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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 3 Page 260

Write the division as a fraction. Use the Multiplicative Inverse Property to isolate z.

z=6

Practice makes perfect

To solve the equation, we have to isolate z on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 23. Then, we will use the Multiplicative Inverse Property.

3z÷ 2=9

a÷ b=a/b

3z/2=9

LHS * 2/3=RHS* 2/3

2/3* 3z/2=2/3* 9

▼

Simplify

MovePartNumRight

a* b/c=a/c* b

2/3* 3/2z=2/3* 9

MultFracByInverse

a/b* b/a=1

1* z=2/3* 9

MoveRightFacToNum

a/c* b = a* b/c

1* z=2* 9/3

Multiply

z=18/3

Calculate quotient

z=6

To check that this solution is correct, let's substitute z=6 into the original equation and simplify.

3z÷ 2=9

z= 6

3( 6)÷ 2? =9

Multiply

18÷ 2? =9

Calculate quotient

9=9 ✓

Since the left-hand side and right-hand side are equal, z=6 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