CHAPTER 5 Decimal Notation Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5.1Decimal Notation, Order, and Rounding 5.2Addition and Subtraction of Decimals 5.3Multiplication of Decimals 5.4Division of Decimals 5.5Using Fraction Notation with Decimal Notation 5.6Estimating 5.7Solving Equations 5.8Applications and Problem Solving

OBJECTIVES 5.8 Applications and Problem Solving Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aTranslate key phrases to algebraic expressions. bSolve applied problems involving decimals.

5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To translate problems to equations, we need to be able to translate phrases to algebraic expressions. Certain key words in phrases help direct the translation.

5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. It is helpful to choose a descriptive variable to represent the unknown. For example, w suggests weight and g suggests the number of gallons of gasoline.

Title 5.8 Applications and Problem Solving Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Use a specific number in the statement before translating using the variable. Write down what each variable represents. Check the translation with another number to see if it matches the phrase. Be especially careful with order when subtracting and dividing.

EXAMPLE 5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. 2 Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Translate each phrase to an algebraic expression. a) Than’s age increased by six b) Half of some number c) Twice the cost d) Seven more than twice the weight e) Fifteen divided by a number f) A number divided by fifteen g) Six less than the product of two numbers h) Nine times the sum of two numbers

EXAMPLE 5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. 2 Slide 12 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.8 Applications and Problem Solving a Translate key phrases to algebraic expressions. 2 Slide 13 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 4Medicine. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A 100-unit syringe is often used by diabetics and nurses to administer insulin. Each unit on the syringe represents 0.01 cc (cubic centimeter). Each day, Wendy averages 42 units of insulin. How many cc’s will Wendy use in a typical week? 1. Familiarize. We let a = the amount of insulin used.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 4Medicine. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate. 3. Solve.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 4Medicine. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. We can obtain a partial check by rounding and estimating: 5. State. Wendy uses 2.94 cc’s of insulin in a typical week.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 5Student Loans. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Upon graduation from college, Eric must repay a loan that totals $12,267. The loan is to be paid back over 5 yr in equal monthly payments. Find the amount of each payment.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 5Student Loans. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let the size of each monthly payment. To find the number of payments, we determine how many months there are in 5 yr. (We could also find the amount paid per year and divide that number by 12.) 2. Translate. To find the amount of the monthly payment, we note that the amount owed is split up, or divided, into payments of equal size. To find the number of payments, we determine that in 5 yr there are 60 months.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 5Student Loans. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

EXAMPLE 4. Check. We first find how much is repaid each year: We then divide this amount by 12: 5. State. Eric’s monthly payments will be $ Applications and Problem Solving b Solve applied problems involving decimals. 5Student Loans. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Title 5.8 Applications and Problem Solving Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In any circle, a diameter is a segment that passes through the center of the circle with endpoints on the circle. A radius is a segment with one endpoint on the center and the other endpoint on the circle. The area, A, of a circle with radius of length r is given by Where The length r of a radius of a circle is half the length d of a diameter:

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 7 Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The Northfield Tap and Die Company stamps 6-cm-wide discs out of metal squares that are 6 cm by 6 cm. How much metal remains after the disc has been punched out?

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 7 Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We make, and label, a drawing. We let a = the amount of metal remaining, in square centimeters, and list the relevant formulas.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 7 Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 7 Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 7 Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve. 4. Check. We can repeat our calculation as a check. Note that 7.74 is less than the area of the disc, which in turn is less than the area of the square. This agrees with the impression given by our drawing. 5. State. The amount of material left over is 7.74 cm 2.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 9Multi-sport Recreation. Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Around the Bend Expeditions offers a 2-day canyon trip combining biking and canoeing. Those participating will ride mountain bikes for 12 miles longer than the distance paddled. The total length of the trip is 43 miles. How long is the biking portion of the trip, and how long is the canoeing portion of the trip?

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 9Multi-sport Recreation. Slide 28Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We first list the quantities we are asked to find: Length of biking portion, in miles Length of canoeing portion, in miles. We will want to represent both quantities using only one variable. To do so, we use the second sentence in the problem:

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 9Multi-sport Recreation. Slide 29Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Those participating will ride mountain bikes for 12 miles longer than the distance paddled. Since the biking portion of the trip is described in terms of the canoeing portion, we let x = the length of the canoeing portion, in miles. Then the length of the biking portion, also in miles, is x Length of biking portion, in miles: x Length of canoeing portion, in miles: x + 12.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 9Multi-sport Recreation. Slide 30Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 9Multi-sport Recreation. Slide 31Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

EXAMPLE 5.8 Applications and Problem Solving b Solve applied problems involving decimals. 9Multi-sport Recreation. Slide 32Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. There are two statements in the problem to verify. First since 27.5 – 15.5 = 12, the biking portion is 12 miles longer than the canoeing portion. Second, since = 43, the total length of the trip is 43 miles. 5. State. The biking portion of the trip is 27.5 miles, and the canoeing portion is 15.5 miles.