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math fun to learn and easy to teach for grades
1 through 9. |
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Find
at which step of the following proof, it becomes
false. And give the reason. |
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Does
2 = 1 ? |
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| 1. |
A
= B |
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Multiply
both sides by A |
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2. |
A
X A = A X B |
| 3. |
AA
= AB |
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Subtract
BB from both sides |
| 4. |
AA
- BB = AB - BB |
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AA - BB
= (A-B)(A+B) |
| 5. |
(A-B)
(A+B) = B (A-B) |
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Divide
both sides by (A-B) |
| 6. |
A
+ B = B |
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If A =
B, A+B= B+B = 2B |
| 7. |
2B
= B |
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Divide
both sides by B |
| 8. |
2
= 1 |
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| 2
can't equal 1! What's wrong with this problem? |
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