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Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

3. Solving Equations Using Multiplication or Division

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Exercise 6 Page 261

Use the Division Property of Equality to eliminate the multiplication.

r=9

Practice makes perfect

To solve the equation, we have to isolate r on one side. Using the Division Property of Equality we will divide both sides of the equation by 9. This will eliminate the multiplier and isolate r.

81=9r

.LHS /9.=.RHS /9.

81/9=9r/9

MovePartNumRight

a* b/c=a/c* b

81/9=9/9* r

a/a=1

81/9=1* r

Calculate quotient

9=1* r

Identity Property of Multiplication

9=r

Rearrange equation

r=9

To check that this solution is correct, let's substitute r=9 into the original equation and simplify.

81=9r

r= 9

81? =9( 9)

Multiply

81=81 ✓

Since the left-hand side and right-hand side are equal, r=9 is the correct solution.

Extra

Properties of Equality

There are four main Properties of Equality that we use when solving linear equations.

Properties of Equality
Addition Property of Equality	If a=b, then a+c=b+c.
Subtraction Property of Equality	If a=b, then a-c=b-c.
Multiplication Property of Equality	If a=b, then ac=bc.
Division Property of Equality	If a=b and c is not 0, then a/c=b/c.

In later chapters, you will learn about some more advanced Properties of Equality. As an example, there is a property for when we need to eliminate a radical or an exponent.

Power Property of Equality
If a=b, then a^m=b^m.

Subchapter links

Try It p.260-261

Self-Assessment for Concepts & Skills p.261

Self-Assessment for Problem Solving p.262

Review & Refresh p.263

Concepts, Skills, & Problem Solving p.263-264