Multiplying fractions with big numbers is best accomplished by simplifying before you multiply to keep the numbers manageable. Here's a breakdown of the process:
1. Simplify Before You Multiply:
- Look for Common Factors: Identify common factors between any numerator and any denominator (not just within the same fraction). This is the most crucial step.
- Divide: Divide the numerator and denominator by their common factor. This reduces the size of the numbers you'll be working with.
2. Multiply the Numerators:
- Multiply the simplified numerators together.
3. Multiply the Denominators:
- Multiply the simplified denominators together.
4. Simplify the Result (If Necessary):
- If the resulting fraction isn't in its simplest form, find the greatest common factor (GCF) of the numerator and denominator and divide both by the GCF.
Example:
Let's say you want to multiply: (24/35) * (15/32)
- Simplify:
- 24 and 32 share a common factor of 8. 24 ÷ 8 = 3, and 32 ÷ 8 = 4.
- 15 and 35 share a common factor of 5. 15 ÷ 5 = 3, and 35 ÷ 5 = 7.
Our problem now looks like this: (3/7) * (3/4)
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Multiply Numerators: 3 * 3 = 9
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Multiply Denominators: 7 * 4 = 28
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Result: 9/28. This fraction is already in its simplest form.
Why Simplify First?
Simplifying first avoids having to multiply large numbers, which can be cumbersome and prone to errors. It also reduces the chances of ending up with a large fraction that requires significant simplification at the end.
Key Takeaway:
Always look for opportunities to simplify before you multiply fractions, especially when dealing with larger numbers. This will make the process much easier and less error-prone.
