definition a mathematical sentence, that shows that two expressions, either numerical or algebraic,...

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.

Examples

16 + 14 = 40 – 10

abc = d ÷ f

x = 412

-32 - -52 = -16y

a2 + b2 = c2

All Have Equal Signs!

Non-examples

17a

abc

(23 x 14) – 162

14,001

83 + 47

Nothing Here To Balance!

Equations

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



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



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



The “Line” In Any Fractions Means Divide

36

― =

2

½ or 0.5

5

― =

10



Any Number Over 1 Is That Number

2

―

12 =

11

―

111 =



Any Number Divided by Itself Is 1

16

― =

6

113

― =

13


2 a = 16

1. Isolate the Variable

2 a = 16

This Also Helps Tell Us What Side Of The Equal Sign to Start.


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 =


3. Whatever Is Done To One Side Of The Equal Sign, Do To The Other.

And Solve

2 a = 16

2 = 2

a = 8

↓

1


3. Double Check by Inserting the Solution Back Into The Original Expression.

Does 2 · 8 = 16

Yes!

= 16

a = 8

2 (8)a ☺

definition a mathematical sentence, that shows that two expressions, either numerical or algebraic,...

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