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Finding Opposites and Absolute Value 2.1 Maduwuba Ugochukwu G-Hour January 7, 2013
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The Real Number Line and Opposites • Two points that are the same distance from 0 or the origin but on opposite sides of the origin are opposites. • The numbers used throughout the world are real numbers for they can be pictured as points on a horizontal line called a realRemember that all numbers that number line. The point can be shown on a number line labeled 0 is the origin. are real numbers. So decimals, Points to the left of zero fractions, ratios, and whole represent negative numbers and points to the right ofnumbers are all real numbers and zero represent positive can be shown on a real number numbers. line.
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Numbers to the right of zero are positive numbers. Basically all real numbers can beshown on a real number line for a real number line continues on forever just like any line so, it never stops. Extend the line to the right to include positive numbers.
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Finding the opposite of a Number• The numbers -3 and 3 are opposites because each is 3 units from the origin. Any negative number can be referred to as negative and the number. So the expression negative and a number three can be stated as “ negative 3”. You can also call it the opposite of 3.
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The Absolute Value• The absolute value of a real number is the distance between the origin and the point representing the real number.• The symbol of the|x|represents the absolute value of a number x.• If x is a positive number, then |x| = x.• |8| = 8• If x is zero, then |x| = 0.• |0| = 0• If x is a negative number the |-x| = x.• |-8| = 8
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The AbsoluteValue • Lets try some examples!!!continued 1. |8.5| = 8.5The absolute value of a number If x is positive, then |x| = x.with a negative in front of theabsolute value symbol requires 8.5 is 8.5 units from zero the origin.certain steps to get the answer. 2. |-5/8| = -(-5/8) = 5/8-|x| when x is 91st- plug in the number. If x is negative, then |x| = -x. - |9|2nd- take the absolute value of -5/8 is 5/8 units from the origin.the number inside the absolute 3. -|-39| = -(39)value symbol. Forget about thenegative for now. The absolute value of -39 is 39. Nine is nine units away fromthe origin so, the absolute = -39value of 9 is 9. 3rd-Then take the absolute Use the definition of opposites.value and then do the opposite The absolute value was 39 and theof it. The opposite of 9 isnegative 9. There is your opposite of 39 is -39.answer!.
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Absolute Value and Opposites• The opposite of 5 is -5. • The symbol for absolute value• The opposite of -2 is 2. is two vertical lines (bars)• *all you need to do in order to around the number. get the opposite of a number • * Absolute value is the is to reverse the sign of an distance from 0 on a number integer. Integers are numbers line… that can be written without a • DISTANCE IS POSITIVE!! fractional or decimal • Opposites and absolute value component, and fall within the are different. set {..., -3,−2, −1, 0, 1, 2, 3, ...}. • Opposite means reverse the The word opposite can be sign replaced by a negative sign. The opposite of -4. –(-4) *Two • Absolute value means remove negatives make a positive. the sign• 4 is your answer. • * Did you know absolute value cannot be negative
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Now You’ve Got it!!! • Opposites• Absolute Value • When opposite numbers are added, it gives zero.• Now you have got • To get the opposite of a the hang of Absolute number, change the sign. value. Absolute • The absolute values of value is distance opposite numbers are the away from zero. If same. • The opposite numbers are you follow the rules equidistant from 0 on a in this presentation number line. then you will have • + 25 and – 25 are opposite success when finding numbers. absolute value. • - 8 is the opposite number of + 8.
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