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Unformatted text preview: Math 110 Placement Exam Solutions FRACTION ARITHMETIC 1. Find the sum. 1 2 + 1 3 Solution Convert to a common denominator. Then add numerators. 1 2 + 1 3 = 3 6 + 2 6 = 3 + 2 6 = 5 6 Google Help: addition of fractions 2. Find the difference. 1 2 2 3 Solution Convert to a common denominator. Then subtract numerators. 1 2 2 3 = 3 6 4 6 = 3 4 6 = 1 6 = 1 6 Google Help: subtraction of fractions 3. Find the difference. 3 1 2 1 2 3 Solution Convert the mixed numbers to fractions. Convert to a common denominator. Then subtract numerators. Convert to a mixed number. 3 1 2 1 2 3 = 7 2 5 3 = 21 6 10 6 = 21 10 6 = 11 6 = 1 5 6 Google Help: subtraction of mixed numbers 4. Find the product. 3 1 2 1 2 3 Solution Convert the mixed numbers to fractions. Compute the product by multiplying numerators and multiplying denominators. Convert to a mixed number. 3 1 2 1 2 3 = 7 2 5 3 = 7 5 2 3 = 35 6 = 5 5 6 Google Help: product of fractions and product of mixed numbers 5. Find the quotient. 6 1 2 1 1 4 Solution Convert the mixed numbers to fractions. Compute the quotient by multiplying the first number by the reciprocal of the second. Convert to a mixed number. 6 1 2 1 1 4 = 13 2 5 4 = 13 2 4 5 = 52 10 = 26 5 = 5 1 5 Google Help: division of fractions and division of mixed numbers WORKING WITH POLYNOMIAL EXPRESSIONS 6. Simplify the expression 2(9 x ) (2 x + 1). Solution Use the distributive property to write 2(9 x ) as 18 2 x . Then 2(9 x ) (2 x + 1) = 18 2 x 2 x 1. Collect like terms and simplify to get the final answer. 18 2 x 2 x 1 = (18 1) + ( 2 x 2 x ) = 17 4 x Google Help: distributive property and addition of polynomials 7. Simplify (4 x 3 2 x 2 + 1) (2 x 3 + x 3). Solution Use the distributive property to remove the parentheses, collect like terms, and simplify. (4 x 3 2 x 2 + 1) (2 x 3 + x 3) = 4 x 3 2 x 2 + 1 2 x 3 x + 3 = (4 x 3 2 x 3 ) 2 x 2 x + (1 + 3) = 2 x 3 2 x 2 x + 4 Google Help: subtraction of polynomials 8. Find the product (3 x + 5)(4 x 7). Solution Take each term inside the first set of parentheses times each term inside the second set of parentheses. (3 x + 5)(4 x 7) = 3 x 4 x + 3 x ( 7) + 5 4 x + 5 ( 7) Multiply out each of the terms, collect like terms, and simplify. 3 x 4 x + 3 x ( 7) + 5 4 x + 5 ( 7) = 12 x 2 21 x + 20 x 35 = 12 x 2 x 35 Google Help: multiplication of polynomials 9. Find the product 3 y 3 (4 y + 3)( y 2)....
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This note was uploaded on 10/24/2011 for the course MATH 110 taught by Professor Staff during the Fall '08 term at BYU.
 Fall '08
 Staff
 Addition, Fractions

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