3 = (1 * 3 + 1) / 3 = 4/3
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Multiply Numerators: 4 * 3 = 12
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Multiply Denominators: 3 * 4 = 12
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Simplify: 12/12 = 1
Therefore, 1 1/3 * 3/4 = 1
