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# Types of Numbers

# Multiplication by Clever Form of 1

This super handy trick lets you simplify an expression without changing its value. Which is good, because fractions should not be subject to inflation.

**Sample Problem**

Here's a horrible fraction. A *really* horrible fraction. This thing is getting coal for Christmas.

If we multiply it by 1, we won't change its value. If we multiply it by anything *equivalent* to 1 (such as ) we also won't change its value. Since each of our two mini-fractions has a 3 in its denominator, what happens if we multiply the whole thing by ?

Our new numerator is , and our new denominator is . Now the fraction's value hasn't changed, it looks much more manageable, and it might even get an Xbox under the tree this year.

We can also use this trick to rewrite decimal division problems...

3.4/7.8 x 10/10 = 34/78

...or when we have a division problem written as a fraction.