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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 34 Page 263

Use the Division Property of Equality to eliminate the multiplication.

n=2.56

Practice makes perfect

To solve the equation, we have to isolate n on one side. Using the Division Property of Equality, we will divide both sides of the equation by 12.5. This will eliminate the multiplication and isolate n.

12.5* n =32

.LHS /12.5.=.RHS /12.5.

12.5* n/12.5 =32/12.5

MovePartNumRight

a* b/c=a/c* b

12.5/12.5* n =32/12.5

Calculate quotient

1* n =2.56

Identity Property of Multiplication

n =2.56

To check that this solution is correct, let's substitute n=2.56 into the original equation and simplify.

12.5* n =32

n= 2.56

12.5* 2.56? =32

Multiply

32=32 ✓

Since the left-hand side and right-hand side are equal, n=2.56 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