﻿ Writing expressions involving percent increase and decrease
WRITING EXPRESSIONS INVOLVING PERCENT INCREASE AND DECREASE
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

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.)