Algebraic Expressions

MATH REVIEW: USEFUL MATH FOR EVERYONE

SECTION 2.3. ALGEBRAIC EXPRESSIONS

Frequently, you will have to consider units of measurement (like centimeters, people, or bushels) in your calculations. Sometimes, it will be important to have all parts of an equation in the same units. To do this, you may have to convert between units. For example, you may need to convert part of your equation from ounces to grams.

The easiest way to do this is to multiply the part of the equation that you need to convert by a fraction that is equal to one. Recall that a number divided by itself is equal to one, like 7/7, 21/21, or 50,000/50,000. Recall also that multiplying any part of an equation by one does not change its value at all.

What does all that mean for us here?

Just this:

If there are 5 ships in a flotilla, then

5 ships/1 flotilla = 1,and

1 flotilla/5 ships = 1

Here's a real example:

There are 0.035 ounces in a gram., so 1 g = 0.035 oz and...

1 g/0.035 oz = 1 = 0.035 oz/1 g

You can treat units like numbers. They can be multiplied or divided. This means they can also be cancelled. If you multiply two fractions, and they both contain the same units, except that one fraction has the unit in the denominator and the other in the numerator, they cancel each other out.

Like this:

oz/person * g/oz = g/person

The ounces cancel each other out.

So, let's say each person in a group got 8 ounces of steak, and we need to know how many grams each person got.

8 oz/1 person * 1g/0.035 oz = 8 g/0.035 people

This is a very awkward fraction, so we change the size of the denominator:

8/0.035 = x/1
0.035x = 8
x = 228.6

so...each person got 228.6 g of steak.

to Algebraic Expressions, Page 4

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