Transcript Subtracting Fractions with Unlike Denominators

Learning Objective
Name __________________________
Today, we will subtract fractions with unlike denominators.
CFU
What are we going to do today?
Fraction
3
4
Activate (or provide) Prior Knowledge
numerator
denominator
A fraction is a number that represents part of a whole.
Fractions with like denominators have the same number of equal parts.
Subtract fractions with like denominators. Hint: Subtract numerators and keep the denominators the same.
1.
5 2 3
 
8 8 8
2.
6
5
1


10 10 10
CFU
Students, you already know how to subtract fractions with like denominators.
Today, we will subtract fractions with unlike denominators.
DataWORKS Educational Research
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5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Concept Development
Fractions with unlike denominators have a different number of equal parts.
The least common denominator (LCD) is the lowest multiple shared by a set of denominators.
To subtract fractions, both fractions must have like denominators.
• To subtract fractions with unlike denominators use the least common denominator (LCD) to create equivalent1 fractions.
1
equal value
Subtracting Fractions with Unlike Denominators
36
15
1


5
2
10
10
10


Equivalent Fractions
The LCD of
3
5
and
1
2
is 10.
2
3
×
5
2
=
6
10
1
5
×
2
5
=
5
10
CFU
Which pair of fractions is ready to be subtracted? How do you know?
A
2 2
 
3 5
B
2 1
 
3 3
In your own words, how do you subtract fractions with unlike denominators?
To subtract fractions with unlike denominators __________.
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice
To subtract fractions, both fractions must have like denominators.
Subtract fractions with unlike denominators.
Step #1: Read the problem and identify2 fractions, if necessary. (circle)
Step #2: Find the least common denominator. Hint: Find the lowest shared multiple.
Step #3: Create equivalent fractions. Hint: Use the least common denominator.
Step #4: Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.
a. Reduce the difference3, if possible.
Step #5: Interpret4 the difference.
2
find
3 answer
1.
1 1 1
 
2 3 6
to a subtraction problem
4 explain
2.
1 2
1
 
2 5 10
1 3
3

×
6
2 3
2: 2, 4, 6, 8
3: 3, 6, 9, 12
1 5
5
×  10
2 5
1 2
2
× 
3 2
6
3 2 1
 
6 6 6
2 2
4
× 
10
5 2
2
3 1

3. 
4 12 3
3 3
9
×  12
4 3
1
1
1
× 
12 1 12
4.
4 3 12
× 
8 3 24
9
1
8
2



12 12 12 3
1
6
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5
4
1


10 10 10
4 1
1
 
8 6
3
4: 4, 8, 12, 16
12: 12, 24, 36, 48
CFU
(#2) How did I/you find the least common denominator?
(#3) How did I/you create equivalent fractions?
(#4) How did I/you subtract fractions?
2: 2, 4, 6, 8, 10
5: 5, 10, 15, 20
×
4
4

4 24
8: 8, 16, 24, 32
6: 6, 12, 18, 24
12 4
8
1



24 24 24 3
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Skill Development/Guided Practice (continued)
To subtract fractions, both fractions must have like denominators.
Subtract fractions with unlike denominators.
Step #1: Read the problem and identify fractions, if necessary. (circle)
Step #2: Find the least common denominator. Hint: Find the lowest shared multiple.
Step #3: Create equivalent fractions. Hint: Use the least common denominator.
Step #4: Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.
a. Reduce the difference, if possible.
Step #5: Interpret the difference.
3
1
5. Sherry bought 4 of a pound of red apples and 2 of a pound of green apples.
How much more red apples than green apples does Sherry have?
4: 4, 8, 12, 16
2: 2, 4, 6, 8
3 1
3
× 4
4 1
1 2
2
× 
4
2 2
3 2 1
 
4 4 4
1
4 of a pound more red apples than green apples.
Sherry has ____
2
1
6. Tom bought 3 of a pound of oranges and 5 of a pound of bananas.
How much more oranges than bananas did he buy?
3: 3, 6, 9, 12, 15
5: 5, 10, 15, 20
2 5 10
× 
3 5 15
1 3
3
× 
5 3 15
10 3
7


15 15 15
7
15 of a pound more oranges than bananas.
Tom bought ____
CFU
(#2) How did I/you find the least common denominator?
(#3) How did I/you create equivalent fractions?
(#4) How did I/you subtract fractions?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Relevance
To subtract fractions, both fractions must have like denominators.
1. Subtracting fractions will help solve real-life problems.
1 of the pie was left over after the party. Erick just ate 1 of the pie. How much pie is left?
2
4

1
2


1
4
There is
1
4

1
4
of the pie left.
2. Subtracting fractions will help you do well on tests.
Sample Test Question
1 1
 
3 4
53.
A
1
5
B
1
10
C
1
12
D
1
11
CFU
Does anyone else have another reason why it is relevant to subtract fractions with unlike denominators? (pair-share) Why is it relevant to
subtract fractions with unlike denominators? You may give me one of my reasons or one of your own. Which reason is more relevant to
you? Why?
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
To subtract fractions, both fractions must have like denominators.
Skill Closure
Subtract fractions with unlike denominators.
Step #1: Read the problem and identify fractions, if necessary. (circle)
Step #2: Find the least common denominator. Hint: Find the lowest shared multiple.
Step #3: Create equivalent fractions. Hint: Use the least common denominator.
Step #4: Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.
a. Reduce the difference, if possible.
Step #5: Interpret the difference.
3 1 5
 
4 8 8
1.
4: 4, 8, 12, 16
8: 8, 16, 24, 32
3 2
6

×
8
4 2
1 1
1
× 
8 1
8
6 1 5
 
8 8 8
3
1
2. Carmen bought 4 of a pound of grapes and 2 of a pound of nectarines.
How many more pounds of nectarines than grapes did Carmen buy?
4: 4, 8, 12, 16
2: 2, 4, 6, 8
3 1
3

×
4
4 1
2
1 2
× 
4
2 2
3 2 1
 
4 4 4
1
Carmen bought ____
4 of a pound more grapes than nectarines.
Constructed Response Closure
Which pair of fractions is ready to be subtracted? Explain your answer.
A
3 1
 
5 6
B
3 1
 
4 4
__________________________________________________
__________________________________________________
Summary Closure
What did you learn today about subtracting fractions with unlike denominators?
Day 1 ______________________________________________________________
Day 2 ______________________________________________________________
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Independent Practice
Name __________________________
To subtract fractions, both fractions must have like denominators.
Subtract fractions with unlike denominators.
Step #1: Read the problem and identify fractions, if necessary. (circle)
Step #2: Find the least common denominator. Hint: Find the lowest shared multiple.
Step #3: Create equivalent fractions. Hint: Use the least common denominator.
Step #4: Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.
a. Reduce the difference, if possible.
Step #5: Interpret the difference.
1.
5 2 1
 
6 3 6
5 1
5

×
6
6 1
2 2
4

×
3 2
6
2.
6: 6, 12, 18, 24
3: 3, 6, 9, 12
5 4 1
 
6 6 6
1
3 3


8
8 12
3 3
9
×  24
8 3
8: 8, 16, 24, 32
12: 12, 24, 36, 48
3
2
6
× 
12 2 24
9
6
3
1



24 24 24 8
2
1
3. The Smith family bought a pizza. Jason ate 7 of the pizza and Jamie ate 4 of the pizza.
How much more pizza did Jason eat than Jamie?
7: 7, 14, 21, 28, 35
4: 4, 8, 12, 16, 20, 24, 28
2 4
8
×  28
7 4
1 7
7
× 
4 7 28
8
7
1


28 28 28
1
28 of a pizza more than Jamie.
Jason ate ____
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Periodic Review 1
Name __________________________
To subtract fractions, both fractions must have like denominators.
Subtract fractions with unlike denominators.
Step #1: Read the problem and identify fractions, if necessary. (circle)
Step #2: Find the least common denominator. Hint: Find the lowest shared multiple.
Step #3: Create equivalent fractions. Hint: Use the least common denominator.
Step #4: Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.
a. Reduce the difference, if possible.
Step #5: Interpret the difference.
1.
11 1 2
 
12 4 3
11 1 11
× 
12 1 12
1 3
3
× 
4 3 12
2.
3 4
1


6 12 6
12: 12, 24, 36
4: 4, 8, 12, 16
3
6
11 3
8 2



12 12 12 3
4
1
4
× 
12 1 12
×
2
6

2 12
6: 6, 12, 18, 24, 32
12: 12, 24, 36, 48
6
4
2 1



12 12 12 6
3
1
3. Geoff has 4 of a pound of cashews and buys 6 of a pound of pecans. How many more pounds of cashews
does he have than pecans?
4: 4, 8, 12, 16
6: 6, 12, 18
3 3
9
×  12
4 3
1 2
2
× 
6 2 12
9
2
7


12 12 12
7
12 of a pound more cashews than pecans.
Geoff has ____
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Periodic Review 2
Name __________________________
To subtract fractions, both fractions must have like denominators.
Subtract fractions with unlike denominators.
Step #1: Read the problem and identify fractions, if necessary. (circle)
Step #2: Find the least common denominator. Hint: Find the lowest shared multiple.
Step #3: Create equivalent fractions. Hint: Use the least common denominator.
Step #4: Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.
a. Reduce the difference, if possible.
Step #5: Interpret the difference.
1.
4 3 7
 
6 8 24
4
6
×
4 16

4 24
3 3
9
× 
8 3 24
2.
6: 6, 12, 18, 24
8: 8, 16, 24
9 1 13
 
10 4 20
9
2 18
×  20
10 2
16 9
7


24 24 24
1 5
5
× 
4 5 20
10: 10, 20, 30, 40
4: 4, 8, 12, 16, 20
18 5 13


20 20 20
5
1
3. Alfredo bought some fruit. He got 8 of a pound of apples and 4 of a pound of pears. How many more
pounds of apples than pears did Alfredo buy?
8: 8, 16, 24
4: 4, 8, 12
5 1
5

×
8
8 1
1 2
2

×
4 2
8
5 2 3
 
8 8 8
3
8 of a pound more apples than pears.
Alfredo bought ____
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.
Periodic Review 3
Name __________________________
To subtract fractions, both fractions must have like denominators.
Subtract fractions with unlike denominators.
Step #1: Read the problem and identify fractions, if necessary. (circle)
Step #2: Find the least common denominator. Hint: Find the lowest shared multiple.
Step #3: Create equivalent fractions. Hint: Use the least common denominator.
Step #4: Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.
a. Reduce the difference, if possible.
Step #5: Interpret the difference.
1.
11 3 1
 
12 4 6
11 1 11
× 
12 1 12
3 3
9
× 
4 3 12
2.
3 3
3


5 10 10
12: 12, 24, 36
4: 4, 8, 12, 16
3
5
11 9
2 1



12 12 12 6
3
1
3
× 
10 1 10
×
2
6

2 10
5: 5, 10, 15, 20
10: 10, 20, 30
6
3
3


10 10 10
2
2
3. Alice bought some beans. She got 8 of a pound of lima beans and 5 of a pound of pinto beans. How many
more pounds of pinto beans than lima beans did she buy?
2 5 10
2 8 16 16  10  6  3
× 
× 
8 5 40
5 8 40 40 40 40 20
3
20 of a pound more pinto beans than lima beans.
Alice bought ____
8: 8, 16, 24, 32, 40
5: 5, 10, 15, 20, 25, 30, 35, 40
DataWORKS Educational Research
(800) 495-1550 • www.dataworks-ed.com
©2012 All rights reserved.
Comments? [email protected]
5th Grade Number Sense 2.3 (5Q)
Solve simple problems, including ones arising in concrete situations, involving
the addition and subtraction of fractions and mixed numbers (like and
unlike denominators of 20 or less), and express answers in the simplest form.
Lesson to be used by EDI-trained teachers only.