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Multiplying and Dividing Fractions

Multiplication of Fractions p. 87

a. Fold your paper into thirds.
b. Color one of your “thirds”.
c. Turn the paper sideways and fold it into fourths.
d. Color one of your “fourths”.
How many regions have double shading?
How many regions are there on the paper?

The problem you have solved is

Use the paper folding method to solve the following (sketch your
paper with folds in the space provided).

Complete problems 2 & 3.

Write the corresponding expression and fill in the
following arrays to find the answer to each
multiplication of fractions problem represented.

→ Now complete #2 & 3

this represents

One whole has 16 pieces
18 pieces have both colors
So the answer is 18/16…

• Saul purchased a rug for his bathroom. Its
dimensions are 4/5 yd by 2/3 yd. What is the
area of the rug?

• In Bedminster, 2/5 of voters are Democrats, 3/10 are
Republicans, 3/10 are independents. Three fourths of
the Democrats and half of the Republicans or
independents are expected to vote in favor of a bond
issue. Will this be enough for it to pass?

YES! More than half.

Fraction Division :

• Of US teachers, only 43% correctly solved this
division problem .

• All of the Chinese teachers computed it
correctly.

• 96% of US teachers failed to come up with a
representation of division of fractions .

• 8% of the Chinese teachers failed to come up
with a representation of division of fractions

• How many ½ foot lengths are there in
something that is 1¾ feet long? (Rep. Subtraction )

• If 1¾ feet is considered ½ of a length, how long
is the whole? (Sharing)

• Yesterday I rode a bicycle from town A to town
B. I spent 1¾ hour for ½ of my journey, how
much time did I take for the whole journey?

Recall Whole Number Division
18 ÷ 3

Repeated subtraction
“How many sets of 3 can be
made from 18?”

Sharing
“If I make 18 into 3 groups, how
many are in each group ?”
-OR-
“If 18 is 3 sets, what is 1 set?”
…what’s the whole?

Extending to Fraction Division (p. 91-92)

• If the Dividend is larger than the divisor…
▫ You can think of repeated subtraction
▫ Especially easy to see when dividend is a whole #

• Otherwise…find the whole!
▫ 18 ÷ 3…18 is 3 groups . What’s 1 group
(the whole)?
of a group . What’s the whole?

• Complete pages 91-92

Problem Solving p . 93

• Raymond is remodeling his living room, and he
bought 7 yd of fabric. He needs ¾ yd to make a
throw pillow. How many pillows can he make?
How much fabric will be left over?

• He can make 9 pillows and has ¼ yard of fabric
left over (1/3 of a pillow worth)

• Associated division problem: 7 ÷ ¾ = 9 1/3

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