By Steve Slavin

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**Sample text**

761. You'll see I was deliberately trying to avoid even numbers. Why? Because even numbers would leave us with fractions that would have to be reduced. Mathematicians, unlike normal citizens, cannot leave unreduced fractions just sitting there. In fact, no mathematician can go to bed at night until his or her fractions have been reduced to their lowest possible denominators (or bottom numbers). Take the fraction 4/10. That might leave you satisfied, but I can't tell you how much the sight of a 4 over a 10 would frustrate a mathematician, who would immediately reduce it to 2/5.

0) You probably noticed that when we multiplied by 10, what we were really doing was adding a zero to the number being multiplied. That observation is fine as long as we're dealing with whole numbers. But when we deal with decimals, we've got to worry about the decimal point. 9? 0, or 9. How did we get that? We moved the decimal one place to the right. But what if we had merely added a zero? 9. So when we're multiplying a decimal by 10, we have to make sure to move the decimal one place to the right.

Remember the law of arithmetic that allows this? What you do to the top of a fraction, you must do to the bottom. So we multiplied the top by 2 and the bottom by 2. Here's another one. Problem 4: Add 1/3 and 2/5. Solution: To repeat, we want the lowest common denominator so we don't have to reduce our answer (or, if it can be further reduced, we'd be able to minimize that reduction). And we want a common denominator so we'll be adding units of the same thing. Just as you can't add apples and oranges, you can't add thirds and quarters without finding their (lowest) common denominator, which happens to be 12.