2. Page ?? #?-?? ANSWERS

3. Student Learning Goal Chart Lesson Reflection

4. Pre-Algebra Learning Goal Student will understand rational and real numbers.

5. Students will understand BLAH BLAH BLAH by being able to do the following: Learn to write rational numbers in equivalent forms (3.1) Learn to add and subtract decimals and rational numbers with like denominators (3.2) Learn to add and subtract fractions with unlike denominators (3.5)

6. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Today’s Learning Goal Assignment Learn to add and subtract fractions with unlike denominators.

7. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators least common denominator (LCD) Vocabulary

8. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators To solve this problem, add and subtract rational numbers with unlike denominators. First find a common denominator using one of the following methods: Method 1 Find a common denominator by multiplying one denominator by the other denominator. Method 2 Find the least common denominator (LCD); the least common multiple of the denominators.

10. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Add or subtract. 1. + 5 14 1717 13 16 2. 1212 2323 8 1 – 7 1616 3. –2 + 3535 2323 4. Evaluate – n for n =. 1 3838 9 16 Lesson Quiz: Part 1 –2 1 15 1212

11. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Lesson Quiz: Part 2 Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 5. 3434 1212 2 in. 3434

12. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Are you ready for the FAST Track? If YES, prepare for Ch. 3 Section 3 YES, BACK to Ch. 3 Section 3! If NO, continue with the Ch. 3 Section 5 lesson!

13. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Pre-Algebra HW: page 7?? #?-?? (3-1, 3-2, 3-5) Page ?? #?-??

14. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators 3-5 Adding and Subtracting with Unlike Denominators Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

15. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1 Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators

16. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Problem of the Day A school installed a new phone system with four-digit extensions. How many extensions are possible? all numbers from 0000 to 9999, or 10,000

17. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Today’s Learning Goal Assignment Learn to add and subtract fractions with unlike denominators.

18. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators least common denominator (LCD) Vocabulary

19. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators A pattern for a double-circle skirt requires 9 yards of 45-inch-wide material. To add a ruffle takes another 2 yards. If the total amount of material for the skirt and ruffle are cut from a bolt of fabric 15 yards long, how much fabric is left? 1313 2525 1212

20. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators To solve this problem, add and subtract rational numbers with unlike denominators. First find a common denominator using one of the following methods: Method 1 Find a common denominator by multiplying one denominator by the other denominator. Method 2 Find the least common denominator (LCD); the least common multiple of the denominators.

21. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Find a common denominator: 8(7)=56. 2727 + 1818 Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify Additional Example 1A: Adding and Subtracting Fractions with Unlike Denominators 2727 + 1818 78 23 56 = 16 56 + 7 56 A. Add or Subtract. Method 1:

22. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers. Remember! 1616 1 + 5858 List the multiples of each denominator and find the LCD Write as an improper fraction. Multiples of 6: 6; 12; 24; 30 Multiples of 8: 8; 16; 24; 32 Rewrite with a common denominator. 5858 + 767643 43 24 = 15 24 + 28 24 19 24 = 1 Multiply by fractions equal to 1. Simplify. 5858 + 7676 B. Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2:

23. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Find a common denominator 3(8)=24. 5858 + 1313 Multiply by fractions equal to 1. Rewrite with a common denominator. 23 24 Try This: Example 1A Add or Subtract. Method 1: = 15 24 + 8 24 A. 5858 + 131383

24. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators 1616 2 + 3434 List the multiples of each denominator and find the LCD Write as an improper fraction. Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 Rewrite with a common denominator. Multiply by fractions equal to 1. Simplify. 3434 + 13 6 3434 + 23 B. 11 12 = 2 35 12 = 9 12 + 26 12 Try This: Example 1B Add or Subtract. Method 2:

25. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Evaluate t – for t =. Additional Example 2: Evaluating Expressions with Rational Numbers 4545 – 5656 24 30 – 25 30 1 30 = Multiply by fractions equal to 1. 4545 5656 Substitute for n. 5656 Rewrite with a common denominator: 6(5) = 30. 4545 – 5656 56

26. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Evaluate – h for h =. Try This: Example 2 Multiply by fractions equal to 1. 5959 –7 12 Substitute for h. –7 12 Rewrite with lowest common denominator (36). –7 12 – 5959 7 12 + 5959 = Simplify. 41 36 or 1 5 36 21 36 + 20 36 –7 12 – 5959 7 12 + 5959 + 595943

27. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Additional Example 3: Consumer Application Subtract both amounts from 36 to find the amount of ribbon left. Write as improper fractions. The LCD is 8. 36 – 12 – 13 7878 3434 Rewrite with a common denominator. Simplify., or 9 3838 75 8 There will be 9 inches left. 3838 103 8 288 8 –– 110 8 103 8 55 4 288 8 –– Two dancers are making necklaces from ribbon for their costumes. They need pieces measuring 13 inches and 12 inches. How much ribbon will be left over after the pieces are cut from a 36-inch length? 7878 3434

28. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Try This: Example 3 Subtract both amounts from 12 to find the amount of board left. Write as improper fractions. The LCD is 12. 12 – 6 – 4 3434 5 12 Rewrite with a common denominator. Simplify., or 5656 10 12 There will be inches left. 5656 81 4 144 12 –– 53 12 27 4 53 12 144 12 –– Fred and Jose are building a tree house. They need to cut a 6 foot piece of wood and a 4 foot piece of wood from a 12 foot board. How much of the board will be left? 5 12 3434

29. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Add or subtract. 1. + 5 14 1717 13 16 2. 1212 2323 8 1 – 7 1616 3. –2 + 3535 2323 4. Evaluate – n for n =. 1 3838 9 16 Lesson Quiz: Part 1 –2 1 15 1212

30. Pre-Algebra 3-5 Adding and Subtracting with Unlike Denominators Lesson Quiz: Part 2 Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 5. 3434 1212 2 in. 3434