1. Definition
A mathematical sentence, that shows that two expressions, either numerical or algebraic, are equivalent. Like a balance.
Characteristics
Isolate the Variable.
Use The Inverse Operation (Undo).
Do The Same Operation to Both Sides of The Equal Sign.
Double Check by Inserting the Solution Back Into The Original Expression.
Equations
Examples
= 40 – 10
abc = d ÷ f
x = 412
= -16y
a2 + b2 = c2
All Have Equal Signs!
Non-examples
17a
abc
(23 x 14) – 162
14,001
Nothing Here To Balance!

2. Solving The Multiplication Equation
Before Solving A Multiplication Equation, Remember…
The Inverse Operation of Multiplication Is Division
This Is How We “Undo” A Multiplication Equation

3. Solving The Multiplication Equation
Before Solving A Multiplication Equation, Remember…
The Commutative Operation of Multiplication
Two or more numbers can be multiplied in any order without changing the product.
4 · 5 · 2 = 40
2 · 4 · 5 = 40

4. Solving The Multiplication Equation
Before Solving A Multiplication Equation, Remember…
There Are A Number of Ways To Indicate Multiplication
3 x 3
3 · 3
3 (3)
(3) (3)
3a means 3 times a (3 is the Coefficient and a is the Variable)
abc means a times b times c

5. Solving The Multiplication Equation
Before Solving A Multiplication Equation, Remember…
The “Line” In Any Fractions Means Divide 3 6 ― = 2 or
0.5 5 ― = 10

6. Solving The Multiplication Equation
Before Solving A Multiplication Equation, Remember…
Any Number Over 1 Is That Number 2 ― 1 2 = 11 ― 1 11 =

7. Solving The Multiplication Equation
Before Solving A Multiplication Equation, Remember…
Any Number Divided by Itself Is 1 1 6 ― = 1 13 ― =

8. Solving The Multiplication Equation
Isolate the Variable
This Also Helps Tell Us What Side Of The Equal Sign to Start.

9. Solving The Multiplication Equation
2. Isolate the Variable or “Undo” The Equation By Using The Inverse Operation.
Since This Is A Multiplication Equation, Use Division.
Also, Divide The Same Number 2 a = 16 2 =

10. Solving The Multiplication Equation
3. Whatever Is Done To One Side Of The Equal Sign, Do To The Other.
And Solve 2 a = 16 2 = ↓ 2 1 a = 8

11. Solving The Multiplication Equation
Double Check by Inserting the Solution Back Into The Original Expression.
Does 2 · 8 = 16
Yes! ☺ 2
(8) a = 16 a = 8