Transcript pp5.3FractionsPart2

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.
Improper fractions
• The value of the numerator is greater than
or equal to the value of the denominator.
Mixed numbers
• Meaning of
2
5
3
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.
Write mixed number as improper
fraction and vice versa
2 13
23
4
Operations with fractions
• Addition
• Subtraction
• Multiplication
• Division
Adding and subtracting fractions
1/2 + 1/3
Multiplying fractions
• Repeated addition model
• Area model
Multiplication of fractions
• Fraction as operator
• The multiplication algorithm is best
explained by the area model.
2/3 of 2 1/2
Mixed number times mixed
number
Dividing fractions
• Division of fractions is most easily
understood as repeated subtraction.
12  2
11 divided by 1 1/2
Multiplicative Inverses
• We know that division is the inverse of
multiplication.
10  2  5
1
10   5
2
Multiplicative inverses
• The multiplicative
inverse of a is 1/a
• The multiplicative
inverse of a/b is b/a
1
a 1
a
a b
 1
b a
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.
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.
Operations with fractions
• Addition
• Subtraction
Operations with fractions
• Multiplication
Operations with fractions
• Division
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.
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.
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.
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.
Exploration 5.14
•
•
•
•
•
Read the directions carefully and do #1
Discuss with your partner
Do #2
Discuss with your partner
Do # 3
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