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Unformatted text preview: e to academic life and beyond…
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College entrance exam and science high school entrance test tips. Conquer UPCAT, ACET, USTET,
DLSUCET, PSHSNCE, and other entrance tests.
Division of monomials. A quotient of two monomials can be simplified, if a dividend and a divisor have some
powers of the same letters or numerical coefficients. In this case an exponent of the power in a divisor is
subtracted from an exponent of the power in a dividend; a numerical coefficient of a dividend is divided by a
numerical coefficient of a divisor.
Example:
35 a 4 x 3 z 9 : 7 a x 2 z 6 = 5 a 3 x z 3 .
Polynomial is an algebraic sum of monomials. Degree of polynomial is the most of degrees of monomials,
forming this polynomial.
Multiplication of sums and polynomials: a product of the sum of two or some expressions by any expression
is equal to the sum of the products of each of the addends by this expression:
( p+ q+ r ) a = pa+ qa+ ra  opening of brackets. Instead of the letters p, q, r, a any expressions can be taken.
Example:
( x+ y+ z )( a+ b )= x( a+ b )+ y( a+ b ) + z( a+ b ) =
= xa + xb + ya + yb + za + zb .
A product of sums is equal to the sum of all possible products of each addend of one sum to each addend of the
other sum. Algebraic fractions
Algebraic fraction is an expression of a shape A / B, where A and B can be a number, a monomial, a
polynomial. As in arithmetic, A is called a numerator, B – a denominator. Arithmetical fraction is a particular
case of an algebraic one.
Canceling fractions
Example: Math I  21  Feel free to pass this on to your friends, but please don’t post it online.
Discuss UPCAT and other college entrance exam questions and answers at AcademicClinic’s
Facebook Page. We encourage you to answer the questions we post there and actively participate in
the discussions on our wall.
For UPCAT, ACET, DLSUCET and USTET tips, tricks, news and other college entrance exam
information, visit the AcademicClinic website. Tell your friends and classmates to come find and join
us. The more, the merrier. Good luck! AcademicAcademic
AcademicClinic.com
The achiever’s guide to academic life and beyond…
W ebsite: http://academicclinic.com
Facebook: http://www.facebook.com/academic.clinic
Twitter: http://twitter.com/acadclinic
College entrance exam and science high school entrance test tips. Conquer UPCAT, ACET, USTET,
DLSUCET, PSHSNCE, and other entrance tests. Addition and subtraction of fractions To add or to subtract two or some fractions it is necessary to make the same operations as in arithmetic.
Example: Multiplication and division of fractions
Multiplication and division of algebraic fractions doesn’t differ from the same operations in arithmetic.
Canceling a fraction can be done both before and after multiplication of numerators and denominators.
Example: Math I  22  Feel free to pass this on to your friends, but please don’t post it online.
Discuss UPCAT and other college entrance exam questions and answers at AcademicClinic’s
Facebook Page. We encourage you to answer the questions we post there and actively participate in
the discussions on our wall.
For UPCAT, ACET, DLSUCET and USTET tips, tricks, news and other college entrance exam
information, visit the AcademicClinic website. Tell your friends and classmates to come find and join
us. The more, the merrier. Good luck!...
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This note was uploaded on 07/21/2013 for the course UPCAT 2014 taught by Professor Otis during the Spring '13 term at University of the Philippines Diliman.
 Spring '13
 OTIS

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