vocabulary cards study your cards everyday! together we will get our cst scores better than ever!...
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Vocabulary Cards
Study your cards everyday! Together we will get our CST scores better than ever!
You can do it if you do your part!
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