#
Section 1-5

#
Solving Equations involving Decimals and Fractions

If an equation involves decimal coefficients, you may find it easier to multiply
both sides by 10 (or 100, or 1000, etc.) to turn everything into integers.
The solution will remain the same.

**
Example 1:
**

Solve for
*
x
*
:

**
0.03
***
x
*
– 0.2 = 0.04

Multiply the whole equation by 100:

**
3
***
x
*
– 20 = 4

Much easier!

You can use the same trick for some equations with fractions.

**
Example 2:
**

Solve for
*
p
*
:

Multiply through by the
Least Common Denominator
(in this case, 66).

Sometimes, even when all the numbers in the equation are integers, you will
end up having to
round
off
your answers. (To review rounding rules,
click
here
.)

**
Example 3:
**

Solve for
*
a
*
. Give the answer correct to the nearest hundredth.

**
56 = –32 + 14
***
a
*

Start off by adding 32 to both sides.

**
88 = 14
***
a
*

Then divide both sides by 14. We can factor a 2 out of numerator and denominator.

Using a calculator, or long division, we get:

The thousandths place is a 5, so we round up.