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Expression, Fractions, Multiple, Factor - Coggle Diagram
Expression
Equation
Explicit form vs implicit form
Explicit form is y=-(1/3)x+3
Implicit form is x+3y=9
Equations might have a
solution
A
solution
is a number that would make the equation true
Ex: in the equation x+1=2. The number that makes this true is when x=1.
We can
solve
an equation to find its solution
Ex: x+4=6.
Subtract
4 from both sides to get x=2.
How can we use Graphing to solve an equation?
If A=B, with A and B as expressions, then we graph y=A and y=B and find the intersection points.
What do we call an equation that does not have a solution?
It is
inconsistent
Contains an equal (=) sign and connects two expressions
Ex: y=4x+1
linear equation
y=mx+b is the slope-intercept form of a line
m=Slope
What does Slope mean?
What is the formula for slope?
intercept at (0,b)
y-intercept
This is where the line crosses the y-axis
We represent it as an ORDERED PAIR (0,y)
x-intercept
This is where the line cross the x-axis
We represent it as an ORDERED PAIR (x,0)
System of Linear Equations
is made of terms
Each term either has a number and/or a variable
Question: What is an example of an expression?
Ex: 3x
Note: the number 3 here is a called a
coefficient
Ex: 11+2x has two terms. The 11 term is just a number. The 2x term has the number 2 and the variable x.
Question: can we combine 11-2x?
Answer: No since they are unlike terms. Four cars plus two computers doesn't equal six cars.
We can
simplify
an expression
To simplify an expression means to write it so that there is no more like terms or similar terms
Ex: 4x+5x simplified is 9x
We can only multiply the expression or parts of the expression by 1. So 15/15 is equal to 1 and we could multiply by 15/15, for example.
What is the Distributive law?
a(b+c)=ab+ac
Fractions
What is a fraction?
A rational number that represents parts to a whole
What are the different types of fractions?
Proper fraction like 3/4
Improper fraction like 9/6
Adding fractions
How do we add fractions with like denominators?
How do we add fractions with unlike denominators?
How do we find a common denominator?
Multiplying fractions
How do we multiply fractions?
Multiply numerators and multiply denominators
Dividing fractions
Multiple
What is a multiple of a number?
Factor
What is a factor of a number or expression?