Solving Problems by Multiplying and Dividing Fractions and Mixed Numbers

DressExample 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.

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Solution:

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


CupcakesExample 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:

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


Group WorkExample 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.

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Solution:

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


Chocolate BarExample 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.

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Solution:

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Answer: 2 pieces


ElectricianExample 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.

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Solution:

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


TapeExample 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.

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Solution:

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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?
 
ANSWER BOX:  cups   

RESULTS BOX: 

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?
 
ANSWER BOX:   oz.  

RESULTS BOX: 

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?
 
ANSWER BOX:   sq ft   

RESULTS BOX: 

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?
 
ANSWER BOX:   pieces   

RESULTS BOX: 

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

RESULTS BOX: 

 

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