Proper fractions
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Transcript of Proper fractions
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Proper fractionsThe value of the numerator is less than the value of the denominator.
Proper in this case does not mean correct or best.
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Improper fractions
The value of the numerator is greater than or equal to the value of the denominator.
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What do we mean by the term unit fraction?
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Unit FractionsUnit fractions are fractions whose numerator
is 1:
1 1 1 1 1
2 7 24 100 8
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Operations with fractions• Addition
• Subtraction
• Multiplication
• Division
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Adding and subtracting fractions
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1/2 + 1/3
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Mixed numbers• Meaning of
325
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Writing mixed numbers as improper fractions
The algorithm that is taught in schools obscures the meaning. This is true for many algorithms, which are “efficient” ways of carrying out operations.
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Write mixed number as improper fraction and vice versa
312
423
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Multiplying fractions
• Repeated addition model
• Area model
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Multiplication of fractions
• Fraction as operator
• The multiplication algorithm is best explained by the area model.
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Use an area model to multiply1/2 by 5/7
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Multiply 2 1/3 by 1 5/6
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Dividing fractions• Division of fractions is most easily
understood as repeated subtraction.
212
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12 ÷ ½
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11 divided by 1 1/2
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Multiplicative Inverses• We know that division is the inverse of
multiplication.
52110
5210
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Multiplicative inverses• The multiplicative
inverse of a is 1/a
• The multiplicative inverse of a/b is b/a
11
aa
1ab
ba
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Dividing fractions
Because division is the inverse operation of multiplication, dividing a number by a fraction is equivalent to multiplying the number by the multiplicative inverse, called the reciprocal, of the fraction.
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Exploration 5.12
• “Drawn to scale”• Part 1 Use reasoning not algorithms to
answer #1• Part 2 Write justifications for the following:
– #1: 3, 6, 8, 13, 16– #2: 1, 2, 7, 8, 9, 13, 15, 16
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Worksheet: Dividing Fractions
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Problems
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Extra Practice• 1. You have from 10:00 - 11:30 to do a project. At
11, what fraction of time remains? At 11:20, what fraction of time remains?
• Use a diagram to explain how you know. Are there certain diagrams that are more effective? Discuss this with your group.
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Extra Practice
• 2. Is 10/13 closer to 1/2 or 1? • Use a diagram to explain how you know.
Are there certain diagrams that are more effective? Discuss this with your group.