Properties of Equality
The property that allows you to add the same number to both sides of an equation
Addition Property of Equality
Translate: “The sum of a number and 7”
x + 7
Simplify: 3x+4x
7x
The result of multiplying numbers together
Product
What mistake is made if you only add to one side of an equation?
Not maintaining equality
If a=b, then b=a. What property is this?
Symmetric Property
Translate: “5 less than a number”
x - 5
Solve: x+5=12
x = 7
The result of dividing one number by another
Quotient
Students often confuse “less than” and “more than.” Translate “8 less than x.”
X - 8
If a=b and b=c, then a=c. What property is this?
Transitive Property
Translate: “Twice a number increased by 3”
2x + 3
Solve: 3x−4=11
x = 5
The result of adding numbers together
Sum
What mistake happens if you forget to distribute a negative sign?
Wrong signs in the expression
The property that allows you to multiply both sides of an equation by the same number
Multiplication Property of Equality
Translate: “The quotient of a number and 4”
x/4
Simplify: 2(3x+5)
6x + 10
The result of subtracting numbers
Difference
If 3(x+2)=15 becomes 3x+2=15, what went wrong?
Didn’t distribute correctly
What property does this show? 3=3
Reflexive Property
Translate: “7 more than three times a number”
3x + 7
Solve: 5x+3=2x+12
x = 3
What is the word for an expression that contains an equal sign?
Equation
Why is “5 – x” not the same as “x – 5”?
Order matters. Subtraction is not commutative