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California Standards

California Standards. NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Also covered: NS2.4.

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California Standards

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  1. California Standards NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. Also covered: NS2.4

  2. To add and subtract fractions with like denominators, add or subtract the numerators and keep the common denominator.

  3. Example 1A: Adding and Subtracting Fractions with Like Denominators Add. Write the answer in simplest form. 5 8 1 8 + 5 + 1 5 8 1 8 Add the numerators and keep the common denominator. + = 8 3 4 6 8 = = Simplify.

  4. 5 11 = Example 1B: Adding and Subtracting Fractions with Like Denominators Subtract. Write the answer in simplest form. 9 11 4 11 – Subtract the numerators and keep the common denominator. 4 11 9 11 9 – 4 = – 11 The answer is in the simplest form.

  5. To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator.

  6. Helpful Hint The LCM of two denominators is the least common denominator (LCD) of the fractions.

  7. 9 12 8 12 – = 1 12 = Example 2A: Adding and Subtracting Fractions with Unlike Denominators Subtract. Write the answer in simplest form. 3 4 2 3 – Use Method 1: Multiply the denominators. 2  4 3  3 3 4 2 3 – – = 4  3 3 4 Write equivalent fractions using a common denominator. Subtract.

  8. In one Earth year, Jupiter completes about of itsorbit around the Sun, while Mars completes about of its orbit. How much more of its orbit does Mars complete than Jupiter? 1 2 1 12 1 12 1 2 1 6 1  1 12 1 – – = 2 6 1 12 6 12 = – 5 12 = 5 12 Mars completes more of its orbit than Jupiter does. Example 3: Astronomy Application Use Method 2: The LCM of the denominators is 12. Write equivalent fractions using a common denominator. Subtract.

  9. Check It Out! Example 1A Add. Write the answer in simplest form. 5 6 1 6 + 5 + 1 5 6 1 6 Add the numerators and keep the common denominator. + = 6 6 6 1 = = Simplify.

  10. 6 10 5 10 – = 1 10 = Check It Out! Example 2A Subtract. Write the answer in simplest form. 1 2 3 5 – 1  5 3  2 Use Method 1: Multiply the denominators. 3 5 1 2 – – = 5  2 2 5 Write equivalent fractions using a common denominator. Subtract.

  11. 5 12 5 12 1 2 1 6 5  1 12 1 – – = 2 6 5 12 6 12 = – 1 12 = 1 12 It takes Luke hour longer to drive to work. Check It Out! Example 3 It takes Michelle hour to drive to work. It takes Luke hour to drive to work. How much longer does it take Luke to drive to work? 1 2 The LCM of the denominators is 12. Write equivalent fractions using a common denominator. Subtract.

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