CHAPTER 2 Fractions Instructor Dr Gehan Shanmuganathan 2

CHAPTER 2 – Fractions Instructor: Dr. Gehan Shanmuganathan

2 -1 Learning Outcomes n Identify types of fractions. n Convert an improper fraction to a whole or mixed number. n Convert a whole or mixed number to an improper fraction. n Reduce a fraction to lowest terms. n Raise a fraction to higher terms. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Identify types of fractions 2 -1 -1 Section 2 -1 Fractions n A fraction is used to identify parts of a whole. – It describes the relationship between the part and the whole. n There are four parts. – One is shaded white, or 1 in 4 which is Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel . © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms… Section 2 -1 Fractions n Denominator – The number appearing below the fraction line. n Numerator – The number appearing above the fraction line. n Fraction line – Horizontal line separating numerator and denominator. n Proper fraction – A fraction with a value less than “ 1” (ex. , Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel ) © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Look at the fraction HOW TO: Section 2 -1 Fractions 2 is the numerator. 3 is the denominator. Is it a proper fraction? Yes, because the value of the fraction is less than “ 1”. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Identify the fraction Section 2 -1 Fractions What part of the area is shaded blue? MORE Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Identify the fraction Section 2 -1 Fractions What part of the area is shaded blue? Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Improper fraction HOW TO: Section 2 -1 Fractions n The numerator is greater than or equal to the denominator. – Therefore the fraction is greater than or equal to “ 1”. Proper or improper? Improper Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel Proper Improper © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Convert an improper fraction to a whole or mixed number 2 -1 -2 Section 2 -1 Fractions n Divide the numerator of the improper fraction by the denominator. – If the remainder is zero, the quotient is a whole number. – If the remainder is not zero, the improper fraction will be expressed as a mixed number. Examples = 12 Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel = = © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Convert a whole or mixed number to an improper fraction 2 -1 -3 Section 2 -1 Fractions n Multiply the denominator of the mixed number by the whole number part. n Add the product from the previous step to the numerator of the mixed number. – This is the numerator of the improper fraction. n Use the denominator of the mixed number as the denominator of the improper fraction. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

An Example… Section 2 -1 Fractions Convert 10 to an improper fraction. The numerator of the fraction is 3. Multiply the whole number—which is 10—by the denominator—which is 4. The result is 40. Add the numerator to the product: 40 + 3 = 43. Retain the same denominator. The improper fraction equivalent is Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Reduce a fraction to lowest terms 2 -1 -4 Section 2 -1 Fractions n Inspect the numerator and denominator to find any whole number by which both can be evenly divided. – Carry out the operation until there is no one number that both can be evenly divided by. TIP: Check if the denominator can be divided by the numerator: Example: can be reduced to Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel when 3 is divided into 15. © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Reduce these examples to the lowest terms… Section 2 -1 Fractions = TIP: Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel = denominator can = Check if the be divided by the numerator: © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Find the greatest common divisor of two numbers Section 2 -1 Fractions n The most direct way to reduce a fraction to lowest terms is to use the GCD. – The GCD is the largest number by which the denominator and numerator can be evenly divided. Example: Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel The GCD of 15 and 20 is 5. Any number greater than 5 would result in a quotient with a remainder © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the GCD HOW TO: Section 2 -1 Fractions Find the GCD of 42 and 28. Divide the larger number by the smaller number: 42 divided by 28 = 1 R 14 Divide the divisor (28) by the remainder of the previous operation: (14) 28 14 = 2 R 0. When the R = 0, the divisor from that operation (14, in this case) is the GCD. More Examples: Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel 30, 36 30, 125 17, 51 GCD = 6 GCD = 5 GCD = 17 © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Raise a fraction to higher terms 2 -1 -5 Section 2 -1 Fractions is equal to 8/4=2 Divide the two denominators. “ 4” goes into “ 8” two (2) times. Multiply “ 3” by “ 2” to get the equivalent numerator. Multiply “ 4” by “ 2” to get the equivalent denominator. 2 = 2 Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Examples… Section 2 -1 Fractions Determine the equivalent fraction in higher terms: = = = Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

2 -2 Learning Outcomes n Add fractions with like (common) denominators. n Find the least common denominator for two or more fractions. n Add fractions and mixed numbers. n Subtract fractions and mixed numbers. . Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Add Fractions with like (common) denominators 2 -2 -1 Section 2 -2 Adding and Subtracting Fractions n Add the numerators. n The denominator remains the same. n If necessary, convert an improper fraction to a mixed number. + Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel + = or © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the least common denominator for two or more fractions 2 -2 -2 Section 2 -2 Adding and Subtracting Fractions n Adding fractions with different denominators. – First find the least common denominator (LCD). n The LCD is the smallest number that can be divided evenly by each original denominator. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the least common denominator for two or more fractions Section 2 -2 Adding and Subtracting Fractions n The common denominator can sometimes be found by inspection. – Mentally selecting a number that can be evenly divided by each denominator. Find the LCD for: Convert and to an equivalent fraction in eighths, Then add the two fractions together. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the least common denominator for two or more fractions Section 2 -2 Adding and Subtracting Fractions n It is not as apparent which number might be the LCD, given different denominators. – Such as 12 and 30. TIP: You can use prime numbers to find the LCD. A prime number is a number greater than 1 that can be divided evenly by only itself and 1. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Find the least common denominator for two or more fractions Section 2 -2 Adding and Subtracting Fractions STEP 1 Write the denominators in a row. STEP 2 Divide each one by the smallest prime number by which any of the numbers can be evenly divided. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel MORE © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Find the least common denominator for two or more fractions Section 2 -2 Adding and Subtracting Fractions STEP 3 Write a new row of numbers using: 1. The quotients from step 1. 2. Any numbers in the first row that cannot be evenly divided by the first prime number. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel MORE © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Find the least common denominator for two or more fractions Section 2 -2 Adding and Subtracting Fractions STEP 4 Divide again by the smallest prime number by which any of the numbers can be evenly divided. STEP 5 Continue this process until you have a row of 1 s. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel MORE © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Find the least common denominator for two or more fractions Section 2 -2 Adding and Subtracting Fractions STEP 6 Multiply all the prime numbers used to divide the denominators. The product is the least common denominator. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the least common denominator for two or more fractions HOW TO: Section 2 -2 Adding and Subtracting Fractions Denominators Add the fractions: , , Multiply the prime numbers from the first column (2 x 2 x 5) to get the LCD. MORE The LCD is 40 Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel Prime numbers First, find the LCD 5 2 8 2 5 1 4 2 5 1 2 2 5 1 1 1 © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the least common denominator for two or more fractions HOW TO: Section 2 -2 Adding and Subtracting Fractions Denominators Add the fractions: , , 5 The LCD is 40 Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel Prime numbers MORE 8 becomes The LCD is 40 Convert the fractions to the equivalent using 40 as the denominator. 2 2 5 1 4 2 becomes 5 1 2 2 5 becomes 1 1 5 1 1 1 © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Find the least common denominator for two or more fractions HOW TO: Section 2 -2 Adding and Subtracting Fractions Add the fractions: , , = + + = If the numerator is greater than. Inspect the denominator, the fraction ittois an improper and determine if itfraction is expressed can be expressed as a in lowest terms. mixed number. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

2 -2 -3 Adding fractions and mixed numbers Section 2 -2 Adding and Subtracting Fractions n Add the whole-number parts. n Add the fraction parts and reduce to lowest terms. n Change improper fractions to whole or mixed numbers. n Add the whole-number parts. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Subtracting mixed numbers 2 -2 -4 Section 2 -2 Adding and Subtracting Fractions STEP 1 – = Convert the fraction portion of each mixed number to equivalent fractions. STEP 2 -1 – – Borrow “ 1” from the whole number = to carry out the operation. = Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel Reduce to lowest terms, if necessary. © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Subtracting fractions with like denominators HOW TO: Section 2 -2 Adding and Subtracting Fractions Subtract the smaller numerator from the greater one—the denominator remains the same. – = = Reduce to lowest terms, if necessary. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Subtracting fractions with different denominators HOW TO: Section 2 -2 Adding and Subtracting Fractions n As in addition, to subtract fractions you must have a common denominator. – Use the same methods of inspection or prime numbers to determine the LCD. n Carry out the operation. – Reduce to lowest terms as needed. – Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel =? MORE © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Subtracting fractions with different denominators HOW TO: Section 2 -2 Adding and Subtracting Fractions Find the LCD, which is 12. Change = to an equivalent fraction. Carry out the operation and reduce to lowest terms, – if = needed. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel ? – = © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Examples… Section 2 -2 Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel Adding and Subtracting Fractions – = – = © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Examples… Section 2 -2 Maria has her recipe. Adding and Subtracting Fractions cups of flour, but only needs cups for How much will she have left? Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Examples… Section 2 -2 Adding and Subtracting Fractions Julia needs Bob brought her a yards of tape to finish a display. yard piece from the supply room. How much will be left? Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

2 -3 Learning Outcomes n Multiply fractions and mixed numbers. n Divide fractions and mixed numbers. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Multiply fractions and mixed numbers 2 -3 -1 Section 2 -3 Multiplying and Dividing Fractions n To multiply two fractions: – Find the numerator of the product by multiplying the numerators of the fractions. – Find the denominator of the product by multiplying the denominators of the fractions. – Reduce to lowest terms, if needed. x Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel 1 x 7= 7 3 x 8 = 24 Can this fraction be reduced further? NO! © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Multiply fractions and mixed numbers Section 2 -3 Multiplying and Dividing Fractions TIP: To keep things simple, if possible, reduce before multiplying. x =? The 3 in the denominator in the first fraction and the 3 in the numerator in the second fraction cancel each other out and become 1. x Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Multiply mixed numbers and whole numbers Section 2 -3 Multiplying and Dividing Fractions n Write the mixed numbers and whole numbers as improper fractions. n Reduce numerators and denominators as appropriate. n Multiply the fractions. n Reduce to lowest terms and/or write as a whole number or mixed number. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

An Example… Section 2 -3 Multiplying and Dividing Fractions x =? = = x The “ 3” can be reduced to “ 1” and the “ 15” to “ 5” before multiplying. 25 = 4 Product: Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel Convert to a mixed number: © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Products and factors Section 2 -3 Multiplying and Dividing Fractions Are products always larger than their factors? No. When the multiplier is a proper fraction, the product is less than the original number. This is also true when the multiplicand is a whole number, fraction or mixed number. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel 5 x x =3 = © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Divide fractions and mixed numbers 2 -3 -2 Section 2 -3 Multiplying and Dividing Fractions n The relationship between multiplying and dividing fractions involves a concept called reciprocals. – Two numbers are reciprocals if their product equals 1. 2 is the reciprocal of What is the reciprocal of ? The reciprocal is 3 Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

HOW TO: Divide fractions or mixed numbers Section 2 -3 Multiplying and Dividing Fractions n Write the numbers as fractions. n Find the reciprocal of the divisor. n Multiply the dividend by the reciprocal of the divisor. n Reduce to lowest terms, and/or write as a whole or mixed number. Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Divide fractions or mixed numbers HOW TO: Section 2 -3 Multiplying and Dividing Fractions ÷ =? Convert to an improper fraction: Change to its reciprocal, which is: Change from division to multiplication. x = Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel x = © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Example… Section 2 -3 Multiplying and Dividing Fractions Madison Duke makes appliqués. A customer has ordered five appliqués. Madison has of a yard of fabric, and each appliqué uses Does she need more fabric? ÷ becomes The answer is Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel x 6 Simplify by dividing 4 and 6 by 2 x 3 She can only make 4 appliqués, and she needs more fabric. © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Example… Section 2 -3 Multiplying and Dividing Fractions A home goods store is stacking decorative boxes on shelves. Each box is inches tall. The shelf space is 45 inches. How many boxes will fit on each shelf? Six Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

EXERCISES SET A Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

PRACTICE TEST Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

PRACTICE TEST Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

PRACTICE TEST Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

PRACTICE TEST Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

PRACTICE TEST Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Business Math, Ninth Edition Cheryl Cleaves, Margie Hobbs & Jeffrey Nobel © 2012 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved