Pre Algebra Review

Math Pre-Algebra Review

by Melissa Krop

​Topic 1: Types of Numbers

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​Whole Numbers 0, 1, 2, 3, ...

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​Positive Numbers all numbers > 0

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​Negative Numbers all numbers < 0

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Integers ... -3, -2, -1, 0, 1, 2, 3 , ...

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Open Ended

Name a negative integer that is less than -5

​Real numbers

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>All numbers on the number line

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>Every number except imaginary numbers, which you learn about in Algebra 2

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​>Basically, every number you've heard about in school so far!

​(pi, negatives, decimals, square roots, fractions)

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Rational numbers - numbers that can be written as fractions

(with integers in the numerator and denominator)

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Numbers that can be written as fractions

• decimals that end

• decimals that repeat the same digit or group of digits

• ​all fractions in any form

• ​all integers​

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Irrational numbers - NOT rational numbers

Numbers that CANNOT be written as fractions

• ​ decimals that go on forever and do NOT repeat the same digit or group of digits

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Hint for repeating decimals

​The denominator consists of 9s instead of 10, 100, 1000, etc

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​Type the following into a calculator:

• ​7/9

• ​2/99

• ​3/9

• ​12/999

Multiple Choice

.1717171717...

or

$$.\overline{17}$$  

• Rational

  (Can be written as $$\frac{17}{99}$$  )

• Irrational

  (Cannot be written as a fraction)

Multiple Select

Which of the following is a whole number? (multiple correct)

• -9

• 0

• 5.4

• 3

Multiple Choice

All whole numbers are integers.

• False
• True

Multiple Choice

-4 is not a whole number because:

• It's negative

• it's irrational.
• it cannot be turned into a fraction.
• it is even.

Multiple Select

Select all sets that the number belongs to:

$$\pi$$  

• Irrational Number

• Rational Number

• Integer

• Whole Number

Multiple Select

Select all sets that the number belongs to:

-6

• Irrational Number

• Rational Number

• Integer

• Whole Number

Multiple Select

Check all classifications for the number: 0

• Whole Number

• Integers

• Rational Number

• Irrational Number

Open Ended

-3 is a rational number because it can be rewritten as _____

Draw

Graph $$\frac{-3}{2}$$   on the number line (mark with a dot)

Open Ended

$$\frac{-3}{2}$$   is a ____ number

Fill in the blank and explain how you knew.

Topic: ​Exponents and Square Roots

Brief review of the basics

Positive Exponents: show how many times the base is multiplied by itself

​Exponential form

​The number has a base and an exponent

Multiple Choice

How do you write 2 x 2 x 2 x 2 with an exponent?

• 4²
• 2⁴
• 2²

Multiple Choice

Simplify 2⁴ x 2⁵

(answer in exponential form)

• 2²⁰
• 4⁹
• 4²⁰
• 2⁹

Multiple Choice

$$\frac{8^7}{8^2}$$  

• 8⁵
• 8⁹
• 8¹⁴
• 1⁵

Multiple Choice

What does the term "squared" mean?

• raised to the power of 3

• raised to the power of 4

• raised to the power of 2

Multiple Choice

What does the term"cubed" mean?

• raised to the power of 2

• raised to the power of 3

• raised to the power of 4

Multiple Choice

Which is equivalent to 2⁴?

• 8

• 20

• 16

• 12

Multiple Choice

Which is GREATER?

2⁷ or 7²

• 2⁷

• 7²

• Neither, they are equal

Multiple Choice

Any number written to the 0 power is always 1
Example: 8⁰=1

• True
• False

​Square Roots

> INVERSE of squaring.

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>Ask "What number times itself gets me this?"

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​Example: Square Root of 49

​>"What number times itself equals 49?"

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Multiple Choice

What is the square root of 100?

√100

• 10

• 200

• 50

• 1000

​Topic 3 Integers

Numbers that are NOT decimals and fractions

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​Can be 0, negative, or positive.

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​Examples: -9, -5, 0, 4, 100

​Adding and Subtracting Integers

​Example: 8 - 9

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The first number is your starting point.

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​Then, figure out if the final answer is higher or lower.

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Taking away 9 will lower the answer.

​The answer is 9 LOWER than 8 = - 1

Multiple Choice

-2 + 4 

• -2
• 2
• 0
• -4

Multiple Choice

-22 + (-9)

• -11
• -31
• 11
• 31

Multiple Choice

-7 - 2

• -9
• 9
• 5
• -5

Multiple Choice

-9 + 9

• 18
• -18
• 0
• 81

Multiple Choice

3 - 11 =

• -8

• 8

• 14

• -14

Multiple Choice

-12 - 3 =

• -15

• 15

• 9

• -9

Multiple Choice

-5 - (-6) =

• 1

• -1

• 11

• -11

​Multiplying and Dividing Integers

​Positive and Positive = Positive

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​Negative and Negative = Positive

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​Negative and Positive = Negative

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​Different signs --> Negative answer

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Fill in the Blanks

8 x (-2)

Fill in the Blanks

(-6) x (5)

Multiple Choice

A positive times a positive number, the answer will be?

• negative

• positive

Multiple Select

A negative number times a positive number

• positive

• negative

Multiple Choice

• 7
• -7
• 63
• 63

Multiple Choice

(-17) (0) =

• -17
• 17
• 0
• -0

Multiple Choice

27÷ -3 = 

• 24
• 9
• -9
• 30

​Fraction Review

​Adding and Subtracting you need a COMMON DENOMINATOR​​

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Multiplying

simplify up-and-down and cross-cancel when possible

then multiply straight across

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​Dividing

​Keep the first fraction

​Change to multipl

Multiple Choice

2/5 x 5/6

• 1 1/3

• 1/3

• 10/30

Multiple Choice

What is the rule for dividing fractions? 

• keep, change, opposite
• keep, change, flip
• keep, keep, change
• keep, keep, opposite

Multiple Choice

Do you need to find a common denominator to solve this?
6/7 ÷ 3/14

• Yes
• No

Multiple Choice

Can you simplify these numbers before you start multiplying?

• Yes
• No

Multiple Choice

How do you rewrite this division problem correctly to solve? 3/4 divided by 6

• 3/4 divided by 1/6
• 4/3 divided by 6/1
• 4/3 x 1/6
• 3/4 x 1/6

Multiple Choice

What is 2/7 ÷ 3/4? 

• 6/21
• 4/5
• 5/11
• 8/21

Multiple Choice

$$\frac{8}{9}\ -\ \frac{1}{3}\ =\$$  

• $$\frac{7}{6}$$  

• $$\frac{5}{9}$$  

• $$\frac{2}{3}$$  

• $$\frac{8}{27}$$  

Multiple Choice

What is  $$\frac{8}{9}$$  -  $$\frac{5}{6}$$ =  ?

• $$\frac{6}{7}$$  

• $$\frac{3}{4}$$  

• $$\frac{1}{18}$$  

• $$\frac{10}{12}$$  

Multiple Choice

Find the product.

• 7/3

• 1 and 5/7

• 14/7

Multiple Choice

Convert into an improper fraction.

• 15/2
• 10/5
• 17/5
• 11/2