Basic Mathematics for College Students

106. POPULATION To find the population densityof a
     state, divide its population by its land area (in square
     miles). The result is the number of people per square
     mile. Use the data in the table to approximate the
     population density for each state.
     109. DIVISIBILTY TEST FOR 7 Use the following rule
     to show that 308 is divisible by 7. Show each of the
     steps of your solution in writing.
     Subtract twice the units digit from the
     number formed by the remaining digits. If
     that result is divisible by 7, then the original
     number is divisible by 7.
     110. DIVISIBILTY TEST FOR 11 Use the following
     rule to show that 1,848 is divisible by 11. Show each
     of the steps of your solution in writing.
     Start with the digit in the one’s place. From
     it, subtract the digit in the ten’s place. To that
     result, add the digit in the hundred’s place.
     From that result, subtract the digit in the
     thousands place, and so on. If the final result
     is a number divisible by 11, the original
     number is divisible by 11.

REVIEW

111. Add:


112. Subtract:


113. Multiply:


114. DISCOUNTS A car, originally priced at $17,550, is
     being sold for $13,970. By how many dollars has the
     price been decreased?

2,903 378

2,903 378

2,903 378

68 Chapter 1 Whole Numbers

2008 Land area*

State Population* (square miles)

Arizona 6,384,000 114,000

Oklahoma 3,657,000 69,000

Rhode Island 1,100,000 1,000

South Carolina 4,500,000 30,000

Source: Wikipedia *approximation

WRITING

107. Explain how can be calculated by repeated
     subtraction.


108. Explain why division of 0 is possible, but division by
     0 is impossible.

24  6

SECTION 1.6

Problem Solving

Objectives

1 Apply the steps of a problem-

solving strategy.

2 Solve problems requiring more

than one operation.

3 Recognize unimportant

information in application

problems.

The operations of addition, subtraction, multiplication, and division are powerful

tools that can be used to solve a wide variety of real-world problems.

Apply the steps of a problem-solving strategy.

To become a good problem solver, you need a plan to follow, such as the following

five-step strategy.

1

Strategy for Problem Solving

1. Analyze the problemby reading it carefully. What information is given?
   What are you asked to find? What vocabulary is given? Often, a diagram
   or table will help you visualize the facts of the problem.


2. Form a planby translating the words of the problem to numbers and
   symbols.


3. Solve the problem by performing the calculations.


4. State the conclusionclearly. Be sure to include the units (such as feet,
   seconds, or pounds) in your answer.


5. Check the result.An estimate is often helpful to see whether an answer is
   reasonable.