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Learn about "Invert and Multiply" method for dividing whole numbers by fractions, using visual representations and conceptual understanding. Explore how to apply this method and differentiate between memorization and conceptualization.
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Dr. Rena Gibbs Amy Edmundson Fractions “the whole story”
Let’s say we want to divide a whole number by a fraction. For example… ÷
÷ This is a visual representation of the first part of our equation “seven wholes”.
÷ This is a visual representation of the number 7 divided by .
÷ So this division problem is really asking us “How many ‘1/3rds’ can we ‘fit’ into the seven wholes?”
÷ = 21 So because twenty-one “1/3rds” fit into seven wholes.
We can verify this result in many ways, but the most common way taught in schools is to “invert and multiply”: ÷ is equivalent to x = 21 Because fits in each “whole” three times. We have seven “wholes” that we multiply by the three that fit into each whole x = 21 and 7 times 3 is 21, therefore
÷ = ● • “Copy, dot, flip” OR “there are three rds in each whole”. • So how do we build this conceptual understanding? • By starting at the beginning… Memorization vs. conceptualization
Let’s say we want to do this math problem Using a 100’s Chart to combine unlike units(finding common denominators) +
+ = or 1 +
> This same data can be used to determine that