Multiplying Fractions: A Comprehensive Guide
Unit 2: Multiplying Fractions
1
Remember that fractions are parts of a whole or a
part of a set of objects. For example, if a bag of
apples contains 10 apples and three of the
apples are used to make apple tarts, three-
tenths, 3/10, of the apples have been used and
seven-tenths, 7/10, of the original set of 10
apples remain.
Often it is necessary to take a part of a part . For
example, if a recipe for cake that will serve 4
people requires three-fourths, ¾, cup of flour,
adjustments to the recipe will have to be
made to make a cake that will serve 2
people. Since 2 is one-half, ½, of 4, half of
the required amount of flour used to make a
4 serving cake could be used to make a cake
that would serve 2 people.
How can we determine the correct amount of
flour to use?
We need half of three-fourths, ¾, cup of flour to
make a cake for two.
Unit 2:
Multiplying Fractions
You will multiply fractions when you want to take a
piece, segment, or part (a fraction) of another
fraction.
There are two to three steps for multiplying fractions.
First, multiply the top numbers, the numerators.
Next, multiply the bottom numbers, the
denominators. The last step is to reduce the product,
that is put the product in simplest terms. Sometimes
the answer may not be reduced further. In that case
there will only be two steps involved.
Please view the video
“Multiplying Fractions”
(2 min and 25 s).
[If the link does not take you to the Website, copy
and paste the following URL into your browser:
https://youtu.be/CTKMK1ZGLuk
.]
[After you view the video you will have the
opportunity to practice multiplying fractions]
2
Designers for Learning
Multiplying Fractions
Unit 2: Multiplying Fractions
3
Do you remember the cake problem from the
beginning of this section? We still need to
determine how much flour to use for the cake
recipe for two people. Remember that we need to
know how much is one-half, ½, of three-fourths,
¾, cup of flour.
We can determine how much flour we need by
multiplying the fractions. We would multiply
¾ times ½. Our multiplication problem would look
like this:
Do you remember the steps for multiplying
fractions?
First , lets multiply the numerators. 3 x 1 = 3
Next, lets multiply the denominators. 4 x 2 = 8
So, we need ⅜ (three-eigths) cup of flour for the
cake recipe for two.
In order to measure ⅜ cup of flour a we could
draw lines on a measuring so that that cup
was divided into eight equal sections. Then
take three of the equal sized ⅛ sections.
Unit 2:
Check Your Knowledge
Now, you have the opportunity to practice
multiplying fractions. Calculate the product of each
multiplication problem below.
[Use a pencil/pen and paper to answer the
questions; then, click on the arrow to see the
correct answers.]
4
Multiplying Fractions:
Visualizing
Correct Answers
1.
3/32
2.
2/24 or 1/12 (simplest form)
3.
24/48 or
1/2
(simplest form)
4.
2
/6
or
1/3
(simplest form)
Designers for Learning
5
Unit 2: Answers
Correct Answers
1.
3/32
2.
2/24 or 1/12 (simplest form)
3.
24/48 or
1/2
(simplest form)
4.
2
/6
or
1/3
(simplest form)
Unit 2:
Practice
Click here
Click here t
o go to a printable
worksheet on multiplying fractions.
[Print the worksheet. Solve the fraction
multiplication problems and give the completed
worksheet to your teacher]
6
Designers for Learning
Unit 2:
Multiplying Fractions: Word Problems
Now that you know how to multiply fractions, it is
time to move to solving real-world problems which
involve multiplying fractions.
Please view the video
“Multiplying Fractions Word
Problem”
(
3
min and
38
s).
[If the link does not take you to the Website, copy
and paste the following URL into your browser:
https://youtu.be/YJgIGwTysk0
]
[After you view the video
move to the next slide to
watch two more short videos on multiplying fractions]
7
Use this type of slide for a link to a video with directions on what
students should do.
Designers for Learning
Multiplying Fractions Word
Problem
Unit 2:
Multiplying Fractions: Word Problems
The following videos provide additional examples of
how to use your knowledge of how to multiply
fractions to provide answers to questions you might
have in everyday life..
Please view the video
“Multiplying Fractions Word
Problems (ex 1)”
(
2
min and
12
s)
and the video ”
Multiplying Fractions
Word Problem 4
” (1 min and 19s).
[If the link does not take you to the Website, copy
and paste the following URL into your browser:
https://youtu.be/jZUgNoj-oHY
]
[After you view the videos you will have the
opportunity to practice
solving word problems using
multiplication of fractions]
]
8
Use this type of slide for a link to a video with directions on what
students should do.
Designers for Learning
Multiplying Fractions Word
Problem (ex 1)
Multiplying Fractions Word
Problem 4
Unit 2: Multiplying Fractions: Word Problems
9
George has a piece of lumber that is 6
feet. He needs 2/3 of the lumber to use
for a doorway on a tree house he is
building. How much of the 6 feet piece of
lumber will George use?
To find out how much lumber George will use
for the doorway, we must use multiplication.
Often, in word problems the word “of” means
multiply. We need to determine what is 2/3
(two-thirds) of six. That is 2/3 x 6.
Here is our fraction multiplication problem:
Here is the solution:
George needs 4 feet of lumber for the doorway.
Practice
Taffy and Margot love a bargain. They heard that the local supermarket has whole
chickens on sale for 2/3 (two-thirds) of the usual price. The supermarket usually charges
9 dollars for whole chickens. How much are the whole chickens now that they are on
sale for 2/3 of the usual price?
Solve the fraction multiplication word problem. Then use the next slide to check your
work.
10
Unit 2: Multiplying Fractions: Word Problems
Unit 2: Multiplying Fractions: Word Problems
11
Taffy and Margot need to know what is
2/3 (two-thirds) of nine dollars.
They want
to know if the sale on chickens is a bargain or not
.
To find out the sale price on the chickens, Taffy
and Margot could use multiplication. They
need to determine what is 2/3 (two-thirds) of
nine dollars.. That is 2/3 x 9.
Here is our fraction multiplication problem:
Here is the solution:
Taffy and Margot can buy whole chickens for
only 6 dollars each. That is a bargain!
Unit 2:
Practice:
Fraction Multiplication Word
Problems
Click here
to go to a printable worksheet on
fraction multiplication word problems.
.
[Print the worksheet. Solve the fraction
multiplication word problems and give the
completed worksheet to your teacher]
12
Designers for Learning
13
Unit 2: Multiplying Fractions
How comfortable are you with multiplying fractions?
1 . . . . . . . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . 4 . . . . . . . . .
Very uncomfortable Somewhat comfortable Comfortable Very Comfortable
If your comfort level is 1 (very uncomfortable or 2 (somewhat comfortable) go back and
review this section.
Unit 2: Multiplying Fractions
Resources
14
“
Multiplying Fractions” 2mins25s
https://youtu.be/CTKMK1ZGLuk
“Multiplying fractions word problem” 3mins38s
https://youtu.be/YJgIGwTysk0
“Multiplying fractions word problems (ex 1)” 2mins12s
https://youtu.be/jZUgNoj-oHY
“Multiplying fractions word problem 4” 1min19s
https://youtu.be/KCehC_3CBBY
Unit 3:
Dividing Fractions
Dividing fractions is very similar to multiplying
fractions. In fact, to solve a problem which involves
dividing fractions, you will actually multiply!
Please view the video
How to Divide Fractions
(6 min and 52 s).
[If the link does not take you to the Website, copy
and paste the following URL into your browser:
https://youtu.be/D5kWGMZdEGM
.]
[After you view the video you will have the
opportunity to practice dividing fractions]
15
Designers for Learning
How to Divide Fractions
Unit 3:
Check Your Knowledge
Now, you have the opportunity to practice
dividing
fractions. Calculate the
quotient
of each
division
problem below. Remember
to flip the fraction after
the division sign, that is get the reciprocal. Then,
multiply the two fractions.
[Use a pencil/pen and paper to answer the
questions; then, click on the arrow to see the
correct answers.]
16
Correct Answers
1.
9/10
2.
8/3
3.
16/10 or 8/5 (simplest form)
4.
6/5
Designers for Learning
17
Unit 3: Answers
Correct Answers
1.
9/10
2.
8/3
3.
16/10 or 8/5 (simplest form)
4.
6/5
Unit 3:
Practice
Click here
to go to a printable worksheet on
dividing
fractions.
[Print the worksheet. Solve the fraction
division
problems and give the completed worksheet to
your teacher]
18
Designers for Learning
Unit 3: Dividing
Fractions: Word Problems
Now that you know how to divide fractions, it is time
to move to solving real-world problems which involve
dividing fractions.
Please view the video
“Solving Fraction Word
Problems- Fraction Division”
(
4
min and
2
s).
[If the link does not take you to the Website, copy
and paste the following URL into your browser:
https://youtu.be/v0GRcwCiVmw
]
[After you view the video
move to the next slide to
watch another video on dividing fractions word
problems]
19
Use this type of slide for a link to a video with directions on what
students should do.
Designers for Learning
Solving Fraction Word
Problems- Fraction Division
Unit 3: Dividing
Fractions: Word Problems
Please view the following video for more instruction
on solving everyday problems by dividing fractions..
Please view the video
“Dividing Fractions Word
Problem”
(
2
min and
7
s).
[If the link does not take you to the Website, copy
and paste the following URL into your browser:
https://youtu.be/PQsgXNggV7Q
]
[
After you view the video you will have the
opportunity to practice dividing fractions]
20
Use this type of slide for a link to a video with directions on what
students should do.
Designers for Learning
Dividing Fractions Word
Problem
Unit 3:
Practice:
Fraction Division Word
Problems
Click here
to go to a printable worksheet on
fraction division word problems.
[Print the worksheet. Solve the fraction
division
word problems and give the completed worksheet
to your teacher]
21
Designers for Learning
22
Unit 3: Dividing Fractions
How comfortable are you with dividing fractions?
1………………………………………2……………………………… 3……………………………4
Very uncomfortable Somewhat comfortable Comfortable Very Comfortable
If your comfort level is 1 (very uncomfortable or 2 (somewhat comfortable) go back and
review this section.
Unit 3: Dividing Fractions
Resources
23
“How to Divide Fractions” 6mins52s
https://youtu.be/D5kWGMZdEGM
“Solving Fraction Word Problems-Fraction Division” 4min2s
https://youtu.be/v0GRcwCiVmw
“Dividing Fractions Word Problem” 2mins7s
https://youtu.be/PQsgXNggV7Q
Fractions represent parts of a whole or a set of objects. Learn how to multiply fractions step by step, including reducing answers to simplest terms. Practice multiplying fractions with visual examples and check your knowledge with provided exercises.
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Presentation Transcript
Unit 2: Multiplying Fractions Remember that fractions are parts of a whole or a part of a set of objects. For example, if a bag of apples contains 10 apples and three of the apples are used to make apple tarts, three- tenths, 3/10, of the apples have been used and seven-tenths, 7/10, of the original set of 10 apples remain. Often it is necessary to take a part of a part . For example, if a recipe for cake that will serve 4 people requires three-fourths, , cup of flour, adjustments to the recipe will have to be made to make a cake that will serve 2 people. Since 2 is one-half, , of 4, half of the required amount of flour used to make a 4 serving cake could be used to make a cake that would serve 2 people. How can we determine the correct amount of flour to use? We need half of three-fourths, , cup of flour to make a cake for two. 1
Unit 2: Multiplying Fractions You will multiply fractions when you want to take a piece, segment, or part (a fraction) of another fraction. There are two to three steps for multiplying fractions. First, multiply the top numbers, the numerators. Next, multiply the bottom numbers, the denominators. The last step is to reduce the product, that is put the product in simplest terms. Sometimes the answer may not be reduced further. In that case there will only be two steps involved. Please view the video Multiplying Fractions (2 min and 25 s). [If the link does not take you to the Website, copy and paste the following URL into your browser: https://youtu.be/CTKMK1ZGLuk.] Multiplying Fractions [After you view the video you will have the opportunity to practice multiplying fractions] Designers for Learning 2
Unit 2: Multiplying Fractions Do you remember the cake problem from the beginning of this section? We still need to determine how much flour to use for the cake recipe for two people. Remember that we need to know how much is one-half, , of three-fourths, , cup of flour. Do you remember the steps for multiplying fractions? First , lets multiply the numerators. 3 x 1 = 3 Next, lets multiply the denominators. 4 x 2 = 8 We can determine how much flour we need by multiplying the fractions. We would multiply times . Our multiplication problem would look like this: So, we need (three-eigths) cup of flour for the cake recipe for two. In order to measure cup of flour a we could draw lines on a measuring so that that cup was divided into eight equal sections. Then take three of the equal sized sections. 3
Unit 2: Check Your Knowledge Now, you have the opportunity to practice multiplying fractions. Calculate the product of each multiplication problem below. Multiplying Fractions: Visualizing [Use a pencil/pen and paper to answer the questions; then, click on the arrow to see the correct answers.] Correct Answers 1. 3/32 2. 2/24 or 1/12 (simplest form) 3. 24/48 or 1/2 (simplest form) 4. 2/6 or 1/3 (simplest form) Designers for Learning 4
Unit 2: Answers Correct Answers 1. 3/32 2. 2/24 or 1/12 (simplest form) 3. 24/48 or 1/2 (simplest form) 4. 2/6 or 1/3 (simplest form) 5
Unit 2: Practice Click here Click here to go to a printable worksheet on multiplying fractions. [Print the worksheet. Solve the fraction multiplication problems and give the completed worksheet to your teacher] Designers for Learning 6
Unit 2: Multiplying Fractions: Word Problems Now that you know how to multiply fractions, it is time to move to solving real-world problems which involve multiplying fractions. Please view the video Multiplying Fractions Word Problem (3min and 38s). [If the link does not take you to the Website, copy and paste the following URL into your browser: https://youtu.be/YJgIGwTysk0] Multiplying Fractions Word Problem [After you view the video move to the next slide to watch two more short videos on multiplying fractions] Use this type of slide for a link to a video with directions on what students should do. Designers for Learning 7
Unit 2: Multiplying Fractions: Word Problems The following videos provide additional examples of how to use your knowledge of how to multiply fractions to provide answers to questions you might have in everyday life.. Please view the video Multiplying Fractions Word Problems (ex 1) (2min and 12s) and the video Multiplying Fractions Word Problem 4 (1 min and 19s). [If the link does not take you to the Website, copy and paste the following URL into your browser: https://youtu.be/jZUgNoj-oHY] Multiplying Fractions Word Problem (ex 1) [After you view the videos you will have the opportunity to practice solving word problems using multiplication of fractions]] Multiplying Fractions Word Problem 4 Use this type of slide for a link to a video with directions on what students should do. Designers for Learning 8
Unit 2: Multiplying Fractions: Word Problems To find out how much lumber George will use for the doorway, we must use multiplication. Often, in word problems the word of means multiply. We need to determine what is 2/3 (two-thirds) of six. That is 2/3 x 6. George has a piece of lumber that is 6 feet. He needs 2/3 of the lumber to use for a doorway on a tree house he is building. How much of the 6 feet piece of lumber will George use? Here is our fraction multiplication problem: Here is the solution: George needs 4 feet of lumber for the doorway. 9
Unit 2: Multiplying Fractions: Word Problems Practice Taffy and Margot love a bargain. They heard that the local supermarket has whole chickens on sale for 2/3 (two-thirds) of the usual price. The supermarket usually charges 9 dollars for whole chickens. How much are the whole chickens now that they are on sale for 2/3 of the usual price? Solve the fraction multiplication word problem. Then use the next slide to check your work. 10
Unit 2: Multiplying Fractions: Word Problems To find out the sale price on the chickens, Taffy and Margot could use multiplication. They need to determine what is 2/3 (two-thirds) of nine dollars.. That is 2/3 x 9. Taffy and Margot need to know what is 2/3 (two-thirds) of nine dollars. They want to know if the sale on chickens is a bargain or not . Here is our fraction multiplication problem: Here is the solution: Taffy and Margot can buy whole chickens for only 6 dollars each. That is a bargain! 11
Unit 2: Practice: Fraction Multiplication Word Problems Click here to go to a printable worksheet on fraction multiplication word problems.. [Print the worksheet. Solve the fraction multiplication word problems and give the completed worksheet to your teacher] Designers for Learning 12
Unit 2: Multiplying Fractions How comfortable are you with multiplying fractions? 1 . . . . . . . . . . . . . . . . . 2 . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . 4 . . . . . . . . . Very uncomfortable Somewhat comfortable Comfortable Very Comfortable If your comfort level is 1 (very uncomfortable or 2 (somewhat comfortable) go back and review this section. 13
Unit 2: Multiplying Fractions Resources Multiplying Fractions 2mins25s https://youtu.be/CTKMK1ZGLuk Multiplying fractions word problem 3mins38s https://youtu.be/YJgIGwTysk0 Multiplying fractions word problems (ex 1) 2mins12s https://youtu.be/jZUgNoj-oHY Multiplying fractions word problem 4 1min19s https://youtu.be/KCehC_3CBBY 14
Unit 3: Dividing Fractions Dividing fractions is very similar to multiplying fractions. In fact, to solve a problem which involves dividing fractions, you will actually multiply! Please view the video How to Divide Fractions (6 min and 52 s). [If the link does not take you to the Website, copy and paste the following URL into your browser: https://youtu.be/D5kWGMZdEGM.] How to Divide Fractions [After you view the video you will have the opportunity to practice dividing fractions] Designers for Learning 15
Unit 3: Check Your Knowledge Now, you have the opportunity to practice dividing fractions. Calculate the quotient of each division problem below. Remember to flip the fraction after the division sign, that is get the reciprocal. Then, multiply the two fractions. Correct Answers [Use a pencil/pen and paper to answer the questions; then, click on the arrow to see the correct answers.] 1. 9/10 2. 8/3 3. 16/10 or 8/5 (simplest form) 4. 6/5 Designers for Learning 16
Unit 3: Answers Correct Answers 1. 9/10 2. 8/3 3. 16/10 or 8/5 (simplest form) 4. 6/5 17
Unit 3: Practice Click here to go to a printable worksheet on dividing fractions. [Print the worksheet. Solve the fraction division problems and give the completed worksheet to your teacher] Designers for Learning 18
Unit 3: Dividing Fractions: Word Problems Now that you know how to divide fractions, it is time to move to solving real-world problems which involve dividing fractions. Please view the video Solving Fraction Word Problems- Fraction Division (4min and 2s). [If the link does not take you to the Website, copy and paste the following URL into your browser: https://youtu.be/v0GRcwCiVmw ] Solving Fraction Word Problems- Fraction Division [After you view the video move to the next slide to watch another video on dividing fractions word problems] Use this type of slide for a link to a video with directions on what students should do. Designers for Learning 19
Unit 3: Dividing Fractions: Word Problems Please view the following video for more instruction on solving everyday problems by dividing fractions.. Please view the video Dividing Fractions Word Problem (2min and 7s). [If the link does not take you to the Website, copy and paste the following URL into your browser: https://youtu.be/PQsgXNggV7Q] Dividing Fractions Word Problem [After you view the video you will have the opportunity to practice dividing fractions] Use this type of slide for a link to a video with directions on what students should do. Designers for Learning 20
Unit 3: Practice: Fraction Division Word Problems Click here to go to a printable worksheet on fraction division word problems. [Print the worksheet. Solve the fraction division word problems and give the completed worksheet to your teacher] Designers for Learning 21
Unit 3: Dividing Fractions How comfortable are you with dividing fractions? 1 2 3 4 Very uncomfortable Somewhat comfortable Comfortable Very Comfortable If your comfort level is 1 (very uncomfortable or 2 (somewhat comfortable) go back and review this section. 22
Unit 3: Dividing Fractions Resources How to Divide Fractions 6mins52s https://youtu.be/D5kWGMZdEGM Solving Fraction Word Problems-Fraction Division 4min2s https://youtu.be/v0GRcwCiVmw Dividing Fractions Word Problem 2mins7s https://youtu.be/PQsgXNggV7Q 23
