Math Concepts Explained Through Fractions and Reciprocals
Explore the concepts of fractions, reciprocals, and their relationships through interactive exercises and insightful explanations. Understand how to find reciprocals, convert between fractions, and grasp the significance of these mathematical principles. Discover key insights and challenges related to reciprocals in this engaging educational content.
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Presentation Transcript
On your whiteboards: ? ? ? 4 1 12 12 5 8 3 3 ?= 4= 5= 8= Fill in the blanks ? ? ? ? 4 9 2 3 3 2 ? 5 1 2 1 ? ?? 1 1
Observation and conclusion If the numerator and denominator of two fractions are inverted, then their product is 1. ? ? ? ?= 1 We say that one is the reciprocal of the other.
Match the pairs 3 9 6 2 5 7 12 5 2 12 7 3 4 4 3 3 5 2 1 6 4 10
True or False 1. If the product of number A and B is 1, then A is the reciprocal of B. T T 2. If C is the reciprocal of D, then the product of C and D is 1. F The reciprocal of 23 5 is 25 3. 3. F 4. Each number has a reciprocal. 5. No number has a reciprocal which is exactly itself. F
On your whiteboards Find the reciprocal of the following fractions 3 7 5 1) : : : 4 2 6 Invert the numerator and denominator 4 : 11 Change integer a to a/1 first 2)3: 4: 15: 1: 0: Change a mixed fraction to improper fraction 3 4 1 2 5 6 4 3)1 : 3 : 1 : 2 : 11
Reflection In your books, write: Reciprocal Definition Reciprocal of a fraction Reciprocal of an integer Reciprocal of a mixed fraction
Some other conclusions Zero does not have a reciprocal because no real number multiplied by 0 produces 1(the product of any number with zero is zero) The only number that has a reciprocal that is itself is 1.
Challenge: Find the reciprocal of the following fractions 1 3 1 1 2 3 3 1 1 4 1 3 3 9
