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Big Ideas Math: Modeling Real Life, Grade 6

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Big Ideas Math: Modeling Real Life, Grade 6 View details

Chapter Review

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Exercise 18 Page 276

Use the Multiplication Property of Equality to eliminate the division.

k=63

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 3. This will eliminate the denominator of the fraction and isolate k.

k ÷ 3 = 21

Write as a fraction

k/3=21

LHS * 3=RHS* 3

k/3* 3=21* 3

FracMultDenomToNumber

a/3* 3 = a

k=21* 3

Multiply

k=63

To check that this solution is correct, let's substitute k=63 into the original equation and simplify.

k ÷ 3 = 21

k= 63

63÷ 3? = 21

Calculate quotient

21=21 ✓

Since the left-hand side and right-hand side are equal, k=63 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

1 Writing Equations in One Variable p.275

2 Solving Equations Using Addition or Subtraction p.276

3 Solving Equations Using Multiplication or Division p.276

4 Writing Equations in Two Variables p.277