Probability
Full Member
- Joined
- Jan 26, 2012
- Messages
- 425
I agree that understanding comes from practice, practice and more practice, but sometimes its easy to be lead down the garden path and if there is no method of checking a result, then a person could believe the result even though that result is incorrect. Look at this example;
[MATH]\frac{5}{2}+a=[/MATH]
Where a = [MATH]-{2}[/MATH]
I understand from arithmetic that a [MATH]{+}{-}[/MATH] becomes a [MATH]{-}[/MATH]
So I rewrite the expression;
[MATH]\frac{5}{2}-{2}=[/MATH]
I now look at the expression and think [MATH]{5}-{2}=\frac{3}{2}[/MATH]
Then I ask myself, how do I know that the answer is correct?
Do I wait for next weeks lesson if I were part of a class?
Using the calculator here can give guidance.
[MATH]\frac{5}{2}-{2}=\frac{5}{2}-\frac{4}{2}= \frac{5-4}{2}=\frac{1}{2}[/MATH]........................................corrected
Now I can start to think about why my answer was wrong, and when I understand that I must cross multiply the fraction I see that I end up with a minus 4 in the expression rather than a minus 2.
[MATH]\frac{5}{2}+a=[/MATH]
Where a = [MATH]-{2}[/MATH]
I understand from arithmetic that a [MATH]{+}{-}[/MATH] becomes a [MATH]{-}[/MATH]
So I rewrite the expression;
[MATH]\frac{5}{2}-{2}=[/MATH]
I now look at the expression and think [MATH]{5}-{2}=\frac{3}{2}[/MATH]
Then I ask myself, how do I know that the answer is correct?
Do I wait for next weeks lesson if I were part of a class?
Using the calculator here can give guidance.
[MATH]\frac{5}{2}-{2}=\frac{5}{2}-\frac{4}{2}= \frac{5-4}{2}=\frac{1}{2}[/MATH]........................................corrected
Now I can start to think about why my answer was wrong, and when I understand that I must cross multiply the fraction I see that I end up with a minus 4 in the expression rather than a minus 2.
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