Fraction Division (With Models) Page 3
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1
2
3
4Fraction Division
To divide two fractions, problem solvers multiply the first fraction by the
®
reciprocal of the second fraction. In the Everyday Mathematics
program,
this is called the Division of Fractions Property, and it is based on several
mathematical rules regarding fractions and the reciprocal relationship
between multiplication and division.
Build Understanding
Review finding reciprocals. Remind students that they need to rename
whole numbers and mixed numbers as fractions before they can find their
1 __
1 __
2 __
3 __
reciprocals. Ask students to find the reciprocal of
(3), 7 (
), 2
(
), and
3
7
3
8
5 __
6 __
1 __
(
, or 1
).
6
5
5
1 __
3 __
÷
Using the example
, walk students through the steps below so that
6
2
they understand why the Division of Fractions Property works.
1 __
3 __
1 __
2 __
÷
=
×
• Multiply the first fraction by the
6
2
6
3
reciprocal of the second fraction.
2 ___
1 __
=
• Simplify as needed.
, or
18
9
3 __
÷ 11 to explain the division of mixed numbers.
Use the example 2
4
3 __
11
11
___
___
÷ 11 =
÷
• Change any whole number or mixed
2
4
4
1
number to an improper fraction.
___
11
1 ___
=
×
• Multiply the first fraction by the
4
11
reciprocal of the second fraction.
11
1 __
___
=
=
• Simplify as needed.
44
4
Error Alert
Watch for students who use incorrect reciprocals or just change
the problem from division to multiplication without using reciprocals. You may
want to have students write and label the reciprocal of each divisor before they
begin each problem.
Check Understanding
Page 81
Answer Key
Divide the class into groups of 3 or 4 and assign a leader in each group to
explain the steps in the examples. Tell group members to direct their questions
2 _
1.
3
to their group leader. When you are reasonably certain that most of your
students understand the algorithm, assign the “Check Your Understanding ”
1 _
2.
exercises at the bottom of page 81. (See answers in margin.)
6
3. 16
1 _
4.
6
2 _
5.
9
6. 6
7. 15
1 _
8. 1
2
Teacher Notes
80
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