Basic Math and Pre-Algebra For Dummies (84 page)

When you understand the basic idea of a conversion chain, you can make a chain as long as you like to solve longer problems easily. Here's another example of a problem that uses a time-related conversion chain:

Jane is exactly 12 years old today. You forgot to get her a present, but you decide that offering her your mathematical skills is the greatest gift of all — you'll recalculate how old she is. Assuming that a year has exactly 365 days, how many seconds old is she?

Here are the conversion equations you have to work with:

To solve this problem, you need to build a bridge from years to seconds, as follows:

So set up a long conversion chain, as follows:

Cancel out all units that appear in both a numerator and a denominator:

 As you cancel out units, notice that there is a
diagonal
pattern: The numerator (top number) of one fraction cancels with the denominator (bottom number) of the next, and so on.

When the smoke clears, here's what's left:

This problem requires a bit of multiplication, but the work is no longer confusing:

• = 378,432,000 sec.
  

The conversion chain from 12 years to 378,432,000 seconds doesn't change the value of the expression — just the unit of measurement.

In some word problems, the problem itself gives you a couple of the conversion equations necessary for solving. Take this problem, for example:

A furlong is 
 of a mile, and a fathom is 2 yards. If I rode my horse 24 furlongs today, how many fathoms did I ride?

This problem gives you two new conversion equations to work with:

• 1 furlong = 1/8 mile
  
• 1 fathom = 2 yards
  

It's helpful to remove fractions from the equations before you begin, so here's a more useful version of the first equation:

You also want to remember two other conversions:

Next, build a bridge from furlongs to miles using the conversions available from these equations:

Now you can form your conversion chain. Every unit you want to cancel has to appear once in the numerator and once in the denominator:

Next, you can cancel out all the units except for fathoms: