1 / 13

California Standards

California Standards. NS1.2 Add and subtract rational numbers ( fractions ) NS2.2 Add and subtract fractions by using factoring to find a common denominator. Notes.

lara-morse
Download Presentation

California Standards

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. California Standards NS1.2 Add and subtractrational numbers (fractions) NS2.2 Add and subtract fractions by using factoring to find a common denominator.

  2. Notes 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).

  3. 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: Notes 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.

  4. 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: Notes 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.

  5. 8 8 1 3 3 3 5 8 + = 23 24 8 24 15 24 + = = 8 + 15 24 = Check It Out! Example 1A Add or subtract. Method 1: Rally Coach B 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.

  6. = 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 = Check It Out! Example 1B Add or subtract. Method 2: Rally Coach A 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.

  7. 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.

  8. 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.

  9. 9 80 19 32 Factors of 32: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 Factors of 80: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 Check It Out! Example 2 Elbow Partners Find + . Write the answer in simplest form. Write the prime factorization of each denominator. Circle the common factors. 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2∙ 5 = 160 Multiply. The LCD is 160.

  10. 9 80 19 32 9 80 19 32 = + 18 160 95 160 = + 113 160 = 5 5 2 2 Check It Out! 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.

  11. 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. Example 3 4 Steps 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.

  12. 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 Notes Evaluate t –for t = . Multiply by fractions equal to 1. Rewrite with a common denominator: 6(5) = 30. Simplify.

  13. 7 12 7 12 Substitute – for h. Check It Out! Example 4 5 9 Evaluate – h for h =– . Face Partners Multiply by fractions equal to 1. Rewrite with the LCD. Simplify.

More Related