Properties of Equality Notes worksheet for math education.

Looking at the worksheet, I need to fill in the blanks for each property of equality. Let me go through each one carefully.

Addition Property:
The definition says "You can ___ a number to both sides of an equation."
Looking at the example: x - 3 = 10 → x = 13
To get from x - 3 = 10 to x = 13, we added 3 to both sides.
So the blank should be "add"

Subtraction Property:
The definition says "You can ___ a number from both sides of an equation."
Looking at the example: x + 4 = 6 → x = 2
To get from x + 4 = 6 to x = 2, we subtracted 4 from both sides.
So the blank should be "subtract"

Multiplication Property:
The definition says "You can ___ both sides of an equation by the same number."
Looking at the example: x/2 = 5 → x = 10
To get from x/2 = 5 to x = 10, we multiplied both sides by 2.
So the blank should be "multiply"

Division Property:
The definition says "You can ___ both sides of an equation by the same number."
Looking at the example: 3x = 6 → x = 2
To get from 3x = 6 to x = 2, we divided both sides by 3.
So the blank should be "divide"

Reflexive Property:
The definition says "A number or variable equals ___."
Looking at the example: 10 = 10 or x = x
This shows that something equals itself.
So the blank should be "itself"

Symmetric Property:
The definition says "If a = b, then ___."
Looking at the example: x = 3 is the same as 3 = x
This shows that if a = b, then b = a.
So the blank should be "b = a"

Transitive Property:
The definition says "If a = b and b = c, then ___."
Looking at the example: If x + 2 = 4 and 4 = y, then x + 2 = y
This shows that if a = b and b = c, then a = c.
So the blank should be "a = c"

Substitution Property:
The definition says "If a = b, then b can ___ a with b."
Looking at the example: If a = b and a + c = d, then b + c = d
This shows that you can replace (substitute) a with b.
So the blank should be "replace"

Final Answer:
Addition Property: add
Subtraction Property: subtract
Multiplication Property: multiply
Division Property: divide
Reflexive Property: itself
Symmetric Property: b = a
Transitive Property: a = c
Substitution Property: replace