Percents and Ratios

Learning about Percents and Ratios

Percent means "one part in a hundred."
Ratio means "the relationship between two amounts." It is expressed as the quotient of one divided by the other.

Percents & Ratios Lessons

(explains what percents and ratios are, provides pictures and explanations)

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Understanding Percents

Percents

A percent is a ratio of a number to 100. Percent means “per hundred.” Thus, 20 percent, or 20%, means . A percent can be written as a fraction or a decimal.

To change a fraction to a percent, find an equivalent fraction with a denominator of 100. To change a percent to a fraction, use the given percent as the numerator of a fraction and 100 as the denominator and then reduce the fraction.

Examples:

To change a percent to a decimal, use the given percent as the numerator of a fraction and 100 as the denominator and then write the fraction as a decimal. To change a decimal to a percent, write the decimal as a fraction with 100 as the denominator and then write the fraction as a percent.

Examples:

Another way to change a percent to a decimal is to write the percent amount and move the decimal point 2 places to the left. To change a decimal to a percent, write the decimal, move the decimal point 2 places to the right, and add the percent sign.

Examples:

Sometimes a zero must be appended to change a percent to a decimal or to change a decimal to a percent.

Examples:

Another way to change a fraction to a percent is to divide the numerator by the denominator and then change the resulting decimal to a percent.

Examples:

Comparisons of fractions, decimals, and percents can be made in several ways including locating each on a number line, rewriting each as a fraction with a common denominator, or rewriting each as a decimal or as a percent.

To find a percent of a number, first change the percent to either a fraction or a decimal and then multiply the given number by that fraction or decimal. The percent of a number can also be found by writing the percent as a fraction and then finding an equivalent fraction with the given number as the denominator.

To find what percent one number is of another number, write the two numbers as a fraction, with the whole as the denominator. Then find an equivalent ratio with a denominator of 100 and write that ratio as a percent. Equivalent ratios are also used to compare ratios.

In later grades, students will learn to use the percent equation, which is usually set up as “whole × percent = part.” Since a percent can be written either as a fraction or as a decimal this equation can have two general forms, where n is the percent amount, x is the part, and w is the whole. w × 0.01n = x or w × = x.

(borrowed from: http://www.eduplace.com/math/mw/models/overview/5_19_3.html)

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Understanding Ratios

A ratio is one thing compared to or related to another thing; it is just a statement or expression. A proportion is two ratios that are equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, ⁵/₁₀ equals ¹/₂. Solving a proportion means that you are missing one part of one of the fractions, and you need to solve for it. For instance, suppose you were given:

^x/₁₀ = ¹/₂

You already know that x must be 5, but suppose you didn't notice this. You can then solve the equation

^x/₁₀ = ¹/₂

Multiply through by 10 to clear the denominators:

10( ^x/₁₀ ) = 10( ¹/₂ )


x = 5

...to get that x = 5, so ⁵/₁₀ = ¹/₂.

Of course, proportions wouldn't be of much use if you only used them for reducing fractions. A more typical use would be something like the following:

• Consider those ducks and geese back at the park. Their ratio is sixteen (16) ducks to nine (9) geese. Suppose that there are 192 ducks. How many geese are there?

.^(ducks)/_(geese) : ¹⁶/₉ = ¹⁹²/_G

I'll multiply the G up to the left-hand side, and then solve for the value of G:

.¹⁶/₉ = ¹⁹²/_G
^16G/₉ = 192
16G = 1728
G = 108

Then there are 108 geese.

Notice how I wrote out the ratio in words:

^(ducks)/_(geese)

This is not standard notation, but it can be very useful for setting up your proportion, because it will help you keep track of what each number stands for. In other words, it will help you set up your proportion correctly. If you do not set up the ratios consistently, you will get an incorrect answer, so clarity can be very important.

Borrowed from http://www.purplemath.com/modules/ratio2.htm