Exercise 37 Page 98

Multiply by the denominator to eliminate the fractions.

z=1/5

Practice makes perfect

We can eliminate fractions in an equation by multiplying the entire equation by the greatest denominator. In this equation, our greatest denominator is 16. Let's try to solve for z.

11z/16+7z/8=5/16

MultEqn

LHS * 16=RHS* 16

(11z/16+7z/8)*16=5/16*16

Distr

Distribute 16

11z/16*16+7z/8*16=5/16*16

FracMultDenomToNumber

a/16* 16 = a

11z+7z/8*16=5

MoveRightFacToNum

a/c* b = a* b/c

11z+7z*16/8=5

ReduceFrac

a/b=.a /8./.b /8.

11z+7z*2/1=5

DivByOne

a/1=a

11z+7z*2=5

Multiply

11z+14z=5

AddTerms

Add terms

25z=5

DivEqn

.LHS /25.=.RHS /25.

z=5/25

ReduceFrac

a/b=.a /5./.b /5.

z=1/5

Let's check our solution by substituting it into the original equation.

11z/16+7z/8=5/16

Substitute

z= 1/5

11( 1/5)/16+7( 1/5)/8? =5/16

MoveLeftFacToNum

a*b/c= a* b/c

11*1/5/16+7*1/5/8? =5/16

DivFracSL

.a/b /c.= a/b* c

11*1/5*16+7*1/5*8? =5/16

Multiply

11/80+7/40? =5/16

ExpandFrac

a/b=a * 2/b * 2

11/80+14/80? =5/16

AddFrac

Add fractions

11+14/80? =5/16

AddTerms

Add terms

25/80? =5/16

ReduceFrac

a/b=.a /5./.b /5.

5/16=5/16

Since the left-hand side and right-hand side are equal, we know our solution is correct.

Subchapter links

Lesson Check p.97

Practice and Problem-Solving Exercises p.98-100

Standardized Test Prep p.100

Mixed Review p.100

Exercise 37 Page 98

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