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Welcome to Brainfuse
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When the value of a fraction's numerator is less than the value of its denominator, we're working with
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a proper fraction. So 3/7 onscreen is an example of a
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proper fraction.
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But what about its reciprocal?
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That is the number we multiply
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3/7 by to equal 1, and that would be
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7/3.
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When the value in the numerator is greater than the value in the denominator, then we're working with
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an improper fraction.
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Improper fractions can also be converted to mixed numbers.
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That often helps us picture the values that they represent.
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So let's say
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We
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need 7/3 cups of water for a recipe
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I'll go ahead and attempt to draw a measuring cup split into thirds to help us do that.
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Okay, here is the beautiful rectangular measuring cup
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Since it is improper we know that we'll need more than one, so I'll copy it a few times.
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Okay now let's fill it with water
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Filling just one part would be 1/3 of a cup
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This would be 2/3 of a cup
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And 3/3 is equal to 1 cup
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But there's more to go
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Here's 4/3
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5/3
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6/3. Okay, we've hit 2 cups.
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And then finally 7/3, so this cup is not complete.
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Only 1/3 of it is filled.
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So our 7/3 cups is also equal to 2 and 1/3 cups
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Delete this proper fraction to make it clear
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As you can see a mixed number consists of
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A whole number
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Or integer
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Plus a proper fraction
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That's the incomplete part of the whole
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Instead of drawing we can also treat the improper fraction as a division problem and
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just divide 7 / 3.
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I'll move it over so we have some room to do that and don't bump into the measuring cup.
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3 goes into 7, 2 times because 3 times 2 is 6 and that leaves us with the remainder of 1
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Out of the next three parts
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So by dividing the numerator by the denominator we converted
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An improper fraction to a mixed number.
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In the next lesson, we'll go in reverse.
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So as you work with mixed numbers, think of how you can convert them back into improper fractions. Thanks.