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Equations and expressions - Coggle Diagram
Equations and expressions
Like terms: are terms whose variables (and their exponents such as the 2 in x2) are the same.
In other words, terms that are "like" each other.
Coefficients (the numbers you multiply by, such as "5" in 5x) can be different.
Combining like terms: When you find all the terms in an expression or equation that have the same variable(s) and the same exponent. You can combing them by identifying the operation (relationship) and using the coefficient to perform designated operations.
Multiplying different terms:
We can combine constants and coefficients by multiplying like normal:
3x(4y+6)=12xy+18x
The 3 and 4 can be multiplied so can the 3 and 6.
We can combine our unknowns only by creating a new type of term:
3x(4y+6)=12xy+18x
Because we do not know x and y, we only create a new type of term: xy
Dividing like terms:
We have to remember that if we divide a value by itself, that the answer is always
99=1 nn=1
We can only divide/simplify like terms other wise they create a new type of term
9x9=1x 8gh2g=82(gg)(h1)=4(1)(h)=4h
Like terms: are terms whose variables (and their exponents such as the 2 in x2) are the same.
In other words, terms that are "like" each other.
Coefficients (the numbers you multiply by, such as "5" in 5x) can be different.
Combining like terms: When you find all the terms in an expression or equation that have the same variable(s) and the same exponent. You can combing them by identifying the operation (relationship) and using the coefficient to perform designated operations.
Multiplying different terms:
We can combine constants and coefficients by multiplying like normal:
3x(4y+6)=12xy+18x
The 3 and 4 can be multiplied so can the 3 and 6.
We can combine our unknowns only by creating a new type of term:
3x(4y+6)=12xy+18x
Because we do not know x and y, we only create a new type of term: xy
Dividing like terms:
We have to remember that if we divide a value by itself, that the answer is always
99=1 nn=1
We can only divide/simplify like terms other wise they create a new type of term
9x9=1x 8gh2g=82(gg)(h1)=4(1)(h)=4h
One step equations:
Addition/Subtractions
Model
Create a key/legend
x=
-x=
+1=
-1=
Set up the problem
How do we indicate Addition/subtractions?
Find zero pairs by adding or subtraction
-1 +1=0
1-1=0
Identify your answer when your variable is isolated (by itself)
Algorithm:
The goal is to get your variable (unknown by itself)
Identify how the constant is connected to the unknown
Add or subtract to get to zero
What you do to one side you must do it to the other side.
Multiplication
Model
Create a key/legend
x=
-x=
+1=
-1=
Set up the problem
How do we indicate multiplication?
Isolate your variable
What action allows you to isolate your values? Goal is to get 1x
What you do to one side you must do to the other side
Identify your answer when you have separated your variables and have separated your constants.
Algorithm
The goal is to get your variable to have an coefficient (number in front) of 1.
Determine what you can divide by to divide the coefficient to 1.
What you do to one side you do to the other.
Division:
Model:
Make sure to create a key
Make sure to divide your variable/unknown appropriately
Figure out how many groups you need to get a whole x (1x)
Fill in all missing parts of x to get a whole x (1x)
Algorithm:
Multiply both sides by what you are dividing by
Translation of word to equations/expressions
Identify the values
Order
Identify the relationship between the values
Operations (+,-,,)
Addition: total, sum, in all,
Check the statement again to see if the equations/expression matches