Exercise 35 Page 98

Multiply by the denominator to eliminate the fractions.

b=56 58

Practice makes perfect

We can eliminate fractions in an equation by multiplying the entire equation by the product of the denominators. In this equation, our denominators are 3 and 8. So, we will multiply by 3*8=24. Let's try to solve for b.

b/3+1/8=19

MultEqn

LHS * 24=RHS* 24

(b/3+1/8)*24=19*24

Distr

Distribute 24

b/3*24+1/8*24=19*24

MoveRightFacToNum

a/c* b = a* b/c

b*24/3+1*24/8=198

Multiply

24b/3+24/8=456

ReduceFrac

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

8b/1+24/8=456

ReduceFrac

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

8b/1+3/1=456

DivByOne

a/1=a

8b+3=456

SubEqn

LHS-3=RHS-3

8b=453

DivEqn

.LHS /8.=.RHS /8.

b=453/8

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

b/3+1/8=19

Substitute

b= 453/8

453/8/3+1/8? =19

DivFracSL

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

453/8*3+1/8? =19

ReduceFrac

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

151/8*1+1/8? =19

AddFrac

Add fractions

151+1/8? =19

AddTerms

Add terms

152/8? =19

CalcQuot

Calculate quotient

19=19

Since the left-hand side and right-hand side are equal, we know our solution is correct. Although b= 4538 is a perfectly valid solution, we can also rewrite it as a mixed number.

b=453/8

Rewrite

Rewrite 453 as 448+5

b=448+5/8

WriteSumFrac

Write as a sum of fractions

b=448/8+5/8

CalcQuot

Calculate quotient

b=56+5/8

Rewrite

Rewrite 56+5/8 as 5 58