Add Fractions and Mixed Numbers

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

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 =

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 =

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 =

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 =

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 =

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 =

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 =

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 =

=

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 =

=

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 =

=

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

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

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

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

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

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

Add and Subtract Fractions

When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.

83

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

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

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

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

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

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

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

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

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

Add and Subtract Fractions

We can also find the LCM by using prime factorizations:

83

Add and Subtract Fractions

We can also find the LCM by using prime factorizations:

Ex) Find the LCM of 21 and 28.

83

Add and Subtract Fractions

We can also find the LCM by using prime factorizations:

Ex) Find the LCM of 21 and 28.

2183

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

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

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

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

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

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

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

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

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

Add and Subtract Fractions

Sometimes, answers will need to be reduced to lowest terms.

83

Add and Subtract Fractions

Sometimes, answers will need to be reduced to lowest terms.

Ex)

83

61

103

Add and Subtract Fractions

Sometimes, answers will need to be reduced to lowest terms.

Ex)

83

61

103

305

309

Add and Subtract Fractions

Sometimes, answers will need to be reduced to lowest terms.

Ex)

83

61

103

3014

305

309

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

Add and Subtract Fractions

Sometimes, answers will need to be reduced to lowest terms.

Ex)

83

61

103

230214305

309

Add and Subtract Fractions

Sometimes, answers will need to be reduced to lowest terms.

Ex)

83

61

103

157

230214305

309

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

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

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

Adding and Subtracting Mixed Numbers

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

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

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

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

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

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?

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

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

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

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

Operations with Mixed Numbers• Ex 3) Add.

726

7215

795

75

74

32

753

742

Operations with Mixed Numbers• Ex 3) Add.

726

7215

795

75

74

32

753

742

Operations with Mixed Numbers• Ex 3) Add.

726

7215

795

75

74

32

753

742

Operations with Mixed Numbers• Ex 3) Add.

726

7215

795

75

74

32

753

742

Operations with Mixed Numbers• Ex 3) Add.

726

7215

795

75

74

32

753

742

Operations with Mixed Numbers• Ex 5) Add.

548

736

Operations with Mixed Numbers• Ex 5) Add.

35288

35156

548

736

Operations with Mixed Numbers• Ex 5) Add.

354314

35288

35156

548

736

Operations with Mixed Numbers• Ex 5) Add.

35815

354314

35288

35156

548

736