5-8 Solving Equations by Multiplying Fractions

Okay. Last section. You can do it!!! :)

We are now solving equations in which we must use multiplication or division. This is no different than what we've done in the past:

3x = 33 ----- To solve, we do the opposite of what's happening to x. Since we're multiplying x by 3,
                      the OPPOSITE would be to divide both sides by 3.

3x  =  33
 3        3

We now solve both sides and are left with x = 11.

What we're doing today is no different - we're just going to see some pesky fractions.

Take a look at Example 1 for this section:

5a = 1/7

Since we're multiplying a by 5, we do the OPPOSITE to both sides (Divide by 5). Here's the thing, though - how do you divide 1/7 by 5??? Going back to what we learned about dividing when there are fractions involved, we know we can multiply instead by the reciprocal (or "inverse"). Remember?

So all we have to do is turn that right side into a multiplication problem:

a = 1/7 x 1/5
a = 1/35

Now jump ahead to see Example 3. I know it looks like a hot mess, but pay close attention to what they're doing - they're remembering their negative rules, and then simplifying by using common factors before solving. I know we haven't touched on simplifying BEFORE solving, but it's there as an option for you if you'd like to try it. Otherwise, be SURE to simplify your answer after you've solved.

Example 4 shows us that, as always, when dealing with mixed numbers in an equation, it's easier to convert them to improper fractions first, and then solve.

Let's try a few:

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