To cross cancel when multiplying fractions, you simplify before multiplying by finding common factors between numerators and denominators. This avoids the need to reduce the final answer.
Steps for Cross Cancelling
Here's a breakdown of the process, incorporating the reference information:
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Identify Common Factors: Look for common factors between any numerator and any denominator in the fractions you are multiplying. It doesn't have to be the numerator and denominator of the same fraction. According to the reference, you must "Find any factors the numerators share with the denominators."
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Cancel the Common Factors: Divide both the numerator and denominator by their common factor. This "cancels" the factor out, replacing the original numbers with their simplified values.
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Multiply the Numerators: Multiply the simplified numerators together. The reference states: "Multiply the uncancelled parts of the numerators."
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Multiply the Denominators: Multiply the simplified denominators together. The reference states: "Multiply the uncancelled parts of the denominators."
Example
Let's say you want to multiply 2/5 by 15/8:
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Original problem: 2/5 * 15/8
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Step 1 & 2: Cross Cancel
- 2 and 8 share a common factor of 2. 2 ÷ 2 = 1 and 8 ÷ 2 = 4.
- 5 and 15 share a common factor of 5. 5 ÷ 5 = 1 and 15 ÷ 5 = 3.
This gives us: 1/1 * 3/4
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Step 3: Multiply Numerators
- 1 * 3 = 3
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Step 4: Multiply Denominators
- 1 * 4 = 4
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Final Answer: 3/4
Benefits of Cross Cancelling
- Simplified Calculations: Working with smaller numbers makes multiplication easier.
- Reduced Fraction: Cross cancelling ensures the product is already in its simplest form. "It will also eliminate the need to reduce your answers!"
