1. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals A2 E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals The Algebra of Rational Numbers KFUPM - Prep Year Math Program (c) 2009 All Right Reserved  Algebraic Operations  Least Common Denominator  Properties of Rational Numbers

2. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Algebraic Operations Prime Numbers A prime number is a natural numbers p > 1 that can not be written as product of two natural numbers other than one or itself. Otherwise p is called a composite number. For example, the natural numbers 2, 3, 5, 7, 11, 13, 19 ………. are prime, while the natural numbers 4, 6, 8, 10, 12, 14, 16, 18, …..… are composite. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

3. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Algebraic Operations Prime Factorization Every non-zero integer n can be written uniquely as a product of the form (prime factorization) where u=±1 and p 1 …….p r are prime factors of n. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Equivalent Fraction Two rational numbers a/b and c/d are equivalent if there is an integer n≠0 such that

4. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) b). c). d). KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 1 Find the prime factorization of the following numbers.

5. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) b). c).. KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 2 Find four equivalents to each given reduced rational numbers.

6. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Algebraic Operations KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

7. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) b). c). d). KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 3 Perform the indicated operation and write the answer in reduced form.

8. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Least Common Denominator (LCD) The least common denominator of two fractions a/b and c/d is an integer N such that both b and d divide N, and N is the least possible such integer. That is, there are two integers s and r such that N = bs and N = dr and N is the least such integer. In this case we have KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

9. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 4 Find the least common denominator of each of the following sets of fractions. Factor all the denominators into their prime factorizations

10. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 4 Find the least common denominator of each of the following sets of fractions. Factor all the denominators into their prime factorizations b)

11. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Properties of Rational Numbers KFUPM - Prep Year Math Program (c) 2009 All Right Reserved

12. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) b) c). d). KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 5 Give the fractional and decimal representation of each of the percentages.

13. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals a) b) c). d). KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 6 Give the percentage representation of each of the numbers.

14. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals KFUPM - Prep Year Math Program (c) 2009 All Right Reserved Example 9 a) Find the 12% of 98. b) What percentage is 54 of 450? b) a)

15. E - BOOK FOR COLLEGE ALGEBRA King Fahd University of Petroleum & Minerals Challenge KFUPM - Prep Year Math Program (c) 2009 All Right Reserved