1. 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

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

3. 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.

4. 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.

6. 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.

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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.

15. 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

16. 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.

17. 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.