## Basic Arithmetic

- The √8 falls between what two whole numbers?

The √8 falls between the whole numbers of 2 and 3. A square root is made up of the same two numbers multiplied together. For instance, 6 x 6 = 36. The square root of 36 is 6. The square root of 8 is not a “perfect” square root. Since a calculator cannot be used on your placement testing, write down a short list of square roots:

√1 = 1 x 1

√4 = 2 x 2

√9 = 3 x 3

√16 = 4 x 4

With just that short list, you can see that the √8 can be placed between 2 and 3.

- Write
^{12}⁄_{15}in decimal form.

^{12}⁄_{15}= 0.8.

To change a fraction to a decimal, you need to divide the numerator by the denominator.

- The shaded region in the figure represents what fraction of the whole rectangle?

^{4}⁄_{12}=^{1}⁄_{3}

The figure contains 12 squares which make up the whole which is 1. Since four of the squares are shaded, you have 4 of the 12 squares shaded or^{4}⁄_{12}which is reduced to^{1}⁄_{3}. All fractions must be reduced to the lowest terms.

- Last year in Liberty, the coldest temperature on January 1 was 15°F below zero. The warmest temperature on July 1 was 96°F above zero. How many degrees warmer was it on July 1 than January 1?

15 + 96 = 111°F

Think of this using a number line.

From -15°F below zero means we have to add 15 to get to 0 and then from 0 to 96°F is another 96 degrees. So we have to add the temperatures together to get the total temperature change.

- If a team received 50 out of a total of 80 points, what percent of the total number of points did it receive?

62.5%

This problem involves ratios, fractions, and percent. You are working with a "part of a whole." Fifty is the part and 80 is the whole. This then becomes a ratio or fraction of^{50}⁄_{80}. You first must change this ratio to a decimal by dividing the numerator by the denominator which is 0.625. The decimal can then be changed to a percent by multiplying by 100 or moving the decimal point two places to the right.

- If F =
^{9}⁄_{5}C + 32 and C = -5, then F = ?

23

You are given the value of the letter C. Plug that number in for C and compute the answer: F =^{9}⁄_{5}(^{-5}⁄_{1}) + 32 = -9 + 32 = 23. Note that any whole number can be changed to a fraction by placing it over 1.

- If the perimeter of the triangle is 17 centimeters, what is the length of the side B?

4.03cm6.3cmB

6.67

To find the perimeter of a figure, we add the outside measurements together. Adding 4.03 + 6.3 = 10.33. We are missing the measurement of one side but know that the entire perimeter equals 17. Subtract 17 and 10.33 to find the missing side of 6.67. If we add the sides up: 4.03 + 6.3 + 6.67 it should equal 17.

- An 8-ounce box of cat food sells for $0.48. A 2.5-ounce can sells for $0.11. Which cat food is the least expensive per ounce?

2.5 ounce can is least expensive.

You need to find the unit cost per ounce in order to compare their values. Divide the cost of the can by the number of ounces in each can. The 8-ounce can is $0.06 per ounce and the 2.5-ounce can is $0.044 per ounce.

- If the price of an item is reduced by 10%, what is the new price if the original price was $28?

$25.20

Multiply the original price by 10%. You must first change the 10% to a decimal. Divide by 100 or move the decimal point two places to the left (0.10). Multiplying 28 x 0.10 = 2.8 or $2.80 reduction in price. Subtract 28.00 – 2.80 to get the reduced selling price of $25.20.

- Subtract the mixed numbers: 14
^{5}⁄_{8}- 10^{7}⁄_{8}(NOTE: Your answer should be given as a mixed number.)

3^{3}⁄_{4}

In this particular problem, you will need to borrow 1 from 14 to make it equal^{8}⁄_{8}which can then be added to the fraction^{5}⁄_{8}to create a fraction so that the two fractions can be subtracted.

14 ^{5}⁄_{8}= 13 ^{5+8}⁄_{8}= 13 ^{13}⁄_{8}-10 ^{7}⁄_{8}= -10 ^{7}⁄_{8}3 ^{6}⁄_{8}= 3 ^{3}⁄_{4}

- Find the product of 0.12 and 55

6.6

"Product" means to multiply. Multiply 0.12 x 55. Since 0.12 has two decimals places, your answer will also have two decimal places.

- If a shipment of 50 cans of soda is received, and there are 12 ounces of soda in each can, how many ounces of soda are in the shipment?

Multiply the number of cans by the number of ounces in each to get the total ounces.

- The school taxes are $2500 on a house that is worth $200,000. What is the ratio of the cost of taxes to the value of the house? Express your answer in fraction form and write in lowest terms.

^{1}⁄_{80}

This problem is like problem number 5. Create the ratio of “2500 to 200,000” as a fraction and reduce.^{2500}⁄_{200,000}=^{1}⁄_{80}

- Evaluate: 3x – 7 when x = -1

-10

Substitute -1 in for x and evaluate the expression: 3(-1) – 7 = -3 – 7 = -10

- Five lima beans were measured and found to have the following lengths: 1.9 cm, 2.1 cm, 2 cm, 1.9 cm, and 2.5 cm. What is the average (mean) length of the beans?

2.08

To find the average (mean), add the five numbers together and then divide by 5.

- Calculate and give your answer in lowest terms:
3 + 5 12 - (-12)

^{8}⁄_{24}=^{1}⁄_{3}

Add the numerator together to get 8. Next add the denominator to get 24. The fraction is^{8}⁄_{24}=^{1}⁄_{3}. Note: A negative outside parentheses is changed to addition and sign of everything inside parentheses changes to its opposite sign.

- Of the following, which is the largest?
^{2}⁄_{3}, 0.66, 0.666, 0.6

^{2}⁄_{3}

Change the fraction into a decimal by dividing the numerator by the denominator. You will get 0.66666 which is larger than the other decimals given.

- A store receives 16,500 cans of Split Pea Soup in 300 cartons. How many cans of Split Pea Soup were in each carton?

55 cans

Divide 16500 by 300 to find the total number of cans in each carton.

- A student who takes out loans totaling $10,000 will have to pay back the loan over a period of ten years. If payments amount to $105 per month, how much will the student have to pay back the lender?

$12,600

First we need the total number of months the loan will need to be paid: 10 years x 12 months = 120 months. Now multiply 120 months x 105 each month.

- Mark attends classes on Monday and Wednesday from 9:30 AM to 11:00 AM and from 12:30 PM to 4:00 PM. How many hours a week does Mark attend class?

10 hours

He attends class a total of 5 hours on both Monday and Wednesday for a total of 10 hours in class.

- If
^{7}⁄_{x}=^{4}⁄_{3}, then x = ? (NOTE: Your answer should be given as an improper fraction.)

^{21}⁄_{4}

Since two fractions are set equal to each other you can cross multiply to get 21 = 4x. To get x by itself, you would then divide both sides by 4 to get the answer.

- Divide: 4
^{1}⁄_{2}÷^{3}⁄_{8}

12

4^{1}⁄_{2}÷^{3}⁄_{8}=^{9}⁄_{2}X^{8}⁄_{3}=^{72}⁄_{6}= 12

When dividing fractions, think of the phrase “keep change flip.” Keep the first fraction the way it is, change the division sign to multiplication, and take the reciprocal of the second fraction and multiply and reduce.

- If 6 = 8 + 4x, then x = ? (NOTE: Your answer should be stated as a fraction.)

-^{1}⁄_{2}

6 = 8 + 4x

-2 = 4x

-^{1}⁄_{2}= x

- City College plans to have 15 computers for every 60 students. How many computers would be needed for 3600 students?

900 computers

^{15}⁄_{60}=^{x}⁄_{3600}

60x = 54,000

x = 900

Again, with two fractions set equal to each other you will cross multiply to get a new equation and solve the equation.

- Find the increase in megawatt usage during the four-year period from 1988 to 1992.

1000 megawatts

Each horizontal line represents 200 megawatts. In the year 1992, 2600 megawatts was used and in 1988, 1600 megawatts was used. Subtract the two amounts to find the difference.

- The length of a rectangle is 32 feet and the width is 14 feet. What is the perimeter?

92 feet

The formula to find the perimeter of a rectangle is P = 2L + 2W. Substitute in the values for the length and width and evaluate the expression.

P = 2(32) + 2(14)

P = 64 + 28

P = 92

- A babysitter earns $1.50 per hour up to 6:00 PM and $2 per hour after 6:00 PM. How much will the sitter earn on a day they babysat from 10:00 AM to 9:30 PM?

$19

Babysitter worked 8 hours at $1.50 and 3.5 hours at $2.00.

8(1.5) + 3.5(2)

12 + 7

19

- Bill receives a 6% salary increase. If Bill’s salary was $12,000 before the raise, what is his new salary?

$12,720

Multiply 12,000 times .06 to get 720. Add 12,000 and 720 to get his new salary of $12,720.

- Calculate 4
^{3}⁄_{4}+ 2^{1}⁄_{2}(NOTE: Your answer should be given as a mixed number.)

7^{1}⁄_{4}

To add fractions, you must have common denominators. Both must be changed into that denominator. The common denominator is 4 so we do not need to change the first fraction. The second fraction becomes 2^{2}⁄_{4}. Now they can be added together.