## Basic Algebra

- Simplify -2.5 + 1.4

-1.1

Follow the sign rules when adding and subtracting:

If the numbers have the same sign, add them together and keep the sign. If the numbers have different signs, subtract the numbers and keep the sign of the larger number.

- Simplify −5 + 2 × 7

9

Follow the Order of Operations at all times. You can remember the Order of Operations by the phrase “Please Excuse My Deal Aunt Sally”. For a more detailed explanation visit http://media.tripod.lycos.com/1782282/1373792.pdf.

Parentheses

Exponents

Multiplication / Division – starting at the left and moving to the right

Addition

Subtraction

- Simplify 3(1-5)
^{2}-8+2^{2}

41

Order of Operations was used to evaluate the expression.

3(1-5) ^{2}-8+2^{2}

3(-4)^{2}-8+2^{2}

3(15)-8+4

45-8+4

49-8

41Do what is inside parentheses first and rewrite the problem. Next do the exponents and rewrite the problem. Next is multiplication, followed by addition and subtraction.

For more examples, visit http://sradai.tripod.com/webonmediacontents/Order%20of%20Operations%20Examples.pdf

Simplify 3-5 ^{2}6-2x3 ^{2}(NOTE: Answer should be written as a fraction.)

11 6

Follow the Order of Operations3-5 ^{2}6-2x3 ^{2}= 3-25 6-2x9 = -22 6-18 = -22 -12 = 11 6

- Translate the following statement into symbols: The sum of six and three is less than ten.

The problem states to “translate” the statement. It does not say to simplify. If it asked you to simplify, you would get 9 < 10.

- Insert <, >, or = in the blank to make the following statement true: −3 __ −4

>

As negative numbers become larger, they are getting smaller.

- Evaluate 2xy
^{2}for x = −2 and y = 3

-36

Follow the sign rules for multiplying signed numbers. For more information, visit http://sradai.tripod.com/webonmediacontents/Basic%20Rules%20to%20Remember.pdf.

2xy^{2}= 2(-2)(3)^{2}= 2(-2)(9) = -4(9) = -36

- Simplify the expression 3(x–5)+11

3x-4

3(x-5)+11

3x-15+11

3x-4

- Solve x-11 = 2

x = 13

To get x by itself, add the opposite of -11 to both sides.

- Solve −4x + 7 = −21

x = 7

-4x + 7 = -21

-4x = -28

x = 7

- Solve
^{3}⁄_{4}x - 5 = -7 (NOTE: Answer should be written as a fraction.)

x = -^{8}⁄_{3}

First we add the opposite of -5 to both sides to get the fraction and x by itself. Then multiply both sides by the reciprocal of the fraction.

^{3}⁄_{4}x - 5 = -7

^{3}⁄_{4}x = -2

(^{4}⁄_{3})(^{3}⁄_{4})x =^{-2}⁄_{1}(^{4}⁄_{3})

x = -^{8}⁄_{3}

- Solve −3(x – 6) = 5x − 12 + 2x

Order of Operations was used to evaluate the expression.

−3(x – 6) = 5x − 12 + 2x

−3x + 18 = 5x − 12 + 2x

−3x + 18 = 7x − 12

30 = 10x

3 = x

To learn more about solving linear equations, visit http://media.tripod.lycos.com/1782282/1668263.pdf

- Solve -0.3(x - 3) + x = 0.5(3 - x)

-0.3(x - 3) + x = 0.5(3 - x)

0.7x + 1.2 = 1.5 - 0.5x

1.2x = 0.3

x = 4To learn more about solving linear equations, visit http://media.tripod.lycos.com/1782282/1668263.pdf

- An item is put on sale with a 30% discount off the original price. The sale price is $49. What was the original price?

x = $70

x - 0.30x = 49Original price - 30% discount of original price = sale price x - 0.30x = 49

0.70x = 49

x = 70

- Jane has $8 more than three times the money that Joe has. Together, Jane and Joe have $80. How much money does Joe have and how much money does Jane have?

x = 18

Joe = x

Jane = 3x + 8

**Equation**

x + 3x + 8 = 80

4x + 8 = 80

4x = 72

x = 18

- 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.