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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up A proper fraction has an odd number as the numerator and 10 as the denominator. This fraction is divided by a proper fraction with denominator 5. Will the denominator of the quotient be odd or even? Explain and show examples.

  3. California Standards NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. NS2.2 Add and subtract fractions by using factoring to find a common denominator.

  4. To add and subtract fractions with unlike denominators, first find a common denominator using one of these methods: Method 1 Find a common denominator by multiplying the denominators. Method 2 Find the least common denominator (LCD).

  5. 8 8 7 7 2 7 1 8 + = 7 56 16 56 + = 7 + 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. + Multiply by fractions equal to 1. Rewrite with a common denominator. Add numerators. Keep the denominator.

  6. 13 8 7 6 – = Multiples of 6: 6, 12, 18, 24, 30 Multiples of 8: 8, 16, 24, 32 4 4 13 8 3 3 7 6 – = 11 24 28 24 39 24 = – – 28 – 39 24 = = Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators Add or subtract. Method 2: Write as improper fractions. 1 6 5 8 – 1 1 List the multiples of each denominator and find the LCD. Multiply by fractions equal to 1. Rewrite with the LCD. Subtract numerators. Keep the denominator.

  7. 8 8 1 3 3 3 5 8 + = 23 24 8 24 15 24 + = = 8 + 15 24 = Partner Share! Example 1A Add or subtract. Method 1: Find a common denominator: 3(8)=24. 5 8 1 3 + Multiply by fractions equal to 1. Rewrite with the LCD. Add numerators. Keep the denominator.

  8. = 3 4 13 6 + Multiples of 6: 6, 12, 18, 24, 30 Multiples of 4: 4, 8, 12, 16 2 2 = 13 6 33 3 4 + 26 12 9 12 + = 11 12 35 12 = 2 = 26 + 9 12 = Partner Share! Example 1B Add or subtract. Method 2: Write as an improper fraction. 1 6 3 4 2 + List the multiples of each denominator and find the LCD Multiply by fractions equal to 1. Rewrite with the LCD. Add numerators. Keep the denominator.

  9. Factors of 56: 2 ∙ 2 ∙ 2 ∙ 7 Factors of 84: 2 ∙ 2 ∙ 3 ∙ 7 Additional Example 2: Using Factoring to Find the LCD 25 56 37 84 Find + . Write the answer in simplest form. Write the prime factorization of each denominator. Circle the common factors. List all the prime factors of the denominators, using the circled factors only once. 2, 2, 2, 7, 3 Multiply. 2 ∙ 2 ∙ 2 ∙ 7 ∙ 3 = 168 The LCD is 168.

  10. 37 84 25 56 = + 74 168 75 168 = + 149 168 = 3 3 2 2 Additional Example 2 Continued 25 56 37 84 Find + . Write the answer in simplest form. 168 ÷ 56 = 3 168 ÷ 84 = 2 Multiply by fractions equal to 1 to get a common denominator. Rewrite using the LCD. Add numerators. Keep the denominator.

  11. 9 80 19 32 Factors of 32: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 Factors of 80: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 Partner Share! Example 2 Find + . Write the answer in simplest form. Write the prime factorization of each denominator. Circle the common factors. List all the prime factors of the denominators, using the circled factors only once. 2, 2, 2, 2, 2, 5 Multiply. 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2∙ 5 = 160 The LCD is 160.

  12. 9 80 19 32 9 80 19 32 = + 18 160 95 160 = + 113 160 = 5 5 2 2 Partner Share! Example 2 Continued Find + . Write the answer in simplest form. 160 ÷ 32 = 5 160 ÷ 80 = 2 Multiply by fractions that equal to 1 to get a common denominator. Rewrite using the LCD. Add numerators. Keep the denominator.

  13. 3 4 7 8 3 4 7 8 36 – 12 –13 55 4 36 1 103 8 – – = 110 8 288 8 103 8 – – = 3 8 There will be 9 inches left. 75 8 3 8 , or 9 = Additional Example 3: Consumer Application 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? Subtract both amounts from 36 to find the amount of ribbon left. Write as improper fractions. The LCD is 8. Simplify.

  14. 3 4 5 12 5 12 3 4 12 – 6 – 4 = 53 12 12 1 27 4 – – = 53 12 144 12 81 12 – – 5 6 10 12 5 6 = , or There will be foot left. Partner Share! Example 3 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? Subtract both amounts from 12 to find the amount of board left. Write as improper fractions. The LCD is 12. Simplify.

  15. 4 5 4 5 5 6 t – = 5 6 – Substitute for t. 6 6 5 5 4 5 5 6 – = 25 30 24 30 – = 1 30 = Additional Example 4: Evaluating Expressions with Rational Numbers 4 5 5 6 Evaluate t –for t = . Multiply by fractions equal to 1. Rewrite with a common denominator: 6(5) = 30. Simplify.

  16. 7 12 7 12 Substitute – for h. Partner Share! Example 4 5 9 Evaluate – h for h =– . Multiply by fractions equal to 1. Rewrite with the LCD. Simplify.

  17. 12 1 6 7 3 4 2 in. 1 15 –2 13 16 Lesson Review! Add or subtract. 5 14 1 7 1. + 12 2 3 – 2. 1 8 3 5 2 3 3. –2 + 9 16 3 8 4.Evaluate – n for n = . 1 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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