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MPM1DE – Review 565328971 Date: _________________________ Number Sets and Integers Symbol Name Definition Natural Numbers The counting numbers starting from 1. Whole Numbers All the natural numbers and 0. Integers All the whole numbers and their opposites. Rational Numbers Irrational Numbers Numbers that can be written as a fraction whose denominator is not 0. In decimal form, rational numbers terminate or repeat. Numbers that cannot be written as a fraction. In decimal form, irrational numbers do not terminate or repeat. Real Numbers All rational and irrational numbers. Imaginary Numbers The result of square-rooting a negative number. Page 1 of 6 Examples MPM1DE – Review 565328971 Integers Numbers like +5, -7 and -10 are called integers. These numbers are used to show direction above or below some zero point. Integers can be shown on a number line: When two integers are compared on a number line, the integer to the right is the greater one. When comparing two values, we used specific language and symbols. For example, since +3 is to the right of -4, we say “+3 is greater than -4” and we write 3 4 . We can also say “-4 is less than +3” and write 4 3 . Note: A positive integer can be written without the + sign. However, a negative integer must always be written with the – sign. Here’s a list of the symbols that we use when comparing two values: Symbol Description Greater than Less than Equal to Not equal to Greater than or equal to Less than or equal to Opposite Integers - integers with the same "number" but have different signs. Every integer, except 0, has an opposite. Examples: Page 2 of 6 MPM1DE – Review 565328971 Adding and Subtracting Integers On a number line, think of positive integers as trips to the right and negative integers as trips to the left. Evaluate 2 3 8 5 . To subtract an integer, you must add its opposite. Evaluate 3 6 2 . We can evaluate expressions like the ones above without using a number line. Just replace all the double signs with single signs, and then add or subtract from left to right. Remember the following rules: Two positives make a positive. Two negatives make a positive. A positive and a negative make a negative. Addition Evaluate. a) 7 2 b) 5 3 e) 5 3 f) Subtraction Evaluate a) 8 3 b) 5 7 e) 5 11 f) 10 2 34 c) 4 6 d) 8 1 g) 7 3 h) 8 4 c) 1 6 d) 10 4 g) 3 7 h) 3 9 Page 3 of 6 MPM1DE – Review 565328971 Multiplying and Dividing Integers We can use the same rules as above to multiply and divide integers. Examples Evaluate the following expressions. a) ( 3)( 4) b) ( 6) ( 4) 3 c) 11(2) d) ( 10) 5 e) ( 12) / ( 3) f) Page 4 of 6 20( 3) ( 6)( 2) MPM1DE – Review 565328971 Integers – Addition and Subtraction To be completed without a calculator. 1. Find each sum. a) 3 2 _____ b) 8 8 _____ c) 4 5 _____ d) 5 7 _____ e) 9 2 _____ f) 4 6 _____ g) 8 4 _____ h) 5 ( 5) _____ i) 43 _____ 2. Find each difference. a) 4 ( 3) _____ b) 5 ( 2) _____ c) 6 ( 6) _____ d) 4 (4) _____ e) 7 ( 8) _____ f) 7 (3) _____ g) 4 ( 7) _____ h) 4 3 _____ i) 4 ( 7) _____ 3. Simplify. a) 5 ( 3) 4 c) b) 4 ( 3) 5 6 4 3 d) 4 7 5 4. Which choice would make each statement true: >, <, =? a) 3 4 5 3 _____ 4 3 1 ( 2) b) 4 7 6 8 _____ 3 5 ( 7) 4 c) 5 13 7 2 _____ 4 5 ( 3) 5 d) 7 3 ( 15) 11 ___ 7 3 ( 11) 15 5. In each row, which expression has the greatest value? The least value? a) 5 3 4, 4 3 ( 4), 5 ( 3) 10 b) 9 ( 2) 7, 5 ( 7) ( 9), 5 3 6 Page 5 of 6 MPM1DE – Review 565328971 Integers – Multiplication and Division To be completed without a calculator. 1. Find each product. a) (3)(2) b) ( 4)( 9) c) (4)(3) d) (5)(4) e) 4(9) f) a) 2 ( 7) b) 3(8) c) 5(7) d) 5(7) e) ( 3)( 7) f) (2)(7) 4(9) 2. Simplify. 3. Find each quotient. a) 18 ( 6) b) 51 ( 17) c) 18 (18) d) 60 ( 12) 4. Simplify. a) 50 5 b) 15 5 c) 48 6 d) 16 16 e) 18 9 f) 81 27 5. Evaluate. a) (4) 2 b) 2 4 c) 3 3 Page 6 of 6 d) (2) 5