DashboardNewsSettingsHelp
Get Premium
Dashboard
Dashboard Sign out
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
Continue to next subchapter

Exercise 29 Page 263

Use the Division Property of Equality to eliminate the multiplication.

m=3/20

Practice makes perfect

To solve the equation, we have to isolate m on one side. Using the Division Property of Equality, we will divide both sides of the equation by 4. This will eliminate the multiplication and isolate m.

3/5=4m
DivEqn

.LHS /4.=.RHS /4.

3/5÷ 4=4m÷ 4
WriteAsFrac

Write as a fraction

3/5÷ 4/1=4m÷ 4/1
DivFracByFracDiv

a/b÷c/d=a/b*d/c

3/5* 1/4=4m* 1/4
CommutativePropMult

Commutative Property of Multiplication

3/5* 1/4=m* 4* 1/4
WriteAsFrac

Write as a fraction

3/5* 1/4=m* 4/1* 1/4
MultFrac

Multiply fractions

3* 1/5* 4=m* 4* 1/1* 4
Multiply

Multiply

3/20=m* 4/4
CalcQuot

Calculate quotient

3/20=m*1
IdPropMult

Identity Property of Multiplication

3/20=m
RearrangeEqn

Rearrange equation

m=3/20

To check that this solution is correct, let's substitute m= 320 into the original equation and simplify.

3/5=4m
Substitute

m= 3/20

3/5? =4( 3/20)
MoveRightFacToNum

a/c* b = a* b/c

3/5? =4* 3/20
Multiply

Multiply

3/5? =12/20
ReduceFrac

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

3/5? =12÷ 4/20÷ 4
SimpQuot

Simplify quotient

3/5=3/5 ✓

Since the left-hand side and right-hand side are equal, m= 320 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
1
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)
10
11
arrow_right Self-Assessment for Problem Solving p.262
12
13
14
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)
9
10
11
12
arrow_right Concepts, Skills, & Problem Solving p.263-264
13
14
15
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)
Concepts, Skills, & Problem Solving 34 (Page 263)
Concepts, Skills, & Problem Solving 35 (Page 263)
36
37
38
39
Concepts, Skills, & Problem Solving 40 (Page 264)
Concepts, Skills, & Problem Solving 41 (Page 264)
42
43
44
45