Add Fractions and Mixed Numbers

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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

Mr. Green’s Pizza =

Mr. Green’s Pizza = Mr. Black’s Pizza =

Can we say that there are 3 slices left?

Can we say that there are 3 slices left? No, because that would ignore the fact that they are different sizes.

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?

We need to change the leftover amounts so that they are in pieces of the same size.

Mr. Black’s Pizza =

Now that we are dealing with pieces of the same size, we can add the amounts together:

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

Remember, just add the numerators!

We can now describe the leftover amount.83

We can now describe the leftover amount.

There is 11/12 of a pizza left.

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

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?

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

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

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

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . 83

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, . . . Multiples of 4:

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.

We can also find the LCM by using prime factorizations:

Ex) Find the LCM of 21 and 28.

21 = 3 x 783

21 28 = 3 x 7 83

21 28 = 3 x 7 = 4 x 7 83

21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 783

21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 7Now, compare them:83

21 28 = 3 x 7 = 4 x 7 = 2 x 2 x 7Now, compare them:

21 = 3 x 783

21 = 3 x 728 = 7 x 2 x 2

LCM = 3 x 7 x 2 x 2 = 84

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

This can be reduced.83

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How did we know to divide by 2?

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How did we know to divide by 2? Two is the greatest common factor of 14 and 30.

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How did we know to divide by 2? Two is the greatest common factor of 14 and 30. GCF(14, 30) = 2

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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

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how many slices do they have?

They have 25 slices of pizza.

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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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They would have needed 6 boxes.

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Operations with Mixed Numbers• Ex 3) Add.

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Add Fractions and Mixed Numbers

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