Calculating with percentages
As we discussed in pre-algebra, percent is a ratio that compares a number to 100. Percent means per hundred. Percent is usually expressed with the percent symbol %.
Percent problems are usually solved by using proportions.
Example
In a classroom 14 of the 21 students are female. How many percent does that correspond to?
We know that the ratio of girls to all students is
$$\frac{14}{21}$$
And we know that this ratio is a proportion to a ratio with the denominator 100.
$$\frac{14}{21}=\frac{x}{100}$$
As we saw in the last section from here we can calculate x
$$x=100\cdot \frac{14}{21}$$
$$x=\frac{1400}{21}$$
$$x\approx 67$$
i.e. 67% of the students in the class are female.
One of the ratios in these proportions is always a comparison of two numbers (above 14/21). This numbers are called the percentage (14) and the base (21). The other ratio is called the rate and always has the denominator 100.
$$\frac{percentage}{base}=rate$$
Another way of saying this is that
$$percent=\frac{part}{whole}$$
Percent of change, or p%, indicates how much a quantity has increased or decreased in comparison with the original amount. It's calculated as:
$$percent\: of\: change=\frac{amount\: of\: increase\: or\: decrease}{old\: amount}$$
Example
Johnny is at the store where there is a big sign telling him that there is a $4.99 discount on a shirt that originally costs $39.99. But how big is the discount in percent?
$$\frac{\$ 4.99}{\$ 39.99}\approx 0.12$$
$$0.12=12\%$$
The price of the shirt has decreased by 12%.
Video lesson
A price increases from $500 to $585. How big is the increase in percent?