Math Review of Percents

Math Review of Percents

Math Review of Percents 150 150 Deborah


Percents are special types of ratios that compare the number to 100. Similar to any ratio, a percent can be expressed as a fraction. Since percents compare to 100, they can also be expressed in decimal form.

Fractions to Percents

Percent or the percent sign (%) means “per 100,” so 5% means the same as 5/100, 31% means 31/100 and so on. Many common fractions can be expressed as percents by converting the fraction in terms of 1/100, so ½ is 50/100 or 50%, ¾ is 75/100 or 75%, 4/5 is 80/100 or 80%. Percentages, like fractions, can be greater than 1, so that something that is 200% is two times as much, just as 200 is twice as much as 100.

Decimals to Percents

Any decimal can be expressed as a percentage, and any percentage as a decimal. (This can be a handy shortcut if the calculator does not have a percent key). For example, 20% is 0.20, and 7% is 0.07. Similarly, 0.003 is .03%, and 3.12 is 312%. A percentage such as 120% can be expressed in decimal form as 1.20.

Percents as Proportions

Percents can be expressed by the formula part/whole =percent/100, so that they can be compared as 2 equivalent ratios, the definition of proportion. Crossproducts can be used to then solve the equation. Suppose the problem were to find 30 is 20% of what number. 30/x = 20/100 is the equation for the proportion, or 20x = 30·100, or 3000. Dividing both sides by 20 to isolate the variable, x = 3000/20, or 150. Similarly, find 50% of 50. In this case, 50/100 = x/50 gives the proportion, so 100x =2500, or x= 2500/100, or x = 25. Also, 30 is what percentage of 150? This is also a proportion, as 30/150 = x/100, or 150x =3000, or x=3000/150, x = 20%.

Applications of Percents

Percents are used in many different ways. For example, if a ring is 24-karat gold, it is nearly 100% pure gold. It is too soft for most jewelry, so most gold is in the 10-karat (41.7% pure gold) to 18-karat (75% pure gold) range. Suppose a ring weighs about 10 g. If it were 10 karat, 4.17 g would be gold and the rest of the ring would be other metals, but if it were 18 karat, 7.5 g would be gold. Percents are often used in sale prices, as items are often on sale for 30% off or 40% off.

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