Transcript Slide 1 - Sage Middle School

Division of Fractions
In this lesson we will be looking at the concept of
division of fractions. This will include the division
of complex fractions, improper fractions, fractions
without whole numbers and fractions with whole
Numbers or mixed numbers.
Division Symbols
• Remember that Math is a language. Therefore
the symbols that we use have meaning. The
following symbols all mean divide by or
represent division.
•
x
y x
x
y
•
y
Hint: All of these division symbols are read as x
divided by y. The variables x and y can
represent any number.
Whole Numbers
• Whole numbers are the numbers beginning
with zero and moving to the right . They do
not include negative numbers. They are not
fractions.
Fraction
• Fraction: The comparison of a part to a whole.
•¼
Complex Fraction
• A fraction in which either the numerator,
denominator, or both contain fractions.
½
¾
2
Denominator ¾
Numerator
½
3
Improper Fraction
• A fraction in which the numerator is greater
than the denominator.
12
4
Hint: 12/4 is equal to 3 wholes. The different
ways to express fractions are representing the
same amounts in different forms.
Mixed Numbers
• A mixed number is a whole number and a
fraction expressed together.
1 whole
1/4
• 1 ¼
1/4
1/4
• Hint: as an improper fraction this would be
5/4.
Story problem
• Maren ordered 4 bags of soil for her raised
flower gardens. Each garden needs threefourths (3/4) of a bag of soil. How many
gardens can she fill completely with soil?
¼ bag
soil
1/3 of a
garden
• Think Pair Share
A bag will complete one garden
and a third of another. Can you
express how many gardens 4
Bags will cover in terms of
Gardens. Can you express how
Much soil is left over in terms of
bags.
Traditional approach
• 4 bags of soil divided by ¾ or the amount
needed to complete one garden.
•
•
•
•
•
Step 1:
4
¾ =
Step 2
4 X 4/3 = 16/3
Step 3 = 5 1/3 gardens.
Questions
• How do we divide by soil and end up
answering in gardens using the traditional
approach?
• Why do we invert and multiply in the standard
algorith?
• Hint remember when we Think Pair Shared?
What did that model reveal.
•Further Questions
• Build a ratio table comparing garden to soil to
show why the standard algorithm works.
• Use a number line to show why the standard
algorithm works.
To get you started
• Ratio Table
Garden
Soil
1
3/4
Number Line Model
Bags
0
3/4
1
1
1 1/3
Lawns
Practice Problems
Solve using the traditional method
and one model
• Jenny is making brownies. It takes 2/3 of a bag of
flour to make one batch of brownies. Jenny has 5
bags of flour. How many batches of brownies can
she make?
Practice Problems continued
Solve using the traditional method
3
5
¼ =
4/3 =
2
3/8 =
6
5/6 =
1 2/3
5 6/3 =