Add Fractions and Mixed Numbers
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Transcript of Add Fractions and Mixed Numbers
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Add Fractions and Mixed Numbers
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Add Fractions and Mixed Numbers
Ex) At the end of the pizza lunch, Mr. Green’s class had 1/4 of a pizza left, and Mr. Black’s class had 2/3 of a pizza left. How can we describe the total amount of leftover pizza?
83
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Add and Subtract Fractions
Ex) At the end of the pizza lunch, Mr. Green’s class had 1/4 of a pizza left, and Mr. Black’s class had 2/3 of a pizza left. How can we describe the total amount of leftover pizza?
83
Mr. Green’s Pizza =
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Add and Subtract Fractions
Ex) At the end of the pizza lunch, Mr. Green’s class had 1/4 of a pizza left, and Mr. Black’s class had 2/3 of a pizza left. How can we describe the total amount of leftover pizza?
83
Mr. Green’s Pizza = Mr. Black’s Pizza =
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Add and Subtract Fractions
Ex) At the end of the pizza lunch, Mr. Green’s class had 1/4 of a pizza left, and Mr. Black’s class had 2/3 of a pizza left. How can we describe the total amount of leftover pizza?
Can we say that there are 3 slices left?
83
Mr. Green’s Pizza = Mr. Black’s Pizza =
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Add and Subtract Fractions
Ex) At the end of the pizza lunch, Mr. Green’s class had 1/4 of a pizza left, and Mr. Black’s class had 2/3 of a pizza left. How can we describe the total amount of leftover pizza?
Can we say that there are 3 slices left? No, because that would ignore the fact that they are different sizes.
83
Mr. Green’s Pizza = Mr. Black’s Pizza =
![Page 7: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/7.jpg)
Add and Subtract Fractions
Ex) At the end of the pizza lunch, Mr. Green’s class had 1/4 of a pizza left, and Mr. Black’s class had 2/3 of a pizza left. How can we describe the total amount of leftover pizza?
Can we say that there are 3 slices left? No, because that would ignore the fact that they are different sizes.ie) Would it be 3 quarters or 3 thirds or something else?
83
Mr. Green’s Pizza = Mr. Black’s Pizza =
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Add and Subtract Fractions
We need to change the leftover amounts so that they are in pieces of the same size.
83
Mr. Green’s Pizza =
Mr. Black’s Pizza =
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Add and Subtract Fractions
We need to change the leftover amounts so that they are in pieces of the same size.
83
Mr. Green’s Pizza =
=
Mr. Black’s Pizza =
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Add and Subtract Fractions
We need to change the leftover amounts so that they are in pieces of the same size.
83
Mr. Green’s Pizza =
=
Mr. Black’s Pizza =
=
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Add and Subtract Fractions
We need to change the leftover amounts so that they are in pieces of the same size.
Now that we are dealing with pieces of the same size, we can add the amounts together:
83
Mr. Green’s Pizza =
=
Mr. Black’s Pizza =
=
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Add and Subtract Fractions
Now that we are dealing with pieces of the same size, we can add the amounts together:83
Mr. Green’s Pizza =
=
Mr. Black’s Pizza =
=
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Add and Subtract Fractions
Now that we are dealing with pieces of the same size, we can add the amounts together:83
Mr. Green’s Pizza = 1/4 = 3/12
Mr. Black’s Pizza = 2/3 = 8/12
1211
128
12332
41
32
41
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Add and Subtract Fractions
Now that we are dealing with pieces of the same size, we can add the amounts together:83
Mr. Green’s Pizza = 1/4 = 3/12
Mr. Black’s Pizza = 2/3 = 8/12
1211
128
12332
41
128
12332
41
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Add and Subtract Fractions
Now that we are dealing with pieces of the same size, we can add the amounts together:83
Mr. Green’s Pizza = 1/4 = 3/12
Mr. Black’s Pizza = 2/3 = 8/12
1211
128
12332
41
1211
128
12332
41
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Add and Subtract Fractions
Now that we are dealing with pieces of the same size, we can add the amounts together:
Remember, just add the numerators!
83
Mr. Green’s Pizza = 1/4 = 3/12
Mr. Black’s Pizza = 2/3 = 8/12
1211
128
12332
41
1211
128
12332
41
![Page 17: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/17.jpg)
Add and Subtract Fractions
Now that we are dealing with pieces of the same size, we can add the amounts together:
We can now describe the leftover amount.83
Mr. Green’s Pizza = 1/4 = 3/12
Mr. Black’s Pizza = 2/3 = 8/12
1211
128
12332
41
1211
128
12332
41
![Page 18: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/18.jpg)
Add and Subtract Fractions
Now that we are dealing with pieces of the same size, we can add the amounts together:
We can now describe the leftover amount.
There is 11/12 of a pizza left.
83
Mr. Green’s Pizza = 1/4 = 3/12
Mr. Black’s Pizza = 2/3 = 8/12
1211
128
12332
41
1211
128
12332
41
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?
83
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.83
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.The LCM can be found by listing multiples:83
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.The LCM can be found by listing multiples:
Multiples of 3:83
![Page 24: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/24.jpg)
Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.The LCM can be found by listing multiples:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . 83
![Page 25: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/25.jpg)
Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.The LCM can be found by listing multiples:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . Multiples of 4:
83
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.The LCM can be found by listing multiples:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . Multiples of 4: 4, 8, 12, 16, 20, 24, . . .
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.The LCM can be found by listing multiples:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . Multiples of 4: 4, 8, 12, 16, 20, 24, . . .
83
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Add and Subtract Fractions
When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.How did we decide to use 12 as the common denominator?Twelve is the lowest common multiple of 3 and 4.The LCM can be found by listing multiples:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . Multiples of 4: 4, 8, 12, 16, 20, 24, . . .
We see that 12 is the first number to appear on both lists.
83
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
83
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
2183
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 = 3 x 783
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 83
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 = 4 x 7 83
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 783
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 7Now, compare them:83
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 7Now, compare them:
21 = 3 x 783
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 7Now, compare them:
21 = 3 x 728 = 7 x 2 x 2
83
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 7Now, compare them:
21 = 3 x 728 = 7 x 2 x 2
83
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Add and Subtract Fractions
We can also find the LCM by using prime factorizations:
Ex) Find the LCM of 21 and 28.
21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 7Now, compare them:
21 = 3 x 728 = 7 x 2 x 2
LCM = 3 x 7 x 2 x 2 = 84
83
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
83
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
83
61
103
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
83
61
103
305
309
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
83
61
103
3014
305
309
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
This can be reduced.83
61
103
3014
305
309
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
83
61
103
230214305
309
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
83
61
103
157
230214305
309
![Page 48: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/48.jpg)
Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
How did we know to divide by 2?
83
61
103
157
230214305
309
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Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
How did we know to divide by 2? Two is the greatest common factor of 14 and 30.
83
61
103
157
230214305
309
![Page 50: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/50.jpg)
Add and Subtract Fractions
Sometimes, answers will need to be reduced to lowest terms.
Ex)
How did we know to divide by 2? Two is the greatest common factor of 14 and 30. GCF(14, 30) = 2
83
61
103
157
230214305
309
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Adding and Subtracting Mixed Numbers
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Operations with Mixed Numbers• Ex 1) After the pizza party, Mickey and his friends had 3 pizzas left over. If the pizzas were all sliced into eighths,
how many slices do they have? 81
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Operations with Mixed Numbers• Ex 1) After the pizza party, Mickey and his friends had 3 pizzas left over. If the pizzas were all sliced into eighths,
how many slices do they have? 81
825
25183813
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Operations with Mixed Numbers• Ex 1) After the pizza party, Mickey and his friends had 3 pizzas left over. If the pizzas were all sliced into eighths,
how many slices do they have? 81
825
25183813
![Page 55: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/55.jpg)
Operations with Mixed Numbers• Ex 1) After the pizza party, Mickey and his friends had 3 pizzas left over. If the pizzas were all sliced into eighths,
how many slices do they have? 81
825
25183813
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Operations with Mixed Numbers• Ex 1) After the pizza party, Mickey and his friends had 3 pizzas left over. If the pizzas were all sliced into eighths,
how many slices do they have?
They have 25 slices of pizza.
81
825
25183813
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Operations with Mixed Numbers• Ex 2) After the birthday party, there were 43 slices of pizza left
on the platters. If the pizzas were all sliced into eighths, how many boxes were needed to take the leftovers home?
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Operations with Mixed Numbers• Ex 2) After the birthday party, there were 43 slices of pizza left
on the platters. If the pizzas were all sliced into eighths, how many boxes were needed to take the leftovers home?
835
35843843
R
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Operations with Mixed Numbers• Ex 2) After the birthday party, there were 43 slices of pizza left
on the platters. If the pizzas were all sliced into eighths, how many boxes were needed to take the leftovers home?
835
35843843
R
![Page 60: Add Fractions and Mixed Numbers](https://reader034.fdocuments.us/reader034/viewer/2022051402/56815bc6550346895dc9bf25/html5/thumbnails/60.jpg)
Operations with Mixed Numbers• Ex 2) After the birthday party, there were 43 slices of pizza left
on the platters. If the pizzas were all sliced into eighths, how many boxes were needed to take the leftovers home?
835
35843843
R
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Operations with Mixed Numbers• Ex 3) After the birthday party, there were 43 slices of pizza left
on the platters. If the pizzas were all sliced into eighths, how many boxes were needed to take the leftovers home?
They would have needed 6 boxes.
835
35843843
R
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Operations with Mixed Numbers• Ex 3) Add.
726
7215
795
75
74
32
753
742
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Operations with Mixed Numbers• Ex 3) Add.
726
7215
795
75
74
32
753
742
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Operations with Mixed Numbers• Ex 3) Add.
726
7215
795
75
74
32
753
742
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Operations with Mixed Numbers• Ex 3) Add.
726
7215
795
75
74
32
753
742
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Operations with Mixed Numbers• Ex 3) Add.
726
7215
795
75
74
32
753
742
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Operations with Mixed Numbers• Ex 5) Add.
548
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Operations with Mixed Numbers• Ex 5) Add.
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Operations with Mixed Numbers• Ex 5) Add.
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Operations with Mixed Numbers• Ex 5) Add.
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