Multiplying fractions mentally involves a few key steps to simplify the process and arrive at the solution efficiently. Here's a breakdown of how to approach fraction multiplication in your head:
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Convert Mixed Fractions:
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The first step, according to the reference, is to convert any mixed fractions into improper fractions. This makes the multiplication process much easier.
- Example: 2 1/2 becomes 5/2.
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Simplify (Optional):
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Look for opportunities to simplify before multiplying. This involves finding common factors between any numerator and any denominator. This is mentioned as method 2 in the reference. Reducing the numbers early makes the mental calculations easier.
- Example: If you're multiplying 3/4 * 8/9, you might notice that 4 and 8 share a common factor of 4, and 3 and 9 share a common factor of 3.
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Multiply Numerators:
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Multiply all the numerators together to get the numerator of the answer.
- Example: If you have simplified to 1/1 * 2/3 then 1 * 2 = 2, so the new numerator is 2.
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Multiply Denominators:
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Multiply all the denominators together to get the denominator of the answer.
- Example: Continuing with 1/1 * 2/3, 1 * 3 = 3, so the new denominator is 3.
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Simplify the Answer:
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Finally, simplify the resulting fraction if possible. Look for common factors between the numerator and denominator and reduce the fraction to its simplest form.
- Example: If your answer is 4/6, both numbers are divisible by 2, so it simplifies to 2/3.
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Example of Mental Calculation:
Let's multiply 2 1/2 * 2/5 mentally:
- Convert: 2 1/2 becomes 5/2. So the problem is now 5/2 * 2/5.
- Simplify: You can see that the 5 in the numerator and the 5 in the denominator cancel each other out to 1. The 2 in the numerator and the 2 in the denominator also cancel each other out to 1.
- Multiply: Now we have 1/1 * 1/1 = 1/1
- Simplify: 1/1 = 1
Therefore, 2 1/2 * 2/5 = 1.
