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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 19 Page 263

Use the Multiplicative Inverse Property to isolate r.

r=32

Practice makes perfect

To solve the equation, we have to isolate r on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by the reciprocal of 34, which is 43. This will isolate r.

24=3/4r

LHS * 4/3=RHS* 4/3

4/3* 24=4/3* 3/4* r

MultFracByInverse

a/b* b/a=1

4/3* 24=1* r

MoveRightFacToNum

a/c* b = a* b/c

4* 24/3=1* r

Multiply

96/3=r

Calculate quotient

32=r

Rearrange equation

r=32

To check that this solution is correct, let's substitute r=32 into the original equation and simplify.

24=3/4r

r= 32

24? =3/4( 32)

MoveRightFacToNum

a/c* b = a* b/c

24? =3* 32/4

Multiply

24? =96/4

Calculate quotient

24=24 ✓

Since the left-hand side and right-hand side are equal, r=32 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