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93153 =
What are we going to do?
CFU
Students, you already know how to generate equivalent fractions. Now, we will use that skill to add fractions with unlike denominators.
Make Connection
We will add fractions with unlike denominators.
Learning Objective
Introduction
23
numerator
denominator
Fraction
Which fraction is equivalent to ?
Equivalent fractions are fractions that have the same value.
25
Which fraction is equivalent to ?12
=35
410
=42
102 =25
510
=55
105 =12
28
=2282 =
14
Common Core Standards 7.NS.1 - 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division
of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.
615
What are we going to do?
CFU
Students, you already know how to generate equivalent fractions. Now, we will use that skill to subtract fractions with unlike denominators.
Make Connection
We will subtract fractions with unlike denominators.
Learning Objective
Introduction
23
numerator
denominator
Fraction
1220
124204 =
Which fraction is equivalent to ?
Equivalent fractions are fractions that have the same value.
35
Which fraction is equivalent to ?12
=35
=63
153 =25
618
=66
186 =13
24
=2242 =
12
Common Core Standards 7.NS.1 - 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division
of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.
What are we going to do?
CFU
Students, you already know how to find the least common denominator of fractions. Now, we will use that skill to add fractions with unlike denominators.
Make Connection
We will add fractions with unlike denominators.
Learning Objective
Activate Prior Knowledge
The least common denominator (LCD) is the lowest multiple shared by a set of denominators.
1 1,
2 5
Find the least common denominator of the fractions below.
1. 2.
5: 5, 10, 15, 20 2: 2, 4, 6, 8, 10
2 1,
3 2
The LCD of and is 10.1
2
1
5
23
numerator
denominator
Fraction
2: 2, 4, 6, 8 3: 3, 6, 9, 12
The LCD of and is 6.2
31
2
Common Core Standards 7.NS.1 - 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division
of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.
What are we going to do?
CFU
Students, you already know how to find the least common denominator of fractions. Now, we will use that skill to subtract fractions with unlike denominators.
Make Connection
The least common denominator (LCD) is the lowest multiple shared by a set of denominators.
We will subtract fractions with unlike denominators.
Learning Objective
Activate Prior Knowledge
2: 2, 4, 6, 8
1 1,
2 3
3: 3, 6, 9, 12
Find the least common denominator of the fractions below.
1. 2.
5: 5, 10, 15, 20 2: 2, 4, 6, 8, 10
3 1,
5 2
The LCD of and is 6.1
2
1
3The LCD of and is 10.
3
51
2
23
numerator
denominator
Fraction
Common Core Standards 7.NS.1 - 7.NS.3 Prerequisite Skills Apply and extend previous understandings of addition, subtraction, multiplication, and division
of integers (AND other rational numbers); Students will reinforce skills learned in 6 th grade.
Concept Development
23
numerator
denominator
FractionFractions with unlike denominators have a different number of equal parts. Fractions with like denominators have the same number of equal parts. To add fractions, both fractions must have like denominators.
• To add fractions with unlike denominators use the least common denominator (LCD) to create equivalent1 fractions with like denominators.
Which pair of fractions is ready to be added? How do you know?
A
B
In your own words, how do you add fractions with unlike denominators? “To add fractions with unlike denominators ________.”
CFU
2 2
3 5
2 1
3 3
410
510
910
+ =
25
The LCD of and12
is 10.
Adding Fractions with Unlike Denominators
=+
25
12
+ =
Equivalent Fractions
22
25
410
=55
12
510
=
1 equal value
Vocabulary
Which pair of fractions is ready to be subtracted? How do you know?
A
B
In your own words, how do you subtract fractions with unlike denominators? “To subtract fractions with unlike denominators ________.”
CFU
Concept Development
23
numerator
denominator
Fraction
Subtracting Fractions with Unlike Denominators
610
510
110
- =35
12
- =
35
The LCD of and12
is 10.
Equivalent Fractions
22
35
× 610
=55
12
× 510
=
- =
Fractions with unlike denominators have a different number of equal parts. Fractions with like denominators have the same number of equal parts. To subtract fractions, both fractions must have like denominators.
• To subtract fractions with unlike denominators use the least common denominator (LCD) to create equivalent fractions with like denominators.
23
25
23
13
Skill Development/Guided Practice
1 explain2 answer to an addition problem
Vocabulary
Find a like denominator by multiplying both denominators.Create equivalent fractions with like denominators. Add fractions. Hint: Add the numerators, keep the denominator the same.
Interpret1 the sum2. “____ plus ____ equals _____.”
Add fractions with unlike denominators.1234
To add fractions, both fractions must have like denominators.
How did I/you find a like denominator? How did I/you create equivalent fractions? How did I/you add fractions?
CFU
1
2
3
2×3
1.12 +
13 =
1×32×3 +
1×23×2 =
36 +
26 =
56
2×5
2.12 +
25 =
1×52×5 +
2×25×2 =
510 +
410 =
910
6×4
3.16 +
34 =
1×46×4 +
3×64×6 =
424 +
1824 =
2224
10×3
4.3
10 +13 =
3×310×3 +
1×103×10 =
930 +
1030 =
1930
Skill Development/Guided PracticeTo subtract fractions, both fractions must have like denominators.
1 explain2 answer to a subtraction problem
Vocabulary
Find a like denominator by multiplying both denominators.Create equivalent fractions with like denominators. Subtract fractions. Hint: subtract the numerators, keep the denominator the same.
Interpret1 the difference2. “____ minus ____ equals _____.”
Subtract fractions with unlike denominators.1234
How did I/you find a like denominator? How did I/you create equivalent fractions? How did I/you subtract fractions?
CFU
1
2
3
2×3
1.12 –
13 =
1×32×3 –
1×23×2 =
36 –
26 =
16
2×5
2.12 –
25 =
1×52×5 –
2×25×2 =
510 –
410 =
110
6×4
3.34 –
16 =
3×64×6 –
1×46×4 =
1824 –
424 =
1424
3×10
4.13 –
310 =
1×103×10 –
3×310×3 =
1030 –
930 =
130
5. Sierra had of a pint of water left in her water bottle. She poured another
of a pint more water into her bottle. How much water does Sierra have?
1
4
1
2
__________________________________________________________________
Skill Development/Guided Practice (continued)
4: 4, 8, 12, 16 2: 2, 4, 6, 8
6. Theodore bought of a pound of apples and of a pound of oranges.
How much fruit did he buy?
2
3
1
5
__________________________________________________________________
1
4
1
24
4
1
11
4
2
2
2
4
1 2
4 4
3
4
3: 3, 6, 9, 12, 15 5: 5, 10, 15, 20
2
3
1
515
15
5
510
15
3
3
3
15
10 3
15 15
13
15
3
4Sierra has of a pint of water.
13
15Theodore bought of a pound of fruit
Adding Fractions
Adding Fractions
How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?
CFU
2
1
3
4
5
Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.Add fractions. Hint: Add the numerators, keep the denominators the same.
Reduce the sum, if possible.Interpret the sum. “____ plus ____ equals _____.”
Add fractions with unlike denominators.
12
3
4a
Skill Development/Guided Practice (continued)
5. Sherry bought of a pound of milk chocolate and of a pound of white
chocolate. How much more milk chocolate than white chocolate does Sherry
have?
3
4
1
2
4: 4, 8, 12, 16 2: 2, 4, 6, 8
6. Tom bought of a pound of cauliflower and of a pound of celery.
How much more cauliflower than celery did he buy?
2
3
1
5
3
4
1
24
4
1
1× ×
3
4
2
2
2
4
3 2
4 4
1
4
3: 3, 6, 9, 12, 15 5: 5, 10, 15, 20
2
3
1
515
15
5
5× ×
10
15
3
3
3
15
10 3
15 15
7
15
1
4Sherry bought ____ of a pound more ______________ than _______________.milk chocolate white chocolate
7
15Tom bought ____ of a pound more __________ than ___________.cauliflower celery
How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?
CFU
2
1
3
4
5
required = needed relevant = has to do with problemreasonableness = possible
1
2
Relevance
To add fractions, both fractions must have like denominators.
Adding fractions will help solve real-life problems.
There is of a pie left.
12
12
14
34
of one pie was left over after the party. There was of another pie left over. How much pie is there?
+ =
14
34+ =
There is of the pie left.
12
12
14
14
of the pie was left over after the party. Erick just ate of the pie. How much pie is left?
+ =
14
14=
12
12 - =
Subtracting fractions will help solve real-life problems.
2. Carmen bought of a pound of grapes and of a pound of nectarines.
How many pounds of fruit did Carmen buy?
3
42
8
_________________________________________________________
_
Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.
Add fractions. Hint: Add the numerators, keep the denominators the same.Reduce the sum, if possible.
Interpret the sum. “____ plus ____ equals _____.”
Add fractions with unlike denominators.12
3
4a
What did you learn today about adding fractions with unlike denominators? (Pair-Share)Use words from the word bank.
Skill Closure
Access Common Core
Summary Closure
To add fractions, both fractions must have like denominators.
Which pair of fractions is ready to be added? Explain your answer.
3 34 7
A 3 14 4
B
3 1
4 8 1. 4: 4, 8, 12, 16
8: 8, 16, 24, 32
3
4
1
88
8
2
26
8
1
1
1
8
6 1
8 8
7
8
7
8
4: 4, 8, 12, 16 8: 8, 16, 32, 40
3
4
2
88
8
2
26
8
1
1
2
8
6 2
8 8
8
8
1Carmen bought pound of fruit
1
Word Bank
fractionslike/unlike
denominatorleast common denominatorequivalent
2. Carmen bought of a pound of grapes and of a pound of nectarines.
How many more pounds of nectarines than grapes did Carmen buy?
What did you learn today about subtracting fractions with unlike denominators? (Pair-Share) Use words from the word bank.
Access Common Core
Summary Closure
Read the problem and identify fractions, if necessary. (circle)Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.
Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.Reduce the difference, if possible.
Interpret the difference. “___ minus ____ equals ____.”
Subtract fractions with unlike denominators.123
4
5a
To subtract fractions, both fractions must have like denominators.
Skill Closure
Which pair of fractions is ready to be subtracted? Explain your answer.
3 15 6
A 3 14 4
B
3 1
4 8 1. 4: 4, 8, 12, 16
8: 8, 16, 24, 32
3
4
1
88
8
2
2× ×
6
8
1
1
1
8
6 1
8 8
5
8
5
8
3
41
2
4: 4, 8, 12, 16 2: 2, 4, 6, 8
3
4
1
24
4
1
1× ×
3
4
2
2
2
4
3 2
4 4
1
41
4Carmen bought ____ of a pound more __________ than ___________.grapes nectarines
Word Bank
fractionslike/unlike
denominatorleast common denominatorequivalent
Independent Practice
To add fractions, both fractions must have like denominators.
6: 6, 12, 18, 24
1 2
6 3 1.
3: 3, 6, 9, 12
3 3
8 12 2.
3. The Smith family bought some pizzas. One pizza had left over. The other had left. How much pizza is there left over?
__________________________________________________________________
1
6
2
3
6
6
1
11
6
2
2
4
6
1 4
6 6
5
6
5
6
8: 8, 16, 24, 32 12: 12, 24, 36, 48
3
8
3
12
24
24
3
39
24
2
2
6
24
9 6
24 24
15
24
5
8
2
71
4
7: 7, 14, 21, 28, 35 4: 4, 8, 12, 16, 20, 24, 28
2
7
1
428
28
4
48
28
7
7
7
28
8 7
28 28
15
28
15
28There is of the pizza left over.
Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.
Add fractions. Hint: Add the numerators, keep the denominators the same.Reduce the sum, if possible.
Interpret the sum. “____ plus ____ equals _____.”
Add fractions with unlike denominators.12
3
4a
Independent Practice
To subtract fractions, both fractions must have like denominators.
6: 6, 12, 18, 24
5 2
6 3 1.
3: 3, 6, 9, 12
3 3
8 12 2.
3. The Smith family bought a pizza. Jason ate of the pizza and Jamie ate of the pizza. How much more pizza did Jason eat than Jamie?
5
6
2
3
6
6
1
1×
×
5
6
2
2
4
6
5 4
6 6
1
6
1
6
8: 8, 16, 24, 32 12: 12, 24, 36, 48
3
8
3
12
24
24
3
3×
×
9
24
2
2
6
24
9 6
24 24
3
24
1
8
1
8
2
71
4
7: 7, 14, 21, 28, 35 4: 4, 8, 12, 16, 20, 24, 28
2
7
1
428
28
4
4× ×
8
28
7
7
7
28
8 7
28 28
1
28
1
28_________ ate ____ of a pizza more than _________.JamieJason
Read the problem and identify fractions, if necessary. (circle)Find the least common denominator. Hint: Find the lowest shared multiple.Create equivalent fractions with like denominators. Hint: Use the least common denominator.
Subtract fractions. Hint: Subtract the numerators, keep the denominators the same.Reduce the difference, if possible.
Interpret the difference. “___ minus ____ equals ____.”
Subtract fractions with unlike denominators.123
4
5a
Periodic Review 1
Access Common Core
7 1
12 4 1.
3 3
6 12 2.
3. Geoff has of a pound of cashews and buys of a pound of pecans. How many pounds of nuts does he have?
__________________________________________________________
3
41
6
Anita added the fractions below. Her teacher, Mrs. Caudill, says that her answer is incorrect. Explain the mistake that Anita made.
10 1
12 4
12: 12, 24, 36 4: 4, 8, 12, 16
7
12
1
4
12
12
1
17
12
3
3
3
12
7 3
12 12
10
12
5
6
5
6
6: 6, 12, 18, 24, 32 12: 12, 24, 36, 48
3
6
3
12
12
12
2
26
12
1
1
3
12
6 3
12 12
9
12
3
4
3
4
4: 4, 8, 12, 16 6: 6, 12, 18
3
4
1
612
12
3
39
12
2
2
2
12
9 2
12 12
11
12
11
12Geoff has of a pound of nuts
Anita did not make sure that the fractions had like denominators before adding. Instead, she just added both the numerators and denominators.
Periodic Review 1
Access Common Core
12: 12, 24, 36
11 1
12 4 1.
4: 4, 8, 12, 1611
12
1
4
12
12
1
1×
×
11
12
3
3
3
12
11 3
12 12
8
12
2
3
2
3
3 4
6 12 2.
6: 6, 12, 18, 24, 32 12: 12, 24, 36, 48
3
6
4
12
12
12
2
2×
×
6
12
1
1
4
12
6 4
12 12
2
12
1
6
1
6
3. Geoff has of a pound of cashews and buys of a pound of pecans. How many more pounds of cashews does he have than pecans?
Geoff has ____ of a pound more ___________ than __________.
3
41
6
4: 4, 8, 12, 16 6: 6, 12, 18
3
4
1
612
12
3
3× ×
9
12
2
2
2
12
9 2
12 12
7
12
7
12
Abdul subtracted the fractions below. His teacher, Mrs. Treadwell, says that his answer is incorrect. Explain the mistake that Abdul made.
10 1
12 4
pecanscashews
¼ was not converted to a common denominator first.
Also, denominators are incorrectly subtracted.
Periodic Review 2
Access Common Core
3 3
6 8 1.
3 1
10 4 2.
10: 10, 20, 30, 40 4: 4, 8, 12, 16, 20
3
10
1
4
20
20
2
2×
×
6
20
5
5
5
20
6 5
20 20
11
20
11
20
For each addition problem, place a check mark in the box to classify the sum as less than ½ or greater than ½.
6: 6, 12, 18, 24 8: 8, 16, 24
3
6
3
8
24
24
4
4×
×
12
24
3
3
9
24
12 9
24 24
21
24
7
8
7
8
3 1
6 8
1 1
3 9
3 1
4 12
1 4
6 5
1 1
4 5
less than ½ greater than ½.
Periodic Review 2
Access Common Core
6: 6, 12, 18, 24
4 3
6 8 1.
8: 8, 16, 24
9 1
10 4 2.
4
6
3
8
24
24
4
4×
×
16
24
3
3
9
24
16 9
24 24
7
24
7
24
10: 10, 20, 30, 40 4: 4, 8, 12, 16, 20
9
10
1
4
20
20
2
2×
×
18
20
5
5
5
20
18 5
20 20
13
20
13
20
Horatio added the fractions below. Some of his answers are incorrect. Circle all the incorrect answers and write the correct solutions.
Periodic Review 3
Access Common Core
7 1
12 4 1.
3 3
5 10 2.
12: 12, 24, 36 4: 4, 8, 12, 16
7
12
1
4
12
12
1
1×
×
7
12
3
3
3
12
7 3
12 12
10
12
5
6
5
6
5: 5, 10, 15, 2010: 10, 20, 30
3
5
3
10
10
10
2
2×
×
6
10
1
1
3
10
6 3
10 10
9
10
9
10
Choose Yes or No to show whether each choice
represents the sum of .
Yes No
Yes No
Yes No
Yes No
Periodic Review 3 (THIS PAGE IS HOMEWORK)
Access Common Core
12: 12, 24, 36
11 3
12 4 1.
4: 4, 8, 12, 16
3 3
5 10 2.
11
12
3
4
12
12
1
1×
×
11
12
3
3
9
12
11 9
12 12
2
12
1
6
1
6
5: 5, 10, 15, 2010: 10, 20, 30
3
5
3
10
10
10
2
2×
×
6
10
1
1
3
10
6 3
10 10
3
10
3
10
Choose Yes or No to show whether each choice is
equal to the difference of .
Yes No
Yes No
Yes No
Yes No