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Pre-Algebra

Learn to add and subtract fractions with unlike denominators. Adding and Subtracting with Unlike Denominators. 3-5. Pre-Algebra. Adding and Subtracting with Unlike Denominators. 3-5. Pre-Algebra. 1 3.

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Pre-Algebra

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  1. Learn to add and subtract fractions with unlike denominators. Adding and Subtracting with Unlike Denominators 3-5 Pre-Algebra

  2. Adding and Subtracting with Unlike Denominators 3-5 Pre-Algebra 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

  3. Adding and Subtracting with Unlike Denominators 3-5 Pre-Algebra 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 quick 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.

  4. 7 56 Adding and Subtracting with Unlike Denominators 8 8 16 56 7 7 23 56 2 7 1 8 3-5 = + + Pre-Algebra Example 1A: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 1: 2 7 1 8 Find a quick common denominator: 8(7)=56. A. + Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify

  5. 28 24 Remember! 7 6 Multiples of 6: 6; 12; 24; 30 4 4 19 24 5 8 5 8 Adding and Subtracting with Unlike Denominators 3 3 7 6 15 24 43 24 = 1 = + + 3-5 + The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers. Multiples of 8: 8; 16; 24; 32 Pre-Algebra 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.

  6. 4 5 Adding and Subtracting with Unlike Denominators 6 6 5 6 1 30 5 6 5 5 4 5 5 6 25 30 24 30 Substitute for t. 3-5 – – = – Pre-Algebra 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.

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

  9. 41 36 5 9 4 4 –7 12 –7 12 7 12 Adding and Subtracting with Unlike Denominators 5 36 –7 12 20 36 21 36 3 3 5 9 5 9 7 12 5 9 5 9 7 12 + Substitute for h. + or 1 – + + = – 3-5 Pre-Algebra Try This Together: Example 2 5 9 –7 12 Evaluate– h for h = . Multiply by fractions equal to 1. Rewrite with lowest common denominator (36). Simplify.

  10. 3 4 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? 7 8 75 8 Adding and Subtracting with Unlike Denominators 55 4 110 8 3 8 3 4 288 8 3 8 103 8 288 8 103 8 7 8 , or 9 – – – – 36 – 12 – 13 There will be 9 inches left. 3-5 Pre-Algebra 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.

  11. 3 4 Sam and Josh 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 10 12 5 12 3 4 Adding and Subtracting with Unlike Denominators 53 12 53 12 5 6 144 12 5 6 27 4 144 12 81 4 , or – – – – 12 – 6 – 4 There will be foot left. 3-5 Pre-Algebra Try This Together: 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.

  12. Multiples of 6: 6; 12; 24; 30 26 12 2 2 11 12 3 4 Adding and Subtracting with Unlike Denominators 35 12 13 6 13 6 33 9 12 3 4 = 2 = + + 3-5 + Multiples of 4: 4; 8; 12; 16 Pre-Algebra 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.

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