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 California Standards

Recall that multiplication can be written as repeated addition 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.

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? Think: How much is of 6? Use multiplication to find a fraction of a number. 2 3 2 3 6  = + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 + 1 3 = 12 3 1 3 = 4 1 1 1 1 1 = $4.00 The George Washington Bridge toll for a car was $4.00 in 1995.

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 4 4  = + + 1 4 = 12 4 1 4 = 3 1 1 = $3.00 The fee to park in the parking garage was $3.00 in 2000.

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

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

Teacher Example 1C: Multiplying Fractions Multiply. Write the answer in simplest form. 1 3  3 8 1 Divide a numerator and denominator by their GCD, 3. 3 8  1 1 3  8 = 1 1 Multiply numerators. Multiply denominators. = 8

Practice 1A: Multiply. Write the answer in simplest form. 1 16  4 1 16 1 16  =  Write 16 as a fraction. 4 1 4 4 16  1 Divide a numerator and denominator by their GCD, 4. = 1  4 1 4 Multiply numerators. Multiply denominators. = = 4 1

Multiply. Write the answer in simplest form. Practice 1B: Multiply. Write the answer in simplest form. 3 1  7 8 3 7  1 8 Multiply numerators. Multiply denominators. 1 8  3 7 = = 3 56

Student Practice 1C: Multiply. Write the answer in simplest form. 1 6  6 9 1 6 9  1 1 6  9 Divide a numerator and denominator by their GCD, 6. = 1 1 Multiply numerators. Multiply denominators. = 9

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

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

Teacher Example 2C: Multiplying Mixed Numbers Multiply. Write the answer in simplest form. 2 2 6  4 3 5 2 2 20 22 Write mixed numbers as improper fractions. 6  4 =  3 5 3 5 4 Divide a numerator and denominator by their GCD, 5. 20 22 =  3 5 1 3 = 88 or 29 1 Multiply numerators. Multiply denominators.

Student Practice 2A: Multiply. Write the answer in simplest form. 3 1  2 5 3 3 1 3 7 Write the mixed number as an improper fraction.  2 =  3 5 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

Multiply. Write the answer in simplest form. Student Practice 2B: Multiply. Write the answer in simplest form. 3 1 3  1 5 3 3 1 18 4 3  1 =  Write mixed numbers as improper fractions. 5 3 5 3 6 18 4 Divide a numerator and denominator by their GCD, 3.  = 5 3 1 = 24 5 or 4 4 Multiply numerators. Multiply denominators.

Multiply. Write the answer in simplest form. Student Practice 2C: Multiply. Write the answer in simplest form. 1 1 3  1 6 3 1 1 19 4 Write mixed numbers as improper fractions. 3 1 =   6 3 6 3 2 Divide a numerator and denominator by their GCD, 2. 19 4 =  6 3 3 9 = 38 or 4 2 Multiply numerators. Multiply denominators.