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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, NS2.2.

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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, NS2.2

  2. Recall that multiplication can be written as repeated addition. For example, 3  5 = 5 + 5 + 5 = 15. You can use repeated addition to multiply a whole number by a fraction.

  3. 2 Think: How much is of 6? Use multiplication to find a fraction of a number. 3 2 2 2 2 2 2 2 6  + + + = + + 3 3 3 3 3 3 3 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 = 1 Example 1: Transportation Application In 2001, the car toll on the George Washington Bridge was $6.00. In 1995 the toll was 2 of that toll. 3 What was the toll in 1995? + + + + + 1 1 Simplify 1 1 Write the fraction as a decimal. = $4.00 The George Washington Bridge toll for a car was $4.00 in 1995.

  4. Example 2A: Multiplying Fractions Multiply. Write the answer in simplest form. 3 12  4 3 12 3  = Write 12 as a fraction. 12  4 1 4 3 Divide a numerator and denominator by their GCD, 4. 12 3 = 1 4 1 9 Multiply numerators. Multiply denominators. Simplify. = = 9 1 Remember! Use the GCD of a numerator and denominator to simplify before multiplying.

  5. 3 1  5 4 1 3   4 5 3 = 1 3 20  5 4 Additional Example 2B: Multiplying Fractions Multiply. Write the answer in simplest form. Multiply numerators. Multiply denominators. =

  6. Example 3A: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2 1  5 3 2 2 5 Writethe mixed number as an improper fraction. 2 1  =  5 3 3 5 1 Divide a numerator and denominator by their GCD, 5. 2 5 =  5 3 1 2 Multiply numerators. Multiply denominators. = 3

  7. Example 3B: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 1 1 4  2 7 5 1 1 21 15 4 = Write mixed numbers as improper fractions. 2   5 7 7 5 3 3 21 15 Divide numerators and denominators by their GCDs, 5 and 7.  = 5 7 1 1 Multiply numerators. Multiply denominators. 9 or 9 = 1

  8. 3 3 3 3 3 4  + + = + + + + 4 4 4 4 4 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 = 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 1 1 1 = 1 Check It Out! Example 1 In 2002, the fee to park in a parking garage was $4. In 2000 the fee was of the fee in 2002. What was the fee in 2000? 3 4 = $3.00 The fee to park in the parking garage was $3.00 in 2000.

  9. 1 3 1 3  =  7 8 8 7  3 = 56 Check It Out! Example 2 Multiply. Write the answer in simplest form. 3 1  7 8 Multiply numerators. Multiply denominators.

  10. Check It Out! Example 3 Multiply. Write the answer in simplest form. 3 1 2  5 3 1 3 7 Writethe mixed number as an improper fraction. 3  2 =  5 3 3 5 1 3 7 =  Divide a numerator and denominator by the GCD, 3. 5 3 1 7 2 Multiply numerators. Multiply denominators. = or 1 5 5

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