MATH 1000 /11 Chapter Symbols and Set of Numbers 1.3 Fractions

MATH100/05/ Dr. H. Melikyan Sets A set is collection of objects, each of which is called a member or element of the set. Notation: A pair of brace symbols { } encloses the list of elements is a the set of elements containing that set of elements.

Sets of numbers Natural numbers – {1, 2, 3, 4, 5, 6...} Whole numbers – {0, 1, 2, 3, 4...} Integers – {... –3, -2, -1, 0, 1, 2, 3...} Rational numbers – the set of all numbers that can be expressed as a quotient of integers, with denominator  0 Irrational numbers – the set of all numbers that can NOT be expressed as a quotient of integers Real numbers – the set of all rational and irrational numbers combined

A Number Line used to represent ordered real numbers has negative numbers to the left of 0 and positive numbers to the right of 0. Order Property for Real Numbers indicates how to use inequality signs. If a and b are real numbers, a < b means a is to the left of b on a number line. a > b means a is to the right of b on a number line. Absolute value of a number is the distance of that number away from 0.  a  0, since distances are non-negative. | -7 | = 7, |- 0.13| = 0.13, | 3| = 3.

MATH100/05/ Dr. H. Melikyan Section 1.3 Fraction is a quotient of two numbers. Numerator is the top number. Denominator is the bottom number. Simplifying fractions (lowest terms) Involves factoring numerator and denominator into prime numbers (natural numbers other than 1 whose only factors are 1 and itself : 2, 3, 5, 7, 13, 37 …). A natural number bigger 1, that is not prime is called Composite number ( 15, 21, 1222)

MATH100/05/ Dr. H. Melikyan Fundamental Principle of Fractions Can cancel common factors in numerator and denominator. If a, b, c are real numbers such that b and c  0.

MATH100/05/ Dr. H. Melikyan Example Simplify the following fractions. Since there are no common terms, the fraction is already simplified.

MATH100/05/ Dr. H. Melikyan Multiplying fractions Multiply numerators and denominators. Dividing fractions Invert the divisor fraction (the reciprocal of divisor ). Then multiply the fractions. b, d  0 b, d, c  0

MATH100/05/ Dr. H. Melikyan Adding and subtracting fractions Required to have the same denominator. Have to change fractions to equivalent ones until they have same denominator. Then combine the numerators, denominator will be the common denominator. b  0

MATH100/05/ Dr. H. Melikyan Example Add the following fractions. Subtract the following fractions.

MATH100/05/ Dr. H. Melikyan