Exercise 24 Page 418

We want to find the serving size of the apple dessert. First we can write the given decimal as a fraction.

Writing the Repeating Decimal as a Fraction

The first step to find the serving size is by rewriting the given repeating decimal as a fraction. Let's remember how we can write a repeating decimal as a fraction. We will follow five steps.

Assign a variable to represent the repeating decimal.
Write an equation by setting the variable and the decimal equal to each other.
Multiply both sides of the equation by 10^d, where d is the number of repeating digits in the repeating decimal.
Subtract equivalent expressions of the variable and the repeating decimal from each side of the equation.
Solve for the variable. If necessary, write an equivalent fraction so that the numerator and denominator are integers.

Let's do it!

Steps 1 and 2

Let's use the variable x to represent the given repeating decimal number. We can write an equation by setting this variable equal to 2.3. x=2.3

Step 3

Since the given number has one repeating digit, we will multiply both sides of the equation by 10^1.

x=2.3

MultEqn

LHS * 10^1=RHS* 10^1

x* 10^1=2.3* 10^1

ExponentOne

a^1=a

x* 10=2.3* 10

Multiply

10x=23.3

Step 4

We will now subtract x from both sides of the equation. Since x=2.3, we will substitute 2.3 for x on the right-hand side.

10x=23.3

SubEqn

LHS-x=RHS-x

10x-x=23.3-x

Substitute

x= 2.3

10x-x=23.3- 2.3

SubTerms

Subtract terms

9x=21

Step 5

Finally, we will solve the equation for x.

9x=21

DivEqn

.LHS /9.=.RHS /9.

9x/9=21/9

CancelCommonFac

Cancel out common factors

9x/9=21/9

SimpQuot

Simplify quotient

x=21/9

ReduceFrac

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

x=7/3

We found that x is equal to 73. Remember that x is also equal to 2.3. The Transitive Property of Equality tells us that the fraction we got is equal to the given repeating decimal number. x= 2.3 x= 73 ⇒ 2.3= 7/3

Finding the Serving Size

We found that the recipe makes 73 pounds of apple dessert. From the exercise, we know that we want this to be 6 servings. We will divide 73 by 6 to find the serving size.

73/6

DivFracD

a/c/b= a/b* c

7/3 * 6

Multiply

7/18

We found that the serving size is 718 pounds.

Hints

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