Page 121 - Basic College Mathematics with Early Integers

98 C HAPTE R 1 I THE WHOLE NUMBERS

Definitions and Concepts Examples

Section 1.8 An Introduction to Problem Solving

PROBLEM-SOLVING STEPS Suppose that 225 tickets are sold for each performance of
a play. How many tickets are sold for 5 performances?
1. UNDERSTAND the problem. 1. UNDERSTAND. Read and reread the problem. Since
we want the number of tickets for 5 performances, we
multiply.
2. TRANSLATE the problem. 2. TRANSLATE.

number number tickets
of is of times per
tickets performances performance

∂ ∂ ∂ ∂

Number
of = 5 # 225
tickets

3. SOLVE the problem. 3. SOLVE: See if the answer is reasonable by also
estimating.
1 2
225 rounds to 200
* 5 * 5
1125 exact 1000 estimate
4. INTERPRET the results. 4. INTERPRET. Check your work.The product is
reasonable since 1125 is close to our estimated
answer of 1000, and state your conclusion:There are
1125 tickets sold for 5 performances.

Section 1.9 Exponents, Square Roots, and Order of Operations

An exponent is a shorthand notation for repeated exponent
multiplication of the same factor. 4
3 =3 3 3 3=81
# # #
A square root of a number is one of two identical base 4 factors of 3
factors of the number.
#
236 = 6 because 6 6 = 36
#
ORDER OF OPERATIONS 2121 = 11 because 11 11 = 121
#
20 = 0 because 0 0 = 0
1. Perform all operations within parentheses ( ), 2
brackets [ ], or other grouping symbols such as square 5 + 3
Simplify:
roots or fraction bars, starting with the innermost set. 217 - 62
2. Evaluate any expressions with exponents. Simplify above and below the fraction bar separately.
3. Multiply or divide in order from left to right. 2
5 + 3 5 + 9 Evaluate 3 2 above the fraction bar.
4. Add or subtract in order from left to right. =
217 - 62 2112 Subtract: 7 - 6 below the fraction bar.
14
= Add.
2 Multiply.
= 7 Divide.
Find the area of a square with side length 9 inches. Copyright 2012 Pearson Education, Inc.
2
The area of a square is 1side2 . Area of the square = 1side2 2
2
= 19 inches2
= 81 square inches