6th Grade Math Textbook, Fundamentals

 &KDSWHU

2-6

Key Concept

Division Property of Equality

When you divide both sides of an

equation by the same nonzero

number, the result is a true statement.

If ab, then acbc, c0.

Update your skills. See pages 411 XI, 412 XII.

Solve Multiplication Equations

Objective To apply the Division Property of Equality to solve algebraic multiplication equations

with integers• To combine numerical terms to simplify multiplication equations

Maya earns $15 each time she works at the concession

stand during a game. Her goal is to earn $345 to buy the

DVD player she wants. At how many games will Maya

need to work in order to buy the DVD player?

To find the number of games at which Maya needs to work,

write and solve a.

Let gthe number of games at which Maya will need to work.

number of

amount earned games cost of DVD player

$15 • g  $345

To solve a multiplication equation, use the.

Multiplication and division are inverse operations because they “undo”

each other.

Solve: 15 g 345

g 23

Check: 15 g 345

15 • 23 345 Substitute 23 for g.

345  345 Tr u e

So 23 is the solution of the multiplication equation

15 g345. Maya needs to work at 23 games to earn

enough money to buy the DVD player.

?

Division Property of Equality

(^15345)
15 15
1
1
23
1
g
 Divide both sides by 15 to “undo” the
multiplication and to isolate g. Simplify.
multiplication equation
Remember:15 • gmeans 15g.
multiplication
equation
Think
Whenever you divide one side
of an equation by a number,
you must divide the other side
by the same number to keep
the equation in balance.
The new equation is equivalent
to the original equation.
Solve:a 78
Simplify.
a 78




1
1
78
1
1
1

• a





1 78

11

• a
  

Divide both sides by  1

to isolate a.

1 Check:a^78

(78) 78 Substitute 78 for a.

78  78 Tr u e

?

Remember:a1 • a