Worksheet 3b - Percentage Of

I. The Formula: (where the % is written as a decimal)

II. Visually: Whole means the entire pie. Part means one of the shaded regions or pieces of the pie.

III. How will you recognize when to use the percentage of formula?

Look for the keywords: percentage of or rate of or fraction of. In particular look for the word of.

Think about the situation being described.

  • Is there a clear part (or subgroup or subset or sub-amount) and a whole (a total group or population or amount)?
  • Are you being asked to compare two quantities multiplicatively? In other words, are you being asked to find out what fraction or multiple one quantity is of another?

IV. What information will you be given?

There are always three quantities involved in the calculation: part, whole, and the %. You will always be given two out of three of these quantities and asked to find the third. Here are examples of all three(an answer is given for the first).

Given part and whole.

There are 25 students in a classroom, 17 of which are female. What percentage of the class is female?

Solution: The part is the number of females. So part=17. The whole is the entire class. So whole=25. Now 17/25 = .68 or 68%.

In Chicago in the year 2000, there were approximately 1.053 million African Americans, 907 thousand whites (non-Hispanic), and 754 thousand Hispanics, and 181 thousand others (other races or two or more races). What percentage of Chicagoans in 2000 were of Hispanic origin? (Note: You have to first compute the whole.)

Given whole and %.

DePaul’s undergraduate student body is approximately 21,000 students. 54% of the student body is female. Approximate how many females attend DePaul?

Solution: The whole is the student body at DePaul. So whole=21,000. The percentage is given as 54% or .54. So now we have to solve the equation:

part/21,000 = .54

Multiply both sides by 21,000 to get:

part = .54*21,000 = 11,340 female students at DePaul.

At one point, the Tribune article refers to a subtotal of murders “with only 10% of the year yet to go.” 10% of the year is how many months?

The sales tax is 8.75% in most counties of Illinois. If you purchase a new car for $15,000, what is the sales tax you will pay?

Given part and %.

There were approximately 7.5 million people in the United States on welfare in the year 2004. If about 2.5% of the population is on welfare, what is the approximate population of the U.S.?

Solution: The part is the number of people on welfare. So part=7.5. The percentage is 2.5% or .025. So now we must solve the equation:

7.5/whole = .025.

By multiplying by whole this becomes

7.5 = .025*whole.

Now dividing by .025, this becomes

whole = 7.5/.025 = 300 million people in the U.S.

If two-thirds of federal spending goes to defense spending, and it is estimated that the government spent around $500 billion on defense in 2004, what was the total amount of federal spending in 2004?

In general, determine if the situation being described is, in fact, a “percentage of” problem, figure out what information is given (remember it will always be two out of the three quantities part, whole or %), plug these values into the equation part/whole = %, and then solve the equation for the remaining unknown. Check your answer for correct units, and make sure it makes sense.