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Pre-Algebra Lesson: Adding and Subtracting with Unlike Denominators

This pre-algebra lesson focuses on teaching students how to add and subtract fractions with unlike denominators. Students will learn to find the least common denominator and use it to solve problems. The lesson includes examples, practice exercises, and a quiz.

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Pre-Algebra Lesson: Adding and Subtracting with Unlike Denominators

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  1. Page ?? #?-?? ANSWERS

  2. Student Learning Goal Chart Lesson Reflection

  3. Pre-Algebra Learning GoalStudent will understand rational and real numbers.

  4. 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)

  5. Today’s Learning Goal Assignment Learn to add and subtract fractions with unlike denominators.

  6. Vocabulary least common denominator (LCD)

  7. 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.

  8. 12 1 6 7 1 15 –2 13 16 Lesson Quiz: Part 1 Add or subtract. 5 14 1 7 1. + 12 2 3 – 2. 1 8 3 5 2 3 3. –2 + 9 16 38 4.Evaluate – n for n = . 1

  9. 3 4 2 in. Lesson Quiz: Part 2 12 Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 5. 3 4

  10. 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!

  11. Pre-Algebra HW: page 7?? #?-?? (3-1, 3-2, 3-5) Page ?? #?-??

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

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

  14. 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

  15. Today’s Learning Goal Assignment Learn to add and subtract fractions with unlike denominators.

  16. Vocabulary least common denominator (LCD)

  17. 1 3 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? 2 5 1 2

  18. 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.

  19. 8 8 7 7 2 7 1 8 + 7 56 16 56 23 56 = + Additional Example 1A: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 1: 2 7 1 8 Find a common denominator: 8(7)=56. A. + Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify

  20. 7 6 5 8 + Multiples of 6: 6; 12; 24; 30 Multiples of 8: 8; 16; 24; 32 4 4 5 8 3 3 7 6 + Remember! The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers. 28 24 15 24 43 24 19 24 = = 1 + Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2: Write as an improper fraction. 1 6 5 8 B. 1 + List the multiples of each denominator and find the LCD Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify.

  21. 8 8 1 3 3 3 5 8 + 8 24 23 24 15 24 = + Try This: Example 1A Add or Subtract. Method 1: Find a common denominator 3(8)=24. 5 8 1 3 + A. Multiply by fractions equal to 1. Rewrite with a common denominator.

  22. 3 4 13 6 + Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 2 2 13 6 33 3 4 + 26 12 35 12 9 12 11 12 = 2 = + Try This: Example 1B Add or Subtract. Method 2: Write as an improper fraction. 1 6 3 4 B. 2 + List the multiples of each denominator and find the LCD Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify.

  23. 4 5 5 6 5 6 – Substitute for n. 6 6 5 5 4 5 5 6 – 1 30 25 30 24 30 = – Additional Example 2: Evaluating Expressions with Rational Numbers 4 5 5 6 Evaluatet –for t = . Multiply by fractions equal to 1. Rewrite with a common denominator: 6(5) = 30.

  24. –7 12 5 9 –7 12 – Substitute for h. –7 12 5 9 5 9 5 9 7 12 7 12 + + = – 4 4 3 3 5 9 7 12 + 20 36 21 36 + 41 36 5 36 or 1 Try This: Example 2 5 9 –7 12 Evaluate– h for h = . Multiply by fractions equal to 1. Rewrite with lowest common denominator (36). Simplify.

  25. 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? 3 4 7 8 3 4 7 8 36 – 12 – 13 55 4 288 8 103 8 – – 110 8 288 8 103 8 – – 75 8 3 8 3 8 , or 9 There will be 9 inches left. 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. Rewrite with a common denominator. Simplify.

  26. 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? 3 4 5 12 5 12 3 4 12 – 6 – 4 53 12 144 12 27 4 – – 53 12 144 12 81 4 – – 5 6 10 12 5 6 , or There will be inches left. Try This: Example 3 Subtract both amounts from 12 to find the amount of board left. Write as improper fractions. The LCD is 12. Rewrite with a common denominator. Simplify.

  27. 12 1 6 7 1 15 –2 13 16 Lesson Quiz: Part 1 Add or subtract. 5 14 1 7 1. + 12 2 3 – 2. 1 8 3 5 2 3 3. –2 + 9 16 38 4.Evaluate – n for n = . 1

  28. 3 4 2 in. Lesson Quiz: Part 2 12 Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 5. 3 4

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