Proper fractions - PowerPoint PPT Presentation

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Proper fractions

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Proper fractions. The value of the numerator is less than the value of ... fractions ... Adding and subtracting fractions. 1/2 1/3. Multiplying fractions. Repeated ... – PowerPoint PPT presentation

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Title: Proper fractions


1
Proper fractions
  • The value of the numerator is less than the value
    of the denominator.
  • Proper in this case does not mean correct or best.

2
Improper fractions
  • The value of the numerator is greater than or
    equal to the value of the denominator.

3
Mixed numbers
  • Meaning of

4
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.

5
Write mixed number as improper fraction and vice
versa
6
Operations with fractions
  • Addition
  • Subtraction
  • Multiplication
  • Division

7
Adding and subtracting fractions
8
1/2 1/3
9
Multiplying fractions
  • Repeated addition model
  • Area model

10
Multiplication of fractions
  • Fraction as operator
  • The multiplication algorithm is best explained by
    the area model.

11
2/3 of 2 1/2
12
Mixed number times mixed number
13
Dividing fractions
  • Division of fractions is most easily understood
    as repeated subtraction.

14
11 divided by 1 1/2
15
Multiplicative Inverses
  • We know that division is the inverse of
    multiplication.

16
Multiplicative inverses
  • The multiplicative inverse of a is 1/a
  • The multiplicative inverse of a/b is b/a

17
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.

18
Exploration 5.12
  • Drawn to scale
  • Part 1 Use reasoning not algorithms to answer 1
  • Part 2 Choose a model from the list that was not
    represented in the problems and make up a story
    problem using the fraction ¾. Are there any
    models that are not possible with fractions?
    Explain.

19
Operations with fractions
  • Addition
  • Subtraction

20
(No Transcript)
21
Operations with fractions
  • Multiplication

22
Operations with fractions
  • Division

23
Exploration 5.13
  • Begin in class and finish for homework 5.13
    Part 1 2-7 Part 2 Choose one of the models
    from the list that was not illustrated in the
    problems in Part 1 and write a story problem
    using the fraction ¾. Also, are there any models
    that are not possible with fractions? Explain.
  • Homework problems from the textbook
  • pp. 303-305 3b,d,e,f, 13, 21, 22, 25
  • Note that in 3, you should not use algorithms
    to calculate the result use reasoning to decide
    the answer to the question.

24
Extra Practice
  • 1. You have from 1000 - 1130 to do a project.
    At 11, what fraction of time remains? At 1120,
    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.

25
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.

26
Extra Practice
  • 3. If a/b 3/4, will the value of (a x)/(b
    x) be less than, equal to, or greater than 3/4.
  • Use a diagram to explain how you know. Are there
    certain diagrams that are more effective?
    Discuss this with your group.

27
Exploration 5.14
  • Read the directions carefully and do 1
  • Discuss with your partner
  • Do 2
  • Discuss with your partner
  • Do 3

28
Homework for Wednesday
  • Exploration 5.14
  • Read section 5.3 in your textbook
  • Do problems pp. 305-307 30, 31, 33, 36, 41,
    44a,c,d,h,k, 45a, 48
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