Hi Ray. Yes, division is the way to go, but there's no need to multiply the top and bottom of the fraction by 100. Those 100s will simply cancel without accomplishing anything. Just divide by the 80% as it's written in the equation (shown after the information below). That solves for our unknown directly (because we defined x as such), without having to first find 1%, followed by doing more math.
Here's a quick review. The word 'percent' is like the words 'dozen', 'pair', 'score', 'gross', 'triple'. It refers to a specific quantity of stuff.
Dozen means 12 of something. Gross means 144 of something. One percent means a hundredth of something.
1% = 1/100
80% =
80/100
80/100 simplifies to
8/10
The decimal form of 8/10 is
0.8
Therefore, we have four common ways to express a percent (shown in bold). In general, we use either the reduced fraction form or the decimal form when doing arithmetic.
We don't do arithmetic with the percent-sign form. Most people use the decimal form of a percent, when working with other decimal quantities (like dollars and cents). That's why the 80% in our equation is written in decimal form.
Therefore, to solve the equation 0.8x = 43567 for the unknown dollar amount, we simply divide each side by 0.8:
0.8x = 43567
x = 43567/0.8
x = 54458.75
The result in red is not accurate; you chopped off three of the decimal digits. (That's called 'truncation', not 'rounding'.) And, I assume the bold 6 is a typo. We don't want that red result rounded or truncated. Rounding or truncating numbers in our work often leads to "rounding error" at the finish line. So, here's another general arithmetic rule:
Do not round or truncate intermediate results. When I know that I'm going to round my
final answer to two decimal places, then I retain four decimal places throughout my work and wait until the last step to round to two places.
The full-time salary is $54,458.75
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