# At a Glance - 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, and it looks way more manageable. It might even get an Xbox under the tree this year.

### Sample Problem

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

^{3.4}/_{7.8} × ^{10}/_{10} = ^{34}/_{78}

We sort of hate it when decimals and fractions are all mixed up like that, so we just multiply the whole fraction by ^{10}/_{10} (a.k.a. a clever form of 1), which turns the numerator and denominator both into nice, whole numbers. Ah, much better.

#### Exercise 1

Find the cleverly disguised form of 1 that will let you simplify the rotten fraction below, then simplify. And quickly, please—it hurts our eyes just to look at it.

#### Exercise 2

What's the cleverly disguised form of 1 that will let you simplify ? What's the simplified version?