WRITING EXPRESSIONS INVOLVING PERCENT INCREASE AND DECREASE

LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
 

Recall that whenever you see the percent symbol, $\,\%\,$, you can trade it in for a multiplier of $\frac{1}{100}$.
(Indeed, per-cent means per-one-hundred.)

For example, $\,20\%\,$ goes by all these names: $$\, \cssId{s11}{20\%} \ \ \cssId{s12}{= \ \ 20\cdot\frac{1}{100}} \ \ \cssId{s13}{= \ \ \frac{20}{100}} \ \ \cssId{s14}{= \ \ \frac{2}{10}} \ \ \cssId{s15}{= \ \ \frac{1}{5}} \ \ \cssId{s16}{= \ \ 0.2}$$

In particular, note that $\,100\% = 100\cdot\frac{1}{100} = 1\,$,
so $\,100\%\,$ is just another name for the number $\,1\,$.

Also recall that it's easy to go from percents to decimals:
just move the decimal point two places to the left.
For example:   $\, \cssId{s22}{20\%} \cssId{s23}{= 20.\%} \cssId{s24}{= 0.20}$
It's good style to put a zero in the ones place (i.e., write $\ 0.20\ $, not $\ .20\ $).

To change from decimals to percents,
just move the decimal point two places to the right.
For example:   $\cssId{s30}{0.2} \cssId{s31}{= 0.20} \cssId{s32}{= 20.\%} \cssId{s33}{= 20\%}$

The ‘Puddle Dipper’ memory device may be useful to you:
PuDdLe: to change from Percents to Decimals, move the decimal point two places to the Left.
DiPpeR: to change from Decimals to Percents, move the decimal point two places to the Right.

EXAMPLES:

Here, you will practice writing expressions involving percent increase and decrease, and related concepts.

Another name for the expression ‘$\,20\%\text{ of } x\,$’ is:   $0.2x$
Why? The mathematical word ‘of ’ indicates multiplication, so:
$\, \cssId{s46}{(20\%\text{ of } x)} \cssId{s47}{= (20\%)(x)} \cssId{s48}{= (0.2)(x)} \cssId{s49}{= 0.2x}\,$.
Another name for the expression ‘$\,100\%\text{ of } x\,$’ is:   $x$
Another name for the expression ‘$\,300\%\text{ of } x\,$’ is:   $3x$
If $\,x\,$ increases by $\,20\%\,$, then the new amount is:   $ \cssId{s55}{x + 0.2x} \cssId{s56}{= 1x + 0.2x} \cssId{s57}{= 1.2x}$
If $\,x\,$ has a $\,20\%\,$ increase, then the new amount is:   $1.2x$
If $\,x\,$ increases by $\,47\%\,$, then the new amount is:   $\cssId{s61}{x + 0.47x} \cssId{s62}{= 1.47x}$
If $\,x\,$ decreases by $\,30\%\,$, then the new amount is:   $\cssId{s64}{x - 0.3x} \cssId{s65}{= 1x - 0.3x} \cssId{s66}{= 0.7x}$
If $\,x\,$ has a $\,30\%\,$ decrease, then the new amount is:   $0.7x$
If $\,x\,$ increases by $\,100\%\,$, then the new amount is:   $\cssId{s70}{x + x} \cssId{s71}{= 1x + 1x} \cssId{s72}{= 2x}$
If $\,x\,$ increases by $\,182\%\,$, then the new amount is:   $x + 1.82x = 2.82x$
If $\,x\,$ increases by $\,200\%\,$, then the new amount is:   $x + 2x = 3x$
If $\,x\,$ doubles, then the new amount is:   $2x$
If $\,x\,$ triples, then the new amount is:   $3x$
If $\,x\,$ quadruples, then the new amount is:   $4x$
If $\,x\,$ is halved, then the new amount is:   $\displaystyle\frac{1}{2}x = 0.5x$
Master the ideas from this section
by practicing the exercise at the bottom of this page.


When you're done practicing, move on to:
Calculating Percent Increase and Decrease

 
 

Answers must be input in decimal form to be recognized as correct.
Also, you must exhibit good style by putting a zero in the ones place, as needed.
For example, input  0.5x , not (say)  .5x  or  1/2x .

    
(MAX is 11; there are 11 different problem types.)