Exercise 33 Page 98

Multiply by the denominator to eliminate the fractions.

m=2 13

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 15. Let's try to solve for m.

2/3+3m/5=31/15

MultEqn

LHS * 15=RHS* 15

(2/3+3m/5)*15=(31/15)*15

Distr

Distribute 15

2/3*15+3m/5*15=31/15*15

FracMultDenomToNumber

a/15* 15 = a

2/3*15+3m/5*15=31

MoveRightFacToNum

a/c* b = a* b/c

2*15/3+3m*15/5=31

ReduceFrac

a/b=.a /3./.b /3.

2*5/1+3m*15/5=31

ReduceFrac

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

2*5/1+3m*3/1=31

DivByOne

a/1=a

2*5+3m*3=31

Multiply

10+9m=31

SubEqn

LHS-10=RHS-10

10+9m-10=31-10

SubTerms

Subtract terms

9m=21

DivEqn

.LHS /9.=.RHS /9.

m=21/9

ReduceFrac

a/b=.a /3./.b /3.

m=7/3

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

2/3+3m/5=31/15

Substitute

m= 7/3

2/3+3( 7/3)/5? =31/15

DenomMultFracToNumber

3 * a/3= a

2/3+7/5? =31/15

ExpandFrac

a/b=a * 5/b * 5

10/15+7/5? =31/15

ExpandFrac

a/b=a * 3/b * 3

10/15+21/15? =31/15

AddFrac

Add fractions

31/15=31/15

Since the left-hand side and right-hand side are equal, we know our solution is correct. Although m= 73 is a perfectly valid solution, we can also rewrite it as a mixed number.

m=7/3

Rewrite

Rewrite 7 as 6+1

m=6+1/3

WriteSumFrac

Write as a sum of fractions

m=6/3+1/3

CalcQuot

Calculate quotient

m=2+1/3

Rewrite

Rewrite 2+1/3 as 21/3