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MPM 1DX Unit 1 Day 3 Rational Numbers Simple Definition: A rational number is a number that can be written as a fraction. 1 2 Examples: , - , 5, 0, … 3 4 All natural numbers (N) are rational. All whole numbers (W) are rational. All integers (I) are rational. These numbers plus the rational numbers make up the REAL numbers Mathematical Definition: A rational number is any number that can be written in the m form where m and n are both integers but n cannot be zero. n Set builder notation: Q = mn m, n I, n 0 Note: Integers are rational numbers, but rational numbers are not necessarily integers. Examples: a) - 3 _________ b) 2 5 _______________ Which of the following are rationals? a) 1 -5 d) 0.125 b) 3 1 2 e) -5.41 c) -0.1 . f) 0. 3 All integers and terminating or repeating decimals are rational numbers. Any number that cannot be written as a terminating or repeating decimal is an irrational number. Examples: π , 2 MPM 1DX Unit 1 Day 3 1. Express three rational numbers equivalent to each of the following. a) - 4 5 c) - -3 7 2. List in order from smallest to largest. - 3 1 -4 , , 5 -3 3 b) - 2 1 4 -2- MPM 1DX Unit 1 Day 3 Operations with Rational Numbers 1. Addition and Subtraction - convert mixed fractions to improper - write each fraction with a single sign - determine a common denominator - write equivalent fractions - add or subtract the numerators only - reduce fractions to lowest terms Evaluate. 7 1 a) 10 10 d) 2 5 9 6 b) 1 2 2 3 3 5 e) 8 4 2 1 c) 4 1 3 2 1 1 f) 5 3 2 3 -3- MPM 1DX Unit 1 Day 3 2. Multiplication - convert mixed fractions to improper - write each fraction with a single sign - multiply numerators together, then denominators (or reduce if possible) - reduce fractions to lowest terms Evaluate. 3 1 a) 4 2 d) 2 3 1 5 7 b) 1 4 8 5 c) 4 3 7 5 2 9 3 5 e) 2 3 4 5 6 3. Division - convert mixed fractions to improper - write each fraction with a single sign - invert the second fraction and change the divide sign to multiply - multiply numerators together, then denominators (or reduce if possible) - reduce fractions to lowest terms Evaluate. 2 4 a) 3 5 1 3 b) 10 4 2 5 -4-