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MPM2D – MATHEMATICS REVIEW – PART 1 A. OPERATIONS (ADDITION, SUBTRACTION, MULTIPLICATION, DIVIDION) WITH INTEGERS Integers are all the numbers that are positive and negative. I = { ... , –3, –2, –1, 0, +1, +2, +3, ... } 1. Addition: - if the signs are the same, then the sum has the same sign as well Ex. (12) (5) 17 (7) (5) 12 - if the signs are different, then the sum takes the sign of the larger number Ex. (18) (5) 13 (7) (2) 5 2. Subtraction: - add the opposite Ex. (15) (8) 15 8 7 3. Multiplication and Division: - if the two integers have the same sign, the answer is + (positive) Ex. (6) (8) 48 (6) (5) 30 - if the two integers have different signs, the answer is – (negative) Ex. (12) (2) 6 (18) (2) 9 4. BEDMAS (Order of Operations) B E D M A S brackets () exponents X2 division / multiplication x addition + subtraction - Ex. 8 (4) 4 2 2 8 4 4 2 2 8 4 4 4 2 1 1 B. OPERATIONS WITH RATIONAL NUMBERS Rational Numbers are numbers that can be written as fractions. a Q = a , b, , b 0 b a “The set of all numbers such that b a, b are integers, and b 0 ” 1. Addition and Subtraction: - to add or subtract fractions, you need to find a common denominator - add or subtract numerators, denominator stays the same - then reduce to lowest terms - if you have a mixed fraction, you need to first change it to an improper fraction and then find a common denominator, add or subtract, and reduce to lowest terms 3 1 4 3 Ex.1 3 1 5 2 Ex.2 9 4 12 12 6 5 10 10 13 12 1 10 2. Multiplication: - multiply the numerators and then multiply the denominators - reduce to lowest terms - if it is a mixed fraction, you need to first change it to an improper fraction a c ac b d bd Ex. 2 4 8 3 5 15 3. Division: - multiply by the reciprocal - reduce to lowest terms - if it is a mixed fraction, you need to first change it to an improper fraction a c a d b d b c Ex. 2 4 2 5 3 5 3 4 ad bc 10 12 4. Changing a Mixed Fraction to an Improper Fraction: - multiply the whole number by the denominator - add the numerator - put this over the denominator Ex.1 2 3 5 13 5 Ex.2 7 3 7 52 7