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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
3. Solving Equations Using Multiplication or Division
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Exercise 33 Page 263

Use the Multiplication Property of Equality to eliminate the division.

b=7.2

Practice makes perfect

To solve the equation, we have to isolate b on one side. Using the Multiplication Property of Equality, we will multiply both sides of the equation by 12. This will eliminate the denominator of the fraction and isolate 7b.

7b÷ 12=4.2
DivToFrac

a÷ b=a/b

7b/12=4.2
MultEqn

LHS * 12=RHS* 12

7b/12* 12=4.2* 12
FracMultDenomToNumber

a/12* 12 = a

7b=4.2* 12
Multiply

Multiply

7b=50.4
DivEqn

.LHS /7.=.RHS /7.

7b/7=50.4/7
MovePartNumRight

a* b/c=a/c* b

7/7* b=50.4/7
CalcQuot

Calculate quotient

1* b=7.2
IdPropMult

Identity Property of Multiplication

b=7.2

To check that this solution is correct, let's substitute b=7.2 into the original equation and simplify.

7b÷ 12=4.2
Substitute

b= 7.2

7( 7.2)÷ 12? =4.2
Multiply

Multiply

50.4÷ 12? =4.2
CalcQuot

Calculate quotient

4.2=4.2 ✓

Since the left-hand side and right-hand side are equal, b=7.2 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 expand_more
arrow_right Try It p.260-261
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Try It 2 (Page 260)
Try It 3 (Page 260)
Try It 4 (Page 261)
Try It 5 (Page 261)
Try It 6 (Page 261)
arrow_right Self-Assessment for Concepts & Skills p.261
Self-Assessment for Concepts & Skills 7 (Page 261)
Self-Assessment for Concepts & Skills 8 (Page 261)
Self-Assessment for Concepts & Skills 9 (Page 261)
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arrow_right Self-Assessment for Problem Solving p.262
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arrow_right Review & Refresh p.263
Review & Refresh 1 (Page 263)
Review & Refresh 2 (Page 263)
Review & Refresh 3 (Page 263)
Review & Refresh 4 (Page 263)
Review & Refresh 5 (Page 263)
Review & Refresh 6 (Page 263)
Review & Refresh 7 (Page 263)
Review & Refresh 8 (Page 263)
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arrow_right Concepts, Skills, & Problem Solving p.263-264
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Concepts, Skills, & Problem Solving 16 (Page 263)
Concepts, Skills, & Problem Solving 17 (Page 263)
Concepts, Skills, & Problem Solving 18 (Page 263)
Concepts, Skills, & Problem Solving 19 (Page 263)
Concepts, Skills, & Problem Solving 20 (Page 263)
Concepts, Skills, & Problem Solving 21 (Page 263)
Concepts, Skills, & Problem Solving 22 (Page 263)
Concepts, Skills, & Problem Solving 23 (Page 263)
Concepts, Skills, & Problem Solving 24 (Page 263)
Concepts, Skills, & Problem Solving 25 (Page 263)
Concepts, Skills, & Problem Solving 26 (Page 263)
Concepts, Skills, & Problem Solving 27 (Page 263)
Concepts, Skills, & Problem Solving 28 (Page 263)
Concepts, Skills, & Problem Solving 29 (Page 263)
Concepts, Skills, & Problem Solving 30 (Page 263)
Concepts, Skills, & Problem Solving 31 (Page 263)
Concepts, Skills, & Problem Solving 32 (Page 263)
Concepts, Skills, & Problem Solving 33 (Page 263)
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Concepts, Skills, & Problem Solving 40 (Page 264)
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