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Understanding Absolute Value, Additive Inverses, and Reciprocals in Mathematics

This guide explores three fundamental concepts in mathematics: Absolute Value, Additive Inverses, and Reciprocals. We define absolute value as the distance a number is from zero, illustrated with examples like |5| = 5 and |-5| = 5. Additive inverses are opposites, demonstrated by how adding pairs like -4.7 and 4.7 yields zero. Lastly, we look at reciprocals, showing how to "flip" a number to find its reciprocal, ensuring that the product of a number and its reciprocal equals one. Mastering these concepts is crucial for mathematical proficiency.

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Understanding Absolute Value, Additive Inverses, and Reciprocals in Mathematics

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  1. Absolute Value, Additive Inverses and Reciprocals

  2. Absolute Value • The distance a number is from zero on the number line. • | | is the symbol for absolute value. • Both 5 and -5 are the same number of units away from zero……….5 • What about this one? This is read as ‘the negative of’ the absolute value of 5.

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  4. Additive Inverses are OPPOSITES. Find the additive inverse of -4.7 Find the additive inverse of -73 Find the additive inverse of 7/8 4.7 73 -7/8 Additive Inverses -4.7 + 4.7 = 0 -73 + 73 = 0 7/8 + -7/8 = 0 When added together, additive inverses produce a sum of ZERO.

  5. To find the reciprocal of any number simply “flip” it over. Find the reciprocal of the following. Reciprocals Whole numbers have a denominator of ONE. To find the reciprocal first change this to an improper fraction. When multiplied together, reciprocals produce a product of ONE.

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