CHAPTER 1 – Whole Numbers and Integers Instructor: Dr.Gehan Shanmuganathan

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Learning Outcomes Read whole numbers. Write whole numbers. Round whole numbers. Read and round integers. 1-1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Read whole numbers Our system of numbers, the decimal number system uses 10 symbols called digits: –0,1, 2, 3, 4, 5, 6, 7, 8, and 9. Place-value system: a number system that determines the value of a digit by its position in a number. Place Value and Our Number SystemSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Read whole numbers Beginning with the ones place on the right, the digits are grouped with three digits in each group. –For example: 286,418,917 Each group is called a period. Place Value and Our Number SystemSection 1-1 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Understanding place value Each period has a name and a ones place, a tens place, and a hundreds place. In a number, the first period from the left may have fewer than three digits. In many cultures, the periods are separated by commas. Place Value and Our Number SystemSection 1-1 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Understanding place value Identify the period name of the leftmost group. Read the three digit number from left to right. Name the period. 4,693,107 would read four million six hundred ninety-three thousand one hundred seven. Place Value and Our Number SystemSection 1-1 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Exceptions… Do not read or name a period that is all zeros. 34,000,892 would read thirty-four million, eight hundred ninety-two. Do not name the units period (892). 000,892 34, Place Value and Our Number SystemSection 1-1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved When reading whole numbers, remember… The period name will be read at each comma. Period names are read in the singular: –(“thousand” not “thousands”). Hundreds is not a period name. Do not say the word “and” when reading whole numbers. Calculator displays ordinarily do not show commas; insert them when writing the number. Place Value and Our Number SystemSection 1-1 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Write whole numbers Begin recording digits from left to right. Insert a comma at each period name. Every period after the first period must have three digits. Insert zeros as necessary. Place Value and Our Number SystemSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved An Example… Eight million, nine hundred three thousand, four hundred twenty-two… …is written 8,903,422. 8,million 903, thousand 422 (units) Place Value and Our Number SystemSection 1-1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Round whole numbers Rounding to a specific place: –Identify the place. “nearest hundred”, for example. –Look at the digit immediately to the right. Is it 5 or higher? Round up. Is it 4 or lower? Specified digit stays the same. –All digits to the right of the specified place become zeros. Place Value and Our Number SystemSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Examples… Round to the nearest hundred: 4,856 10, ,567 8,648, ,600 4,900 10,500 8,648,100 Place Value and Our Number SystemSection 1-1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Key Terms… Addends –The numbers being added. Sum or total –The answer or result of addition. Place Value and Our Number SystemSection 1-1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Key Terms… Commutative property of addition –Two or more numbers can be added in either order without changing the sum. Example: = = 11 Associative property of addition –When more than two numbers are being added, the addends can be grouped by two at a time in any way. Example: 5 + (2 + 1) = (5 + 2) + 1 = 8 Place Value and Our Number SystemSection 1-1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Read and round integers In the business world we sometimes want to express numbers that are smaller than 0. –These are referred to as negative numbers. When the set of whole numbers is expanded to include negative numbers, this set is called the set of integers. Place Value and Our Number SystemSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Read and round integers When reading integers: –The rules are the same as for reading whole numbers. State the word negative or minus to read a number less than zero. When rounding integers: –The rules are the same as for rounding whole numbers. Place Value and Our Number SystemSection 1-1 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved An Example… Read the number for the U.S. national debt: - $11,936,042,802,503 Negative eleven trillion, nine hundred thirty-six billion, forty-two million, eight hundred two thousand, five hundred three dollars. Place Value and Our Number SystemSection 1-1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved An Example… Round the previous example to the nearest trillion: The answer is -$12 trillion. Place Value and Our Number SystemSection 1-1 -$11,936,042,802,503 The trillions digit is 1. -$11,936,042,802,503 The digit to the right is 9. 9 is more than 5, so increase the 1, by 1, to get 2. Replace all digits to the right of 2 with zeros. -$12,000,000,000,000

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Learning Outcomes Add and subtract whole numbers. Add and subtract integers. Multiply and divide integers. Apply the standard order of operations. to a series of operations. 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Add and subtract whole numbers To add whole numbers, write the numbers in a vertical column, aligning digits according to their place values. –Beginning with the ones column, add the place digits. –Add, if necessary, to the tens column. Repeat the operation, adding to the hundreds column, if necessary, until you have reached the farthest column of digits to the left. Operations With Whole Numbers and IntegersSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Add the ones column. –Place 8 at the bottom of the ones column. –Carry the 2 to the tens column. Place the 4 in the tens column. –Carry the 2. Finish the operation __ 99 = Operations with Whole Numbers and IntegersSection 1-2 An Example… 2211 Answer: 64,948 Add

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Estimating Estimate: to find a reasonable approximate answer for a calculation. –Use estimating as a quick tool when an exact number is not required. Round whole numbers to the place desired for an estimate. Operations with Whole Numbers and IntegersSection 1-2 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved What was the week’s total to the nearest hundred? $200 + $900 + $500 + $600 + $1000 = $3,200 Sales for last week’s concession stand. Monday: $219 Tuesday:$877 Wednesday:$455 Thursday:$614 Friday:$980 An Example… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Subtract whole numbers When subtracting whole numbers, the order of the numbers is important. –Therefore, subtraction is not commutative. 9 – 4 ≠ 4 – 9 Grouping in subtraction is important. –Subtraction is not associative. (8 - 3) -1 = 5 – 1 = 4 but 8 - (3 -1) = = 6 4 ≠ 6 Operations with Whole Numbers and IntegersSection 1-2 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Minuend –The beginning amount or number that a second number is being subtracted from. Subtrahend –The number being subtracted. Difference –The answer or result of subtracting. Borrow –Regroup digits in the minuend by borrowing 1 from the digit to the left of the specified place, and adding 10 to the specified place. Key Terms… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 18 Subtract Borrow 1 from the ten column, add 10 to the ones column. –Subtract 8 from 13. Borrow 1 from the hundreds column, add 10 to the tens column. –Subtract 9 from 18. Borrow 1 from the thousands column. –Subtract 5 from = An Example… Operations with Whole Numbers and IntegersSection Answer: 695

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Subtract 128 from 1,345 by rounding each number to the nearest hundred to estimate the difference. –128 would become 100. –1,345 would become 1,300. The estimated difference would be 1,200. Using rounding in subtraction Operations with Whole Numbers and IntegersSection 1-2 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved To add two negative integers, add the numbers without regard to the signs. –Assign a negative to the sum. Last year Murphy’s Used Car Co. lost $23,000. This year they lost another $16,000. What is the total loss? -$23,000 + (-$16,000) = -$39,000 The two-year loss is -$39,000. Add and subtract integers Operations with Whole Numbers and IntegersSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved To add a positive and a negative integer, subtract the numbers without regard to the signs. Look at the numbers without the signs. –Choose the larger of these numbers; Assign the sum the sign of the larger number. Add and subtract integers Operations with Whole Numbers and IntegersSection 1-2 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Jeremy has a bank balance of $47, then writes a check for $89. What is the new balance, including a $30 overdraft fee? $47 + (-$89) = -$42 -$42 + (-$30) = -$72 The final balance is -$72. An Example… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Numbers can be multiplied in any order without affecting the result –Commutative property of multiplication. 8 x 12 = 12 x 8 96 = 96 Multiply whole numbers Operations with Whole Numbers and IntegersSection 1-2 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Multiplicand –The number being multiplied. Multiplier –The number multiplied by. Factor –Each number involved in multiplication. Key Terms… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Product –The answer or result of multiplication. Partial product –The product of one digit of the multiplier and the entire multiplicand. Key Terms… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Multiply 79 x _ 1817 Multiplicand Multiplier Partial product PRODUCT Partial product An Example… Operations with Whole Numbers and IntegersSection 1-2 1

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 418 x 107 = ? Answer: 44, x 120 = ? Answer: 10, x 27 = ? Answer: 9,396 Examples to try without a calculator… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved To multiply a negative and a positive integer, multiply the two integers without regard to the signs. –Assign a negative sign to the product. What is the total loss generated from selling 87 frames each for $2 below cost? 87 x (-$2) = -$174 The total loss is -$174. Multiply integers Operations with Whole Numbers and IntegersSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved To multiply two negative or two positive integers, multiply the two integers without regard to the signs. –The product is positive. What is the product of (-16)(-3)? 16 x 3 = 48 The product is positive and is 48. Multiply integers Operations with Whole Numbers and IntegersSection 1-2 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Division is used to find the number of equal parts into which a whole quantity can be separated. A $40 tip is shared equally among 5 servers. How much does each server receive? $40 ÷ 5 servers = $8 each. Divide integers Operations with Whole Numbers and IntegersSection

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Dividend –The number being divided or the total quantity. Divisor –The number to divide by. Quotient –The answer or result of the operation. Whole-number part of the quotient –The quotient without regard to its remainder. Key Terms… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Remainder of quotient –A number that is smaller than the divisor that remains after division is complete. Partial dividend –The part of the dividend that is being considered at a given step of the process. Partial quotient –The quotient of the partial dividend and the divisor. Key Terms… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved There will be a remainder if an amount is too small to be further divided by the divisor. –For example: 152 ÷ 3 = 50 R 2 That amount may be expressed as… –A remainder (R 2). –A fraction. –A decimal. Remainders Operations with Whole Numbers and IntegersSection 1-2 HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved –Is it 1?No. –Is it 12? Yes. –5 goes into 12 two times. Place the 2 above the 2 in the dividend. STEP 1 Beginning with its leftmost digit, identify the first group of digits of the dividend that is larger than or equal to the divisor ÷ 5 = ? Divide integers Operations with Whole Numbers and IntegersSection 1-2 HOW TO: MORE

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved STEP 2 Multiply 2 by the divisor. Place 10 under the 12 and subtract. The result is 2. STEP 3 Bring down the following digit which is 3, and divide 5 into 23. STEP 4 The result is 4. Place the 4 directly above the 3 in the dividend. Divide integers Operations with Whole Numbers and IntegersSection ÷ 5 = ? HOW TO: MORE

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved STEP 5 Multiply 4 by the divisor. Place 20 under the 23 and subtract. The result is 3. STEP 6 Bring down the last digit, which is 5, and divide 5 into 35. The result is 7. STEP 7 Place 7 directly above the 5. You have finished and the answer is 247. Divide integers Operations with Whole Numbers and IntegersSection ÷ 5 = ? HOW TO:

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved Adams-Duke Realty Company estimates that its losses for the year will be $36,000,000. What is the average loss per month? Answer: -$3,000,000 Divide the following: 63,500,000 ÷ 1,000 (mentally eliminate the ending zeros from both numbers) Answer: 63,500 Examples to try without a calculator… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved STEP 1 Perform all operations that are inside grouping symbols, such as parentheses. STEP 2 Perform all multiplications and divisions as they appear from left to right. STEP 3 Perform all additions and subtractions as they appear from left to right. Apply the standard order of operations to a series of operations Operations with Whole Numbers and Integers Section 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved 15 – (4 + 7) = ? Answer: 4 ( ) ÷ 5 = ? Answer: x 9 = ? Answer: 9 Examples to try… Operations with Whole Numbers and IntegersSection 1-2

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved EXERCISES SET A

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved PRACTICE TEST

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ All Rights Reserved