Page ANSWERS Student Learning Goal Chart Lesson Reflection
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Page ? ? #? -? ? ANSWERS
Student Learning Goal Chart Lesson Reflection
Pre-Algebra Learning Goal Student will understand rational and real numbers.
Students will understand 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)
3 -5 Adding and Subtracting with Unlike Denominators Today’s Learning Goal Assignment Learn to add and subtract fractions with unlike denominators. Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators Vocabulary least common denominator (LCD) 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. Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators Lesson Quiz: Part 1 Add or subtract. 1. 5 1 + 14 7 2. 2 83 3. 3 5 1 2 12 – 1 + 7 1 – 2 15 – 2 23 38 4. Evaluate 1 – n for n = Pre-Algebra 1 6 9. 16 13 16
3 -5 Adding and Subtracting with Unlike Denominators Lesson Quiz: Part 2 1 62 inches tall. Judy is 5 5. Robert is 5 feet 3 4 inches tall. How much taller is Robert than Judy? 3 24 Pre-Algebra in.
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! Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators Pre-Algebra HW: page 7? ? #? -? ? (3 -1, 3 -2, 3 -5) Page ? ? #? -? ? Pre-Algebra
Adding and Subtracting with 3 -5 Unlike Denominators Warm Up Problem of the Day Lesson Presentation Pre-Algebra Unlike
3 -5 Adding and Subtracting with Unlike Denominators Warm Up Add or subtract. 1. 1 35 +– 2 5 7 2. 3 11 12 – 2 12 1 15 1 13 3. 6. 5 + – 1. 2 5. 3 4. 3. 4 – 0. 9 2. 5 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 Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators Today’s Learning Goal Assignment Learn to add and subtract fractions with unlike denominators. Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators Vocabulary least common denominator (LCD) Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators 1 3 A pattern for a double-circle skirt requires 9 yards of 45 -inch-wide material. To add a 2 ruffle takes another 2 5 yards. If the total amount of material for the skirt and ruffle are 1 cut from a bolt of fabric 15 2 yards long, how much fabric is left? 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. Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators Additional Example 1 A: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 1: A. Pre-Algebra 2 1 + 7 8 2 8 1 7 + 7 8 8 7 Find a common denominator: 8(7)=56. Multiply by fractions equal to 1. 7 16 23 = + 56 56 56 Rewrite with a common denominator. Simplify
3 -5 Adding and Subtracting with Unlike Denominators Additional Example 1 B: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2: Write as an improper fraction. 1 5 B. 1 6 + 8 List the multiples of each 7 6 + 5 8 5 3 7 4 Remember! 6 4 +8 3 denominator and find the LCD Multiples of 6: 6; 12; 24; 30 Multiples of 8: 8; 16; 24; 32 Multiply by fractions equal to 1. The least common multiple of two numbers is the a acommon 28 smallest 15 43 19 Rewrite number other than zerowith that is multiple of = 24 = 1 24 denominator. Simplify. 24 + the 24 two numbers. Pre-Algebra
3 -5 Adding and Subtracting with Unlike Denominators Try This: Example 1 A Add or Subtract. Method 1: 5 1 A. 3 + 8 1 8 5 3 + 3 8 8 3 8 23 15 = + 24 24 24 Pre-Algebra Find a common denominator 3(8)=24. Multiply by fractions equal to 1. Rewrite with a common denominator.
3 -5 Adding and Subtracting with Unlike Denominators Try This: Example 1 B Add or Subtract. Method 2: B. 1 26 13 6 26 12 13 6 2 2 + 9 12 Pre-Algebra + 3 4 Write as an improper fraction. List the multiples of each denominator and find the LCD Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 3 3 Multiply by fractions equal to 1. Rewrite with a common 35 = 12 = 2 11 12 denominator. Simplify.
3 -5 Adding and Subtracting with Unlike Denominators Additional Example 2: Evaluating Expressions with Rational Numbers 4 Evaluate t – 5 5 for t =. 6 4 5 – 5 6 Substitute 4 6 5 5 – 5 6 6 5 Multiply by fractions equal to 1. 1 25 24 = – 30 30 30 Rewrite with a common denominator: 6(5) = 30. Pre-Algebra 5 6 for n.
3 -5 Adding and Subtracting with Unlike Denominators Try This: Example 2 Evaluate 5 9 – h for h – 7 = 12 . – – 7 12 Substitute + 7 12 5 9 5 4 9 4 20 36 5 9 + + 41 36 Pre-Algebra or 7 3 12 3 21 36 5 1 36 – – 7 12 = – 7 12 5 9 for h. 7 + 12 Multiply by fractions equal to 1. Rewrite with lowest common denominator (36). Simplify.
Adding and Subtracting with 3 -5 Unlike Denominators Additional Example 3: Consumer Application Two dancers are making necklaces from ribbon for their costumes. They need pieces measuring 3 7 13 4 inches and 12 8 inches. How much ribbon will be left over after the pieces are cut from a 36 -inch length? Subtract both amounts 3 7 36 – 12 8 – 13 4 from 36 to find the amount of ribbon left. Write as improper fractions. 288 103 55 – 8 – 4 8 The LCD is 8. Rewrite with a common 110 288 103 – 8 denominator. Simplify. 8 75 , 8 Pre-Algebra or 9 38 3 There will be 9 8 inches left.
3 -5 Adding and Subtracting with Unlike Denominators Try This: Example 3 Fred and Jose are building a tree house. They 3 need to cut a 6 4 foot piece of wood and a 4 5 12 foot piece of wood from a 12 foot board. How much of the board will be left? 12 – 144 12 3 64 – 27 4– 53 12 144 81 4 – 12 10 , 12 Pre-Algebra – 5 412 or 5 6 – 53 12 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. 5 There will be 6 inches left.
3 -5 Adding and Subtracting with Unlike Denominators Lesson Quiz: Part 1 Add or subtract. 1. 5 1 + 14 7 2. 2 83 3. 3 5 1 2 12 – 1 + 7 1 – 2 15 – 2 23 38 4. Evaluate 1 – n for n = Pre-Algebra 1 6 9. 16 13 16
3 -5 Adding and Subtracting with Unlike Denominators Lesson Quiz: Part 2 1 62 inches tall. Judy is 5 5. Robert is 5 feet 3 4 inches tall. How much taller is Robert than Judy? 3 24 Pre-Algebra in.