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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 31 Page 263

Use the Multiplicative Inverse Property to isolate k.

k=8/3

Practice makes perfect

To solve the equation, we have to isolate k on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by the reciprocal of 14, which is 41. This will isolate k.

2/3=1/4k

LHS * 4/1=RHS* 4/1

4/1* 2/3=4/1* 1/4k

MultFracByInverse

a/b* b/a=1

4/1* 2/3=1* k

Multiply fractions

4* 2/1* 3=1* k

Multiply

8/3= k

Rearrange equation

k=8/3

To check that this solution is correct, let's substitute k= 83 into the original equation and simplify.

2/3=1/4k

k= 8/3

2/3? =1/4* 8/3

Multiply fractions

2/3? =1* 8/4* 3

Multiply

2/3? =8/12

a/b=.a /4./.b /4.

2/3? =8÷ 4/12÷ 4

Calculate quotient

2/3=2/3 ✓

Since the left-hand side and right-hand side are equal, k= 83 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