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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 27 Page 263

Use the Multiplication Property of Equality to eliminate the division.

v=45

Practice makes perfect

To solve the equation, we have to isolate v on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 5. This will eliminate the division and isolate v.

9=v÷ 5

a÷ b=a/b

9=v/5

LHS * 5=RHS* 5

9* 5=v/5* 5

MoveRightFacToNum

a/c* b = a* b/c

9* 5=v* 5/5

MovePartNumLeft

a* b/c=a*b/c

9* 5=v*5/5

Calculate quotient

9* 5=v*1

Multiply

45=v

Rearrange equation

v=45

To check that this solution is correct, let's substitute v=45 into the original equation and simplify.

9=v÷ 5

v= 45

9? = 45÷ 5

Calculate quotient

9=9 ✓

Since the left-hand side and right-hand side are equal, v=45 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