 # Adding and Subtracting Mixed Numbers

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Adding and Subtracting Mixed Numbers
I can subtract fractions expressing solutions in simplest form. G5.1M.C2.PO1B

Essential Questions 1. What are positive fractions? How do we add and subtract them? 2. What are unlike denominators? How do we find a common denominator? 3. What is simplification? How do we simplify? 4. What are lowest terms? How do we reduce a fraction? 5. What is a mixed number? How do we convert it into an improper fraction? 6. What is an improper fraction? How do we convert it into a mixed number? 7. What is regrouping? How do we borrow from a mixed number? 8. What is a division line? Why do we use it to represent a fraction? 9. What is a numerator? How is it different from a denominator? 10. What is a denominator? Why do we use common denominators?

Anticipatory Set On your slate:
What is a least common denominator? and How do you find it? Share with your shoulder partner

Separate the whole number parts from the fraction parts. Find common denominators for the fractions and then add them. Add the whole numbers together. Simplify.

Example 9 9 3 9 12 4 3 3 5 10 + 12 6 12 19 12 The LCM of 4 and 6 is 12.

Now, Simplify 1 12 19 12 19 12 12 7 12 + 1 7 = 13 7 12 12

Your Turn: 2 1/ /3 = 3 4/ /6 = 1 1/ /2 =

Subtracting Mixed Numbers-Process:
Use the least common multiple to write equivalent fractions if the denominators are not the same. Subtract numerators. If you cannot subtract numerators, then rename the first mixed number. Subtract whole numbers. Simplify.

Borrowing not required:
7 7 3 6 4 8 5 5 5 5 8 8 2 1 8 This answer is in simplest form.

A Picture of Renaming: 3 1 3 1 5 6 This is a picture of three and one third. We want to take away one whole and five sixths. To do this, we need to rename to sixths. Now we can cross out five of the sixths. We have subtracted the fractions. Now subtract the wholes. Take away one whole. Now we have two sixths, but we need to take away five sixths. We don’t have enough sixths. Rename one whole to six sixths. We are left with one whole and three sixths.

Rename Mathematically:
2 3 x 2 1 3 8 1 = 2 6 3 6 6 1 1 5 x 1 5 6 6 1 = 3 We already had two sixths, and now we have borrowed one whole, which is six more sixths. The LCM of 3 and 6 is 6. 6 We have equivalent fractions, but we don’t have enough sixths to subtract. 1 Two and six are eight. We now have eight sixths. 1 Borrow from the whole number. Rename the whole as six sixths. 2 Subtract the fractions, then the whole numbers. Simplify.

8 1 = 9 9 4 4 4 Another Example: x 7 x 2 The LCM of 2 and 7 is 14.
21 1 x 7 7 14 2 x 2 4 4 10 5 14 7 The LCM of 2 and 7 is 14. 4 11 14 This answer is in simplest form. We do not have enough fourteenths, so we must borrow from the 9.

Subtracting from a whole number:
If you are subtracting a mixed number from a whole number, then rename the whole number. Borrow one whole and use the denominator from the fraction.

We choose eight eighths because the denominator of the fraction is 8.
Example: 7 1 = 8 8 8 8 8 3 We choose eight eighths because the denominator of the fraction is 8. 5 8 4 3 8

Your Turn: 5 1/ /4 = 2 2/ /6 = 4 1/ /3 =

Closure: On your slates explain the steps of adding mixed numbers.
Share with your shoulder partner On your slate explain the steps of subtracting mixed numbers. Share with you face partner

Brain Pop Adding and subtracting fractions