DIVIDING FRACTIONS
WARM-UP

How can you write (84 + 48) in distributive form?
12(7 + 4)

How can you write (64 + 16) in distributive form?
16(4 + 1)
STANDARD

MCC6.NS.1 Interpret and compute quotients of
fractions, and solve word problems involving division
of fractions by fractions, e.g., by using visual fraction
models and equations to represent the problem. For
example, create a story context for (2/3) ÷ (3/4) and
use a visual fraction model to show the quotient; use
the relationship between multiplication and division
to explain that (2/3) ÷ (3/4) = 8/9 because ¾ of 8/9 is
2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much
chocolate will each person get if 3 people share ½ lb.
of chocolate equally? How many ¾ - cup servings are
in 2/3 of a cup of yogurt? How wide is a rectangular
strip of land with length ¾ mi and area ½ square
miles?
IMPORTANT VOCABULARY!!
Numerator: top number of the fraction (parts of
the whole)
 Denominator: bottom number of the fraction
(whole)
 Vinculum: line that separates the numerator
and denominator
 Reciprocal: inverse of the fraction; when you
“flip” the fraction

REVIEW: SIMPLIFYING FRACTIONS

The easiest way is to divide the numerator and
denominator by their GCF!
18: 1, 2, 3, 6, 9, 18
24: 1, 2, 3, 4, 6, 8, 12, 24
GCF: 6
18 ÷ 6
3
=
24 ÷ 6
4
http://www.brainpop.com/math/numbers
andoperations/reducingfractions/
Simplest
Form
SPEED ROUND!!!

Simplify these fractions as fast as you can!!
12
20
3
5
17
34
1
2
10
15
2
3
16
20
4
5
YOU MAY ALSO NEED TO KNOW…

How do you change a mixed number into an
improper fraction?
+4
5
7
First, multiply
the whole
number by the
denominator.
Second, add the numerator
to the product of the whole
number and denominator.
39
7
FINALLY, IN ORDER TO DIVIDE FRACTIONS
YOU MUST BE ABLE TO…
Multiply Fractions!!!
 When you are multiplying, all you do is multiply
the numerators together then multiply the
denominators together!

Option #1
Multiply across
first and then
simplify!
8
9

6 48 16
=
=
7 63 21
Option #2
Simplify/Cross Simplify first and then
multiply across
8
3 9

6 2
7
16
21
Your answer will
be the same no
matter what
method you use!
WARM-UP
1.
What is 3/4 times 12/18?
1/2
2.
What is 8 ½ times 6/7?
7 2/7
Brainstorm!!
Why is it important to know how to divide
fractions?
One of the biggest ways you will
use this skill is when you are
dealing with measurements.
-Cooking
-Construction
-Time
-Dividing up food evenly (very
important)
FRACTION MODELS

Problem: Jeremy has a wooden board that is 2/3
yard long. He wants to cut the board into pieces
that are 1/9 yard long. How many pieces will
Jeremy cut?
Step One: Write
out the division
sentence.
2
3
÷
1
9
STEP TWO: DRAW A FRACTION BAR OF THE
FIRST FRACTION IN YOUR DIVISION SENTENCE
2
3
Draw a rectangle
and divide it into
thirds.
Then shade in
two of the thirds
to represent the
fraction 2/3.
STEP 3: DIVIDE THE RECTANGLE INTO THE
NUMBER OF PIECES THAT EQUALS THE
DENOMINATOR OF THE SECOND FRACTION
1
9
So…how many 1/9s are there in 2/3?
Jeremy will be able to cut the board
into 6 pieces.
NOW YOU CAN TRY ONE!

Jessica is making a cake and the recipe calls for
¾ of a cup of milk. She can only find the 1/8
measuring cup. How many times will she have to
fill up her 1/8 measuring cup to get enough milk
in the cake batter?
Jessica will have to fill up the measuring cup 6
times.
MORE PRACTICE

Spencer drew the model below to represent a
division sentence.
What division sentence does this model
represent?
3/4 ÷ 1/12
IMPORTANT VOCABULARY

Reciprocal: when you “flip” a fraction over; the
product of the original number and its reciprocal
is always 1
WARM-UP

Sasha has a piece of ribbon that is 4/5 of a yard
long. She needs 1/10 of a yard to make a hair
ribbon for her friends. How many hair ribbons
can she make? Draw a model to answer the
question.
Sasha can make 8 hair ribbons.
WARM-UP CHALLENGE PROBLEMS


Compare different pay scales. Decide if it is
better to receive $300 a week or to be paid hourly
at a rate of $7.50 per hour. What factors could
affect your decision?
Three watermelons and two cantaloupes weigh
32 pounds. Four watermelons and three
cantaloupes weigh 44 pounds. All watermelons
weigh the same and all cantaloupes weigh the
same. What is the weight of two watermelons
and one cantaloupe?
BASIC ALGORITHM
1. Leave
2. Change
3. Flip
It’s just that easy!
Change the
division sign to
multiplication!
EXAMPLE #1
Leave the
first
fraction!
3
4
3
4
÷

9
1
9
Flip: What is
the reciprocal
of 9?
1
12
EXAMPLE #2

Jake has 6 pounds of coconut. He will use 2/3
pound of the coconut to make one cake. How
many cakes can he make?
How do you set
up the
problem?
6÷
2
3
Jake will be able to make 9 cakes.
EXAMPLE #3

Stacy is making a recipe that calls for 3/4
teaspoon of cinnamon. Her only measuring spoon
holds 1/8 teaspoon. How many times will she
need to fill his measuring spoon to get enough
cinnamon for the recipe?
3
4
÷
1
8
She will have to fill up the
measuring spoon 6 times.
JEOPARDY GAME!!!

http://www.superteachertools.com/jeopardy/userg
ames/Oct201040/game1286214246.php
WHAT ABOUT IF THERE’S A MIXED NUMBER?
You have to change the mixed number to an improper
fraction before you can leave, change, flip!
Diego practices guitar for a total of 9 ¾ hours each
week. He practices for 1 ½ hour each time. How
many times does Diego practice guitar each week?
1
3
=
1
2
2
3
39
9
=
4
4
Diego practices guitar for a total of 9 ¾ hours each week. He
practices for 1 ½ hour each time. How many times does Diego
practice guitar each week?
Flip: What is
the reciprocal
3/2?
39 2

4
3
Leave the
first
fraction!
Change the
division sign to
multiplication!
=
13
2
=
1
6
2
He practices
guitar 6 ½ times
each week.