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- 1. I.E.S. MARÍA BELLIDO - BAILÉN 1º E.S.O. BILINGUAL SECTION – MARÍA ESTHER DE LA ROSA UNIT 1. INTEGERS 1. INTEGERS • Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed! The number line goes on forever in both directions. This is indicated by the arrows. • Whole numbers greater than zero are called positive integers. These numbers are to the right of zero on the number line. • Whole numbers less than zero are called negative integers. These numbers are to the left of zero on the number line. • So, integers can be negative {-1, -2,-3, -4, -5, … }, positive {1, 2, 3, 4, 5, … }, or zero {0} The integer zero is neutral. It is neither positive nor negative. • Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line. One will have a positive sign, the other a negative sign. In the number line above, +3 and - 3 are labeled as opposites. • We can put that all together like this: Z = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
- 2. 2. COMPARING INTEGERS We can compare two different integers by looking at their positions on the number line. For any two different places on the number line, the integer on the right is greater than the integer on the left. Note that every positive integer is greater than any negative integer. Examples: 9>4 6 > -9 -2 > -8 0 > -5 3. OPERATIONS WITH INTEGERS 1. Adding Integers • When adding integers of the same sign, we add their absolute values, and give the result the same sign. Examples: 2+5=7 (-7) + (-2) = -(7 + 2) = -9 • When adding integers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the integer with the larger absolute value. Example: 8 + (-3) = + 5 8 + (-17) = -9 2. Subtracting Integers • Subtracting an integer is the same as adding its opposite. Examples: 7 - 4 = 7 + (-4) = 3 12 - (-5) = 12 + (5) = 17 -8 - 7 = -8 + (-7) = -15
- 3. 3. Multiplying Integers Rules for Multiplication Positive x Positive Positive Positive x Negative Negative Negative x Positive Negative Negative x Negative Positive • Like signs yield a positive result. • Unlike signs yield a negative result. • If one or both of the integers is 0, the product is 0. Examples: 4 × 3 = 12 (-4) × (-5) = 20 (-7) × 6 = - 42 12 × (-2) = -24. 4. Dividing Integers The rules for division are exactly the same as those for multiplication. If we were to take the rules for multiplication and change the multiplication signs to division signs, we would have an accurate set of rules for division. Examples: 4÷2=2 (-24) ÷ (-3) = 8 (-100) ÷ 25 = -4

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