Dividing Fractions – Part I
Opening Question
How many 4’s are there in 12? When we are dividing, we are finding the number of
________ groups that there are in a number. Circle groups of 4 stars below.
*There are _________ equal groups of 4 in 12.
Another way to think about this problem is by finding out how many times 4 can be
subtracted from 12. Show how many times you can subtract 4 from 12, below.
Four (4) can be subtracted from 12 __________ times.
Building Fractions
If the yellow hexagon represents one whole, use the pattern blocks to determine how many of
each shape would be needed to make one whole, or a hexagon.
Table 1
hexagon = one whole
____ trapezoids = one whole
____ rhombi = one whole
____ triangles = one whole
Write the fraction that the pattern block is of the one whole.
1 whole
____ of the whole
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____ of the whole
_____ of the whole
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Dividing Fractions
Using what you learned about the pattern blocks in Building Fractions, answer the following
questions.
1) a) Look at your drawing of the trapezoids in Table 1. How many trapezoids are there in 1
hexagon (whole)? _________
b) So, a ℎ𝑒𝑥𝑎𝑔𝑜𝑛 1 ÷ by a 𝑡𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑
!
!
is equal to ____________________.
!
c) Using math, 1 ÷ ! = _______.
2) a) Look at your drawing of the rhombi in Table 1. How many rhombi are there in 1 hexagon
(whole)? _________
b) So, a ℎ𝑒𝑥𝑎𝑔𝑜𝑛 ÷ by a 𝑟ℎ𝑜𝑚𝑏𝑢𝑠 is equal to ____________________.
!
c) Using math, 1 ÷ ! = ________. 3) a) Look at your drawing of the triangles in Table 1. How many triangles are there in 1
hexagon (whole)? _________
b) So, a ℎ𝑒𝑥𝑎𝑔𝑜𝑛 ÷ by a 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 is equal to ____________________.
!
c) Using math, 1 ÷ ! = ________. Dividing a Whole Number by a Fraction
Instead of asking the question “How many equal triangle pieces fit into the whole hexagon?”
another way we could ask this question is “How many sixths
rectangle as one whole, the problem would look like:
𝟏
𝟔
are there in 1?” Using a
!
4) For 4 ÷ !:
a) Write the problem in words: How many _________ are there in ________?
!
b) Using a rectangle, show 4 ÷ !:
c) There are _______ halves in 4.
!
d) Math: 4 ÷ ! = ______.
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!
5) For 8 ÷ !:
a) Write the problem in words: How many _________ are there in ________?
!
b) Use rectangle(s) to show 8 ÷ !:
c) There are _______ fourths in 8.
!
d) Math: 8 ÷ ! = _______.
!
6) For 6 ÷ !:
a) Write the problem in words: How many _________ are there in ________?
!
b) Using a rectangle, show 6 ÷ !:
c) There are _______ thirds in 6.
!
d) Math: 6 ÷ ! = _____.
Practice
Use rectangle(s) to solve questions 7 – 10.
!
7) 5 ÷ ! =
!
8) 9 ÷ ! =
9) How many thirds of a cup are in two cups?
10) Jaime baked 6 large cookies and there are 24 students in the class. How should she divide
up the cookies so that each student receives an equal piece?
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Dividing Fractions – Part II
Opening Prompt
A) How many groups of 4 are there in 2; 2 ÷ 4 ? ___________
B) Why is it difficult to ask, “how many groups of 4 are there in 2?” Support your reasoning
with a picture.
C) What about 12 ÷ 4? Does it make sense to ask, “I have 12 stars and need to make 4 equal
groups. How many are in each group?” Draw a picture to represent the statement.
If 12 stars are shared equally among 4 groups, each group has _________.
Dividing a Fraction by a Whole Number
1) I have 2 cookies and need to make 4 equal groups. How many in each group? (You have
four children who all want a piece of cookie!  )
Each child will get _______ of a cookie.
2) From problem 1, the math is 2 cookies ÷ 4 children, which means that when the 2 cookies
(the whole amount) are shared equally amongst the 4 children and each child receives an
equal piece. That piece is ________ of a cookie.
!
3) For ! ÷ 2, let the rectangle represent one whole.
a) I have ______ and need to make ________ equal groups.
b) Divide the rectangle in to _________ and shade what we have.
!
c) We are looking for the result of dividing ! in to _____ equal groups. Divide the rectangle in
to 2 equal groups.
d) How much is in each group? ________
!
e) Math: ! ÷ 2 = _____.
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!
4) For ! ÷ 3, let the rectangle represent one whole.
a) I have ______ and need to make ________ equal groups.
b) Divide the rectangle in to _________ and shade what we have.
!
c) We are looking for the result of dividing ! in to _____ equal
groups. Divide the rectangle in to 3 equal parts.
d) How much is in each group? ________
!
e) Math: ! ÷ 3 = _____.
!
5) For ! ÷ 2, let the rectangle represent one whole.
a) I have ______ and need to make ________ equal groups.
b) Divide the rectangle in to _________ and shade what we have.
!
c) We are looking for the result of dividing ! in to _____ equal groups. Divide the rectangle in
to 2 equal groups.
d) How much is in each group? ________
!
e) Math: ! ÷ 2 = _____.
!
6) For ! ÷ 4, let the rectangle represent one whole.
a) I have ______ and need to make ________ equal groups.
b) Divide the rectangle in to _________ and shade what we have.
!
b) We are looking for the result of dividing ! in to _____ equal groups. Divide the rectangle
into 4 equal groups.
d) How much is in each group? ________
!
e) Math: ! ÷ 4 = _____.
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Practice
Use a rectangle to help you solve problems 7 – 10.
!
7) ! ÷ 2 =
!
9) ! ÷ 2 =
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!
8) ! ÷ 6 = 10) A family of four has one-half of a
chocolate cake left for dessert. If each family
member gets an equal piece, how much of the
whole cake will each person be eating?
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Dividing Fractions – Part III
Using the problems from Dividing Fractions Part I and Part II, fill in the table
below and then answer the conclusion questions.
Part I Problems: Write your answer to each question in the top row. For the bottom row, fill in the blank with the number that
would make the equation true.
!
!
!
!
!
!
!
!
3) 1 ÷ ! =
7) 5 ÷ ! =
1) 1 ÷ ! = 2) 1 ÷ ! =
4) 4 ÷ ! =
5) 8 ÷ ! =
6) 6 ÷ ! =
8) 9 ÷ ! =
Original
Problem
Problem as
Multiplication
1 × ____ = 2
1 × ____ = 3
1 × ____ = 6
4 ×___ = 20
8 ×___ = 32
6 ×___ = 18
5× ___ = 25
9× ___ = 18
Part II Problems: Write your answer to each question in the top row. For the bottom row, fill in the blank with the number that
would make the equation true.
!
!
!
!
!
!
!
7) ! ÷ 2 = 3) ! ÷ 2 = 4) ! ÷ 3 = 5) ! ÷ 2 = 6) ! ÷ 4 = 8) ! ÷ 6 = 9) ! ÷ 2 = Original
Problem
Problem as
Multiplication
1
1
× ___ = 3
6
1
1
× ___ = 2
6
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1
1
× ___ = 4
8
1
1
× ___ = 3
12
1
1
× ___ = 5
10
7
1
1
× ___ = 2
12
2
2
× ___ = 3
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Conclusions
Looking at the patterns between the problem in the top row and the problem in the bottom row, answer the following
questions.
1) Was the answer (quotient/product) for each of the problems the same or different when comparing the top row division
problem, to the bottom row multiplication problem?
2) A) Go back and circle the second number in each of the problems. (The divisor in the top row, the second factor in the
bottom row.)
B) What relationship is there between the divisor in the top row, and the factor in the bottom row? Does it hold true for
every problem? Give an example from above and explain.
!
3) A) The number 3 and ! are known as ______________ of each other.
!
B) The fraction ! and _______ are _____________ of each other.
C) Another pair of reciprocals are ____________.
!
4) If given the problem 3 ÷ ! = _____, how can the problem be written as a multiplication problem with the same answer?
Rewrite the problem and explain.
5) Make a conjecture about the relationship between dividing fractions and multiplying the reciprocal.
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