Vocabulary Cards

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RATIONAL NUMERS

Rational numbers can be written as RATIOS (FRACTIONS)!!!!

Rational Numbers include:

Whole Numbers (0,1,2,3, . . . .)Integers (the number line: . . .-1, 0, 1 . . .)Fractions Decimals: repeating or terminatingPerfect square because there answers are whole numbers

Irrational Numbers

These numbers cannot be written in fraction form

They include things like:Nonrepeating, Nonterminating Decimals: .324789768452462. . . (no pattern and continues FOREVER)

Pi

Imperfect squares √7: because their answers are nonrepeating and nonterminating decimals

Coefficient The number in front of a variable.

Example: 7x

The coefficient is 1Constant A number that stands alone.

No variable attached to it. Value doesn’t change

Example: 1 + 2xThe constant is 1

Variable A letter or symbol that can represent any number

Example:

x, 7y, 8j

The variables are: x, y , j

Adding Integers with the same sign

Add the numbers keep the sign

Ex: -3 + (-9) = - 12 3 + 9 = 12

Adding integers with different signs

Subtract numbers take the sign of the “bigger” number

Ex: -3 + 9 = 6 3 + (-9) = -6

Subtracting Integers Add the opposite then follow the adding rules

Ex: -3 – 9 = -3 + (-9) = -12 -3 – (-9) = -3 + 9 = 6 3 – 9 = 3 + (-9) = -6 3 – (-9) = 3 + 9 = 12

Multiplying integers with the same sign

Multiply the numbers and your final answer will be POSITIVE

Ex: - 2 (-9) = 18 2 (9) = 18

Multiplying integers with different signs

Multiply the numbers and your final answer will be NEGATIVEEx: - 2 (9) = -18 2 (-9) = -18

Dividing integers with the same sign

Divide the numbers and your answer will be positive

Ex: 18 = 2 9

-18 = 2 - 9

Dividing integers with different signs

Divide the number and your answer will be negative

Ex: - 18 = - 2 9

18 = - 2 - 9

Fractions Part to whole comparison.Set up as: Denominator (Part) Numerator (Whole) Ex: We ordered a 12 piece pizza and John ate 4 of the twelve pieces, what fraction of the pizza did John eat? (Simplify)

4 ÷ 4 = 112 ÷ 4 = 3

Least Common Multiple (Denominator) Is the smallest multiple two or more numbers have in common on the multiplication table

Ex:Find the LCM of 3 and 8

List of multiples3 = 3,6,9,12,15,18,21,24,27, 30, 33, 36 . . 8 = 8, 16, 24,32,40,48, 56, 64,72,80, 88 . . .

The first number they share is 24!!! That’s there LCM!!!

Adding Fractions With the same Denominator

Add the Numerators KEEP the Denominator. Reduce/Simplify if possible.

Numerator + Numerator Denominator

Ex: 2 + 3 = 5 7 7 7

Adding Fractions with Different Denominator

You MUST always have the same denominator!!!! Change so you have the same denominator:

Find the LCM of the denominators (refer to LCM card if forgotten)

Ex: the LCM between 7 and 3 = 21

4 3 = 12 7 3 = 21+ 1 7 = 7 3 7 = 21 19 Add numerators

21 keep denominators

Subtracting Fractions with the Same Denominator

Subtract the Numerators and KEEP the denominators!!!

Numerator - Numerator Denominator

Ex: 3 - 2 = 1 7 7 7

Subtracting Fractions with Different Denominators

You MUST always have the same denominator!!!! Change so you have the same denominator:

Find the LCM of the denominators (refer to LCM card if forgotten)

Ex: the LCM between 7 and 3 = 21

4 3 = 12 7 3 = 21- 1 7 = 7 3 7 = 21 5 Subtract the Numerators

21 Keep the denomnators

Multiplying Fractions Just numerator with numerator and denominator with denominator. Reduce/Simplify if possible

Numerator Numerator Denominator Denominator

Example:

2 8 = 2 8 = 165 9 5 9 = 45

Dividing Fractions To Divide Fraction we multiply by the reciprocal (flip the second fraction upside down). Simplify/reduce if possible.

Numerator Denominator Denominator Numerator

Example:

2 ÷ 8 = 2 9 = 185 ÷ 9 = 5 8 = 40

18 ÷ 2 = 9 reduce!!!40 ÷ 2 = 20

Power Repeated Multiplication

Parts:

Baseexponent

Example:

x5 = x x x x x

Zero Exponents Any power with an exponent of zero =

1x0 = 1

100 0= 1

30= 1

150,000,0000 = 1

Negative Exponents We can NOT have negative exponents, so we reciprocal (flip) our power and change the exponent to positive. Move the power down or up to make the exponent positive.

Examples:

x-3 = 1 x3

1 = y5

Y-5

2k-2 = 2 k2

Multiplying powers with the same base

Add the exponents keep the base

Example

x3 x6 = x3 + 6 = x9

103 10 = 103 101 = 10 3+1 = 104

Dividing powers with the same base

Subtract the exponents KEEP the base

Examples:

y7 = y 7-5 = y 2

y5

810 = 8 10 - 12 = 8-2 = 1 negative exponent

8 12 82

Power of a power Multiply the exponents and keep the base

Example:

( x3)4 = x34 = x 12

(x4)2 = x42 = x8

(y) = y12 y2

Monomials A number, or a product of a number and one or more variables with whole number exponents

Examples:

7, 7x, 7x2, 7x4y7

Simplifying Monomials in Multiplication

1. Separate the coefficients and variables 3x2 2x2 = 3 x2 2 x 2

2. Multiply the constants3 2 = 6

3. Follow power rules for multiplication for the same base

x2 x2 = x 2+2 = x4

4. Bring together6x4

Simplifying Monomials in Division

1. Separate the coefficients and variables 6x2 = 6 x3

2x2 = 2 x 2

2. Divide the constants6 = 32

3. Follow power rules for Division for the same base

x3 = x 3-2 = x1

x2

4. Bring together3x1 or just 3x