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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 32 Page 263

Use the Multiplicative Inverse Property to isolate c.

c=66

Practice makes perfect

To solve the equation, we have to isolate c on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by the reciprocal of 215, which is 152. This will isolate c.

2c/15=8.8

LHS * 15/2=RHS* 15/2

15/2* 2c/15 =15/2* 8.8

MovePartNumRight

a* b/c=a/c* b

15/2* 2/15* c =15/2* 8.8

MultFracByInverse

a/b* b/a=1

1* c =15/2* 8.8

Calculate quotient

1* c =7.5* 8.8

Multiply

c =66

To check that this solution is correct, let's substitute c=66 into the original equation and simplify.

2c/15=8.8

c= 66

2( 66)/15? =8.8

Multiply

132/15? =8.8

Calculate quotient

8.8=8.8 ✓

Since the left-hand side and right-hand side are equal, c=66 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