Solving Equations 1-7
Equations use an = sign to show that two expressions are equivalent
Equations can be true, false, or open
If an equation is NUMERICAL (numbers), it must be either TRUE or FALSE:
3 + 5 = 8 is TRUE
3 + 5 = 9 is FALSE
If an equation is ALGEBRAIC (variables), it is OPEN for discussion
(it all depends on what the variable is!)
y + 4 = 10 is OPEN
SOLUTION = answer
REPLACEMENT SET: The set of answers that you have to choose from for the answer.
SOLUTION SET: All the answers that make a statement true.
{ } set symbol
EXAMPLE: Solve y + 4 = 10 for the replacement set {2, 6, 10}
Substitute each element of the replacement set into the equation to see which one(s) work
Only 6 works, so only 6 is a true solution
The solution set is {6}
Note that if the replacement set was {2, 7, 10} for y + 4 = 10, then the solution set would be the NULL SET which means the solution does not exist in the replacement set.
The symbol for the null set is a zero with a line through it.
Equations must always be in balance.
GOLDEN RULE: WHATEVER YOU DO TO ONE SIDE OF AN EQUATION, YOU MUST DO TO THE OTHER SIDE or you'll be out of balance.
One way they might ask this question on the STAR Test is to ask:
What was done to the first equation to get the second?
EXAMPLE: 3x - 5 = 12 and 9x - 15 = 36
The first equation was multiplied by 3 to get to the second equation so they are equivalent.
Wednesday, September 2, 2009
Tuesday, September 1, 2009
Math 6H Period 3, 6 & 7
Mathematical Expressions 1-1
A variable is a symbol used to represent one or more numbers. The numbers are called the values of the variable.
An expression, such as 3 x n, that involves a variable is called a variable expression.
Expressions, such as 3 x 2, that name a certain number are called numerical expressions
When we write a product that involves a variable, we usually omit the multiplication symbol (whether that be written as x or as ∙ or even with parentheses). Thus, 3 x n is written as 3n
and 2 x a x b is written as 2ab
In numerical expressions for products a multiplication symbol must be used to avoid confusion.
9 x 7 may be written as 9 ∙ 7 or even 9(7)
When a mathematical sentence uses an equal sign, it is called an equation. An equation tells us that two expressions name the same number. The expression to the left of the equals sign is called the left side of the equation and the expression to the right of the equals sign is called the right side.
When a number is substituted for a variable in the variable expression and the indicated operation is carried out, we say that the variable expression has been evaluated. For example, if n has the value 6 in the variable expression 3 x n, then 3 x n has the value 3 x 6, or 18
Example: Evaluate the expression 6a when the variable has the following values:
6a; 2, 4, 6, 8
You would substitute in each vvalue for the variable a
6(2) = 12
6(4) = 24
6(6) = 36
6(8) = 48
A variable is a symbol used to represent one or more numbers. The numbers are called the values of the variable.
An expression, such as 3 x n, that involves a variable is called a variable expression.
Expressions, such as 3 x 2, that name a certain number are called numerical expressions
When we write a product that involves a variable, we usually omit the multiplication symbol (whether that be written as x or as ∙ or even with parentheses). Thus, 3 x n is written as 3n
and 2 x a x b is written as 2ab
In numerical expressions for products a multiplication symbol must be used to avoid confusion.
9 x 7 may be written as 9 ∙ 7 or even 9(7)
When a mathematical sentence uses an equal sign, it is called an equation. An equation tells us that two expressions name the same number. The expression to the left of the equals sign is called the left side of the equation and the expression to the right of the equals sign is called the right side.
When a number is substituted for a variable in the variable expression and the indicated operation is carried out, we say that the variable expression has been evaluated. For example, if n has the value 6 in the variable expression 3 x n, then 3 x n has the value 3 x 6, or 18
Example: Evaluate the expression 6a when the variable has the following values:
6a; 2, 4, 6, 8
You would substitute in each vvalue for the variable a
6(2) = 12
6(4) = 24
6(6) = 36
6(8) = 48
Pre Algebra Period 1
The Order Of Operations 1-2
O3 = Order Of Operations
It’s Aunt Sally’s Rule—Please Excuse My Dear Aunt Sally
Please (XX)
Excuse E2
My Dear (or even Dear My) × ÷ or ÷ ×
Aunt Sally (Sally Aunt) + - or - +
PEMDAS
The most common mistake of O3
when you see multiplication and division—you do whichever comes first in order!!
So if you see division then multiplication, you do division first then multiplication
When you see addition and subtraction, you do whichever comes first in order!
So if you see subtraction then addition, do the subtraction first!
When you see more than one set of parentheses, do the innermost ones first, then work outwards.
They're called nested parentheses because a bird builds his nest from the inside out.
Posted by Jani Nelson at 6:17 AM 0 comments
O3 = Order Of Operations
It’s Aunt Sally’s Rule—Please Excuse My Dear Aunt Sally
Please (XX)
Excuse E2
My Dear (or even Dear My) × ÷ or ÷ ×
Aunt Sally (Sally Aunt) + - or - +
PEMDAS
The most common mistake of O3
when you see multiplication and division—you do whichever comes first in order!!
So if you see division then multiplication, you do division first then multiplication
When you see addition and subtraction, you do whichever comes first in order!
So if you see subtraction then addition, do the subtraction first!
When you see more than one set of parentheses, do the innermost ones first, then work outwards.
They're called nested parentheses because a bird builds his nest from the inside out.
Posted by Jani Nelson at 6:17 AM 0 comments
Monday, August 31, 2009
Pre Algebra Period 1
Our Class Blog
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!
Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!
Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!
Math 6Honors Period 3, 6, & 7
Our Class Blog
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!
Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!
Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!
Algebra Period 4
Our Class Blog
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!
Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!
Exponential Notation A product in which the factors are the same is called a power
We can write 2∙2∙2∙2∙2∙2 as 26. The number 6 is called the exponent and 2 is called the base.
When an expression is written with exponents it is written using exponential notation.
b1 means b for any number b
If n is a whole number greater than 1 bn means b∙b∙b∙b∙…∙b
n times
Remember Order of Operations O3
Parentheses
Exponents
Multiply and Divide in order from left to right
Add and Subtract in order from left to right
Calculate
(3a)3 for a= 2
(3a)3 = (3a)(3a)(3a) Now substitute in for a (3∙2)(3∙2)(3∙2) = (6)(6)(6)= 216
Notice the difference for
3a3 for a = 2
What is the exponent touching this time? only the a
3∙a∙a∙a Now substitute in for a 3∙2∙2∙2 = 24
Welcome to our class blog... where you can earn extra credit by adding your own relevant comments about our class notes for the day.. or where you can find answers from others in your class. Check here often, especially if you have been absent. You might just find out the math strategy that works for you!!
Email me if you are interested in adding notes and/or comments to this blog-- for extra credit!!
Exponential Notation A product in which the factors are the same is called a power
We can write 2∙2∙2∙2∙2∙2 as 26. The number 6 is called the exponent and 2 is called the base.
When an expression is written with exponents it is written using exponential notation.
b1 means b for any number b
If n is a whole number greater than 1 bn means b∙b∙b∙b∙…∙b
n times
Remember Order of Operations O3
Parentheses
Exponents
Multiply and Divide in order from left to right
Add and Subtract in order from left to right
Calculate
(3a)3 for a= 2
(3a)3 = (3a)(3a)(3a) Now substitute in for a (3∙2)(3∙2)(3∙2) = (6)(6)(6)= 216
Notice the difference for
3a3 for a = 2
What is the exponent touching this time? only the a
3∙a∙a∙a Now substitute in for a 3∙2∙2∙2 = 24
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