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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. 4 3. 2 3. 2 3. 9. =. 12. 21 +. +. 1 3.

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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. 4 3 2 3 2 3 9 = 12 21 + + 1 3 = 21 + 1 1 3 = 22 Example 1A: Adding Mixed Numbers Add. Write the answer in simplest form. 2 3 2 3 + 12 9 Add the integers, and then add the fractions. Rewrite the improper fraction as a mixed number. Add.

  3. 3 24 1 8 20 24 5 6 + 3 5 = 5 + 3 23 24 = 8 + 23 24 = 8 Example 1B: Adding Mixed Numbers Add. Write the answer in simplest form. 1 8 5 6 5 + 3 Find a common denominator. Add the integers, and then add the fractions. Add.

  4. 1 8 1 8 = 6 + 1 + 7 1 8 8 8 + = 6 + 9 8 = 6 Sometimes when you subtract mixed numbers, the fraction portion of the first number is less than the fraction portion of the second number. In these cases, you must regroup before subtracting. REGROUPING MIXED NUMBERS WORDS NUMBERS Regroup. Rewrite 1 as a fraction with a common denominator. Add.

  5. Remember! Any fraction in which the numerator and denominator are the same nonzero number is equal to 1.

  6. 2 3 1 3 = 4 2 – 1 3 2 Example 2A: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. 1 3 2 3 2 4 – Subtract the integers, and then subtract the fractions. + 1 3 2 Add (combine integer and fraction .

  7. 8 9 6 9 8 9 2 3 = 8 12 12 8 – – 2 9 = 4 Example 2B: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. 2 3 8 9 8 12 – Find a common denominator. Subtract the integers, and then subtract the fractions.

  8. 1 8 1 8 8 8 1 8 3 8 9 8 3 8 = 16+ – + Regroup 17 . 17 – 12 = 16 12 6 8 3 4 = = 4 4 Example 2C: Subtracting Mixed Numbers Subtract. Write the answer in simplest form. WRITE THIS AT THE TOP OF YOUR PAGE 1 8 3 8 BORROWING (regrouping) – 17 12 Subtract the integers, and then subtract the fractions. Simplify.

  9. 3 8 5 8 Kevin is 48 inches tall. His brother Keith is 5 inches taller. How tall is Keith? 1 2 1 2 3 8 5 8 1 2 1 2 + Round to and to . 5 = 54 48 Example 3: Measurement Application Add the integers, and then add the fractions. 8 8 3 8 5 8 + 5 48 + = 53 8 8 Rewrite as 1. 53 + 1 = Keith is 54 inches tall. Estimate 54 equals 54, so the answer is reasonable.

  10. 6 5 4 5 2 5 7 = 10 17 + + 1 5 = 17 + 1 1 5 = 18 Check It Out! Example 1 Add. Write the answer in simplest form. 2 5 4 5 + 10 7 Add the integers, and then add the fractions. Rewrite the improper fraction as a mixed number. Add.

  11. 1 4 1 4 4 4 = 13+ + Regroup 14 . 1 4 3 4 5 4 3 4 13 – 14 – 10 = 10 2 4 1 2 = 3 = 3 Check It Out! Example 2C Subtract. Write the answer in simplest form. 1 4 3 4 – 14 10 Subtract the integers, and then subtract the fractions. Simplify.

  12. 1 3 Round 72 to 73 and 15 to 15. 2 3 Check It Out! Example 3 Alvin weighs 72 lbs. His baby brother weighs 15 lbs. How much do they weigh together? 2 3 1 3 1 3 Add the integers, and then add the fractions. 3 3 2 3 + 15 72 87 + = 3 3 as 1. Rewrite 87 + 1 = Together they weigh 88 pounds. Estimate 73 + 15 = 88 88 equals 88, so the answer is reasonable.

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