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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?**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? 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? Mr. Black’s Pizza = 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? Can we say that there are 3 slices left? Mr. Black’s Pizza = 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? Can we say that there are 3 slices left? No, because that would ignore the fact that they are different sizes. Mr. Black’s Pizza = 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? 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? Mr. Black’s Pizza = Mr. Green’s Pizza =**Add and Subtract Fractions**We need to change the leftover amounts so that they are in pieces of the same size. Mr. Black’s Pizza = Mr. Green’s Pizza =**Add and Subtract Fractions**We need to change the leftover amounts so that they are in pieces of the same size. Mr. Black’s Pizza = Mr. Green’s Pizza = =**Add and Subtract Fractions**We need to change the leftover amounts so that they are in pieces of the same size. Mr. Black’s Pizza = = Mr. Green’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: Mr. Black’s Pizza = = Mr. Green’s Pizza = =**Add and Subtract Fractions**Mr. Black’s Pizza = = Mr. Green’s Pizza = = Now that we are dealing with pieces of the same size, we can add the amounts together:**Add and Subtract Fractions**Mr. Black’s Pizza = 2/3 = 8/12 Mr. Green’s Pizza = 1/4 = 3/12 Now that we are dealing with pieces of the same size, we can add the amounts together:**Add and Subtract Fractions**Mr. Black’s Pizza = 2/3 = 8/12 Mr. Green’s Pizza = 1/4 = 3/12 Now that we are dealing with pieces of the same size, we can add the amounts together:**Add and Subtract Fractions**Mr. Black’s Pizza = 2/3 = 8/12 Mr. Green’s Pizza = 1/4 = 3/12 Now that we are dealing with pieces of the same size, we can add the amounts together:**Add and Subtract Fractions**Mr. Black’s Pizza = 2/3 = 8/12 Mr. Green’s Pizza = 1/4 = 3/12 Now that we are dealing with pieces of the same size, we can add the amounts together: Remember, just add the numerators!**Add and Subtract Fractions**Mr. Black’s Pizza = 2/3 = 8/12 Mr. Green’s Pizza = 1/4 = 3/12 Now that we are dealing with pieces of the same size, we can add the amounts together: We can now describe the leftover amount.**Add and Subtract Fractions**Mr. Black’s Pizza = 2/3 = 8/12 Mr. Green’s Pizza = 1/4 = 3/12 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.**Add and Subtract Fractions**When working with fractions, changing amounts into pieces of the same size is called finding a common denominator.**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?**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 multipleof 3 and 4.**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 multipleof 3 and 4. The LCM can be found by listing multiples:**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 multipleof 3 and 4. The LCM can be found by listing multiples: Multiples of 3:**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 multipleof 3 and 4. The LCM can be found by listing multiples: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . .**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 multipleof 3 and 4. The LCM can be found by listing multiples: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . Multiples of 4:**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 multipleof 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, . . .**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 multipleof 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, . . .**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 multipleof 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.**Add and Subtract Fractions**We can also find the LCM by using prime factorizations:**Add and Subtract Fractions**We can also find the LCM by using prime factorizations: Ex) Find the LCM of 21 and 28.**Add and Subtract Fractions**We can also find the LCM by using prime factorizations: Ex) Find the LCM of 21 and 28. 21**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 7**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**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**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 7**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 7 Now, compare them:**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 7 Now, compare them: 21 = 3 x 7**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 7 Now, compare them: 21 = 3 x 7 28 = 7 x 2 x 2**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 7 Now, compare them: 21 = 3 x 7 28 = 7 x 2 x 2**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 7 Now, compare them: 21 = 3 x 7 28 = 7 x 2 x 2 LCM = 3 x 7 x 2 x 2 = 84**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms.**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms. Ex)**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms. Ex)**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms. Ex)**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms. Ex) This can be reduced.**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms. Ex)**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms. Ex)**Add and Subtract Fractions**Sometimes, answers will need to be reduced to lowest terms. Ex) How did we know to divide by 2?**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.**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