ARITHMETIC STUDY GUIDE

FINDING A PERCENT OF A NUMBER:

Translate the problem to mathematical symbols: “of” means multiply; “%” means per hundred (use decimal number.)

Example: What is 25% of $6500.00

n = 25% x 6500

n = .25 x 6500

n = $1625

or another way to do this problem is to change the percent to a fraction:

n = $1625

FINDING A PERCENT:

What percent of 8 is 6?

	Translate to mathematics. Note “is” means =.
	Using a fraction bar, divide both sides of equation by 8.
	Dividing a number by itself equals one.
	Reduce the fraction.
	Write the fraction as a percent.

FINDING WHAT PERCENT ONE NUMBER IS OF ANOTHER:

There are key words to remember that will help you solve the problem it is asking you.
The word “of” in the sentence means to multiply.
The word “is” means it is equal to.
Example:

The variable “a” is being multiplied by 45.

		Need to divide by 45
		Therefore, 20% of 45 is 9.

 

FINDING A NUMBER WHEN A PERCENT OF IT IS GIVEN

Step 1: Change the % to fraction form.

Example: 20% of what number is 16?

		Change the percent to fraction form.
		Need to multiply both sides of the equation by 5.

SQUARE ROOT

To square a number you multiply it by itself. For instance, . Finding the
square root of a number is the inverse operation of squaring that number. The symbol for square-
rooting is , the “radical” symbol.
Square of

Examples:

Square of thus

so

, so

Example:

MEAN (AVERAGE):

The mean (average) is found by adding up all the numbers given and then dividing by the number of
numbers.

Example: to find the average of four numbers: 9, 5, 20 and 13:

Add the four numbers:

9 + 5 + 20 + 13 = 47

Divide by the quantity of numbers (in this case four)

47 4 = 11.75 average = 11.75

PROBLEMS FOR YOU TO TRY:

5) An empty box weighs pounds. It is then filled with pounds of fruit. What is the weight of the box when it is
full?

A. 20 pounds

B. pounds

C. 22 pounds

D. pounds

6) A father leaves his money to his four children. The first received , the second received , and the third received .
How much did the remaining child receive? (Hint: think of the father’s money as 1 whole.)

A. of the money

B. of the money

C. of the money

D. of the money

7) Yanni is making formula for the baby. Each bottle contains scoops of formula. The formula container holds 320
scoops of formula. How many bottles of formula can Yanni make?

A. 50 bottles

B. 60 bottles

C. 12 bottles

D. 100 bottles

8) Sam has a budget of $45 to spend on entertainment for the weekend. If he spent of his budget on Friday and of his
budget on Saturday, how many dollars does he have left over to spend on Sunday?

A. $12

B. $33

C. $9

D. $36

9) Three people who work full-time are to work together on a project, but their total time on the project is to be equivalent to
that of only one person working full-time. If one of the people is budgeted for one-half of his time to the project and a
second person for one-third of her time, what part of the third worker’s time should be budgeted to this project?

12) Which of the following is closest to 27.8 x 9.6?

A. 280

B. 300

C. 2800

D. 3000

13) At the beginning of the month, Jim’s bank balance was $275.38. During the month he wrote the following checks:
$174.89, $68., and $57.76. He made deposits of $250. and $350. Find his bank balance at the end of the month.

A. $586.21

B. $604.00

C. $574.73

D. $524.73

14) The $146.30 cost of a party was shared by 10 people. How much did each person have to pay?

A. $1.46

B. $14.63

C. $146.3

D. $15.00

15) A car traveled at 65 miles per hour for a total of 390 miles? How many hours did the car travel?

A. 7 hours

B. 39 hours

C. 25350 hours

D. 6 hours

16) A garden is 33.75 feet long and 21.6 feet wide. Draw a diagram of the garden with the lengths written on all four
sides. What is the total distance around the garden?

A. 110.7 inches

B. 67.5 inches

C. 43.2 feet

D. 110.7 feet

17) Which of the following is the least?

A. 0.105

B. 0.501

C. 0.015

D. 0.15

18) The perimeter of a rectangle is 60 inches. If the width of the rectangle is 12 inches, then what is the length of the
rectangle?

A. 18 inches

B. 5 inches

C. 48 inches

D. 24 inches

19) What is 40% of 85?

A. 21.25

B. 36

C. 34

D. 212.5

20) 15 is what percent of 60?

A. 90%

B. 25%

C. 40%

D. 9%

21) John learned that after overhauling the carburetor in his car he would use only 80% as much gas. Last month, before
overhauling his carburetor, he used 125 gallons of gas. Assuming that John drives the same number of miles next month,
how many gallons of gas can he expect to save next month after overhauling his carburetor?

A. 20

B. 25

C. 45

D. 100

22) Debra took a test that consisted of 150 questions and she got 78% correct. How many questions did Debra miss on the
test?

A. 28

B. 33

C. 24

D. 117

23) A survey of 250 people showed that 220 people favored a candidate for re-election. What percent of the people surveyed
favored the candidate?

A. 75%

B. 88%

C. 1.2%

D. 25%

24) 4% of 625 is what number?

A. 60

B. 72

C. 156

D. 25

25) Mr. Smith, a professional wine tester, made $32,800. last year. This year he had a raise of $2132. What was the percent
of the raise?

A. 6.5%

B. 5.5%

C. 35%

D. 7.5%

26) All of the following are ways to write 25 percent of n EXCEPT:

27) A soccer team played 160 games and won 65 percent of them. How many games did it win?

31) Find the average of the following numbers: 66, 21, 48, 50, 10

A. 23.5

B. 39.25

C. 29

D. 39