# Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers

## Fraction Word Problems With Interactive Exercises

Example 1: If it takes 5/6 yards of fabric to make a dress, then how many yards will it take to make 8 dresses?

Analysis: To solve this problem, we will convert the whole number to an improper fraction. Then we will multiply the two fractions.

Solution:

Answer: It will take 6 and 2/3 yards of fabric to make 8 dresses.

Example 2: Renee had a box of cupcakes, of which she gave 1/2 to her friend Juan. Juan gave 3/4 of his share to his friend Elena. What fractional part of the original box of cupcakes did Elena get?

Analysis: To solve this problem, we will multiply these two fractions.

Solution:

Answer: Elena got 3/8 of the original box of cupcakes.

Example 3: Nina’s math classroom is 6 and 4/5 meters long and 1 and 3/8 meters wide. What is the area of the classroom?

Analysis: To solve this problem, we will multiply these mixed numbers. But first we must convert each mixed number to an improper fraction.

Solution:

Answer: The area of the classroom is 9 and 7/20 square meters.

Example 4: A chocolate bar is 3/4 of an inch long. If it is divided into pieces that are 3/8 of an inch long, then how many pieces is that?

Analysis: To solve this problem, we will divide the first fraction by the second.

Solution:

Answer: 2 pieces

Example 5: An electrician has a piece of wire that is 4 and 3/8 centimeters long. She divides the wire into pieces that are 1 and 2/3 centimeters long. How many pieces does she have?

Analysis: To solve this problem, we will divide the first mixed number by the second.

Solution:

Answer: The electrician has 2 and 5/8 pieces of wire.

Example 6: A warehouse has 1 and 3/10 meters of tape. If they divide the tape onto pieces that are 5/8 meters long, then how many pieces will they have?

Analysis: To solve this problem, we will divide the first mixed number by the second. First, we will convert each mixed number into an improper fraction.

Solution:

Answer: The warehouse will have 2 and 2/25 pieces of tape.

Summary: In this lesson we learned how to solve word problems involving multiplication and division of fractions and mixed numbers.

**Exercises**

Directions: Subtract the mixed numbers in each exercise below. ** Be sure to simplify your result, if necessary. **Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

**Note: To write the mixed number four and two-thirds, enter 4, a space, and then 2/3 into the form.**

1. |
One batch of cookies contains 1 and 3/4 cups of melted chocolate. How many cups of melted chocolate are needed to make 8 batches of cookies? |

2. |
Todd drank 5/8 of a 24-ounce can of juice. Lila drank 1/3 as much juice as Todd did. How many ounces did Lila drink? |

3. |
A rectangular area rug has a length of 3 and 2/3 feet and a width of 2 and 3/4 feet. What is the area of the rug? |

4. |
Janet has 5 and 3/4 centimeters of licorice. She divides the licorice into pieces that are 1 and 7/8 centimeters long. How many pieces of licorice will she have? |

5. |
A piece of wood is 15 feet long. How many 3/4-foot sections can be cut from it? |