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NOTES: Adding Fractions

2. Sylvia went to Florida on vacation. She spent of a day on the beach and of the day at a park. What fraction of the day did she spend outdoors?. 5. 1. 5. 7.

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NOTES: Adding Fractions

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  1. 2 Sylvia went to Florida on vacation. She spent of a day on the beach and of the day at a park. What fraction of the day did she spend outdoors? 5 1 5 7 Xavier received 2 gift cards on his birthday. He used of one card on clothes and of the other card on shoes. What fraction represents how much he used altogether? 10 4 10

  2. NOTES: Adding Fractions • Steps: • Find common denominator (if needed). • 2. Add numerators. • Keep denominator! • ALWAYS simplify!

  3. Layout your fraction circles. Three Thirds One Whole Two Halves Six Sixths Four Fourths Five Fifths Eight Eighths Ten Tenths Twelve Twelfths

  4. So far, we have been… Adding Fractions with Common Denominators. 2 1 3 + = 5 5 5 5 is the common denominator 7 4 11 + = 10 10 10 10 is the common denominator • Notice: The denominator stays the same. • Simply add the numerators. 11 Note: is an improper fraction. Improper fractions have “numerators greater than or equal to” their denominators. 10

  5. Improper fractions can be “written as a combination of whole numbers and fractions” known as mixed numbers. Think back to the example with 2 gift cards. Combine the parts used. 11 10 1 1 1 1 1 = + = + = 10 10 10 10 10 improper fraction mixed number

  6. To make the improper fraction a mixed number, we divided. 11 1 1 = 10 10 improper fraction mixed number 1 10 11 10 1 10 goes into 11 one whole time with a remainder of 1.

  7. Now let’s find the sum of fractions with different denominators. Use your knowledge of fractions and number lines to model the following situations and solutions. 1 Pete was able to mow of the lawn before having to get more gas. He then mowed of the lawn. How much has he mowed altogether? 2 2 5 Remember, the denominator “shows the total number of parts.” 1 2 + 2 5 Notice: We are working with number lines that “have different numbers of parts.” 5 total parts 2 total parts 0 1 0 1 2 2 2 2 0 1 + 0 5 1 2 3 4 5 5 5 5 5 5

  8. Remember that with common denominators, the denominator stays the same. Simply add the numerators. 1 2 Let’s find a common denominator for and . 2 5 For maximum efficiency, let’s find the Least Common Denominator for and . This will make our calculations as simple as possible. 1 2 2 5

  9. Finding Common Denominators Step 1: List multiples of each denominator. Step 2: Highlight common multiples. Step 3: The Least Common Denominator (LCD) “is the Least Common Multiple (LCM) of their denominators.” Step 4: The “fractions can be replaced by fractions having the same denominator,” the LCD.

  10. Step 1: List multiples of each denominator. 2 5 Finding Common Denominators 2 5 4 10 10 is the LCD 6 8 10 Step 2: Highlight common multiples. Step 3: The Least Common Denominator (LCD) “is the Least Common Multiple (LCM) of their denominators.”

  11. Note: The goal of step 1 is to find the Least Common Denominator, so it is not necessary to create an over exhausted list of multiples. Finding Common Denominators Continued… Step 4: The “fractions can be replaced by fractions having the same denominator,” the LCD. 1 ? 5 2 ? 4 = = **Notice: These are equivalent fractions. 10 10 2 5

  12. 5 4 = + With 10 as the common denominator, 10 10 0 1 + 0 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 10 10 10

  13. 1 2 9 + = 2 5 10 5 9 4 + = 10 10 10

  14. A baseball game consists of 9 innings. Last week, Brandon watched of a game. This week, he saw 2 innings. How much total game time has he viewed? 1 3 Let’s try another example. 1 2 + 3 9 0 1 0 3 1 2 3 3 3 3 0 1 + 0 1 2 4 5 7 8 9 3 6 9 9 9 9 9 9 9 9 9 9

  15. 1 2 Add and by finding the Least Common Denominator. 3 9 3 9 Step 1: List multiples of each denominator. Step 2: Highlight common multiples. Step 3: The Least Common Denominator (LCD) “is the Least Common Multiple (LCM) of their denominators.” Step 4: The “fractions can be replaced by fractions having the same denominator,” the LCD. 3 9 6 9 is the LCD 9 2 1 ? 3 = stays the same 9 3 9 + 3 2 5 + = 9 9 9

  16. EXAMPLES: Adding Fractions 2. 3 x3 x3 1

  17. NOTES: Adding Mixed Numbers • Steps: • Change to common denominator (if needed). • 2. Add whole numbers & numerators! • Keep denominator. • ALWAYS simplify!

  18. EXAMPLES: Adding Mixed #’s 2 1. x2 x2 3

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