To review these concepts, go to Fraction Word Problems Study Guide.

**Fraction Word Problems Practice Questions**

**Practice 1**

**Problems**

Fill in each answer blank with the correct solution.

- The greatest common factor of 8 and 32 is __________.
- The least common multiple of 15 and 25 is __________.
- The fraction in simplest form is equal to __________.
- The improper fraction is equivalent to the mixed number __________.
- The mixed number written as an improper fraction is equivalent to __________.

**Solutions**

- 8
- 75

**Practice 2**

**Problems**

- Subtract:
- Add:
- Multiply:
- Divide:

**Solutions**

- Subtract the numerators and keep the denominator: .
- Change to a common denominator of 6: .
- Change to improper fraction form first, then cross cancel common factors..
- Divide by multiplying by the reciprocal: .

**Practice 3**

**Problems**

- Phil is making two different types of cookies. For one recipe, he needs cups of sugar and for the other recipe he needs cups of sugar. What is the total amount of sugar he needs for both recipes?
- Ally measured a board to be feet long. If she cuts off a piece that measures feet long, what is the length of the remaining piece?
- Becky is building a square pen for her pet rabbit. The directions for the pen call for a foot-long chain link fence that will surround the pen. How long is each side of the pen?
- Thirty students in Mr. Joyce's room are working on projects. The first day he gave them of an hour to work. On the second day, he gave them half as much time as the first day. How much time did the students have altogether to work on their projects?

**Solutions**

*Read and understand the question*. This question is looking for the total amount of sugar needed for two cookie recipes.*Read and understand the question*. The question is asking for the length of a board after it has been cut. The length of the board before the cut and the amount cut off are given in the problem.*Read and understand the question*. This problem is asking for the length of a square pen when the total length of all four sides is given.*Read and understand the question*. This problem asks for the total amount of time the students had to work on their projects in class, given time on two different days.

*Make a plan*. The key word *total* in this context tells you to add. Add the amounts for each recipe to find the solution.

*Carry out the plan*. Add by first finding a common denominator. The least common multiple of 3 and 4 is 12, so the problem then becomes . Change this amount to a mixed number. The final answer is cups.

*Check your answer*. Check your answer by subtracting one of the values from the total: , which was the other value being added. This answer is checking.

*Make a plan*. Because you are looking for the length of the remaining piece, or the amount left over, subtract the amount cut off from the original length.

*Carry out the plan*. Use subtraction and your knowledge of fractions to carry out this plan. Subtract by getting a common denominator of 4 and subtracting the whole number parts and the fraction parts:

. The remaining board is feet long.

*Check your answer*. Check your answer by adding. . This problem is checking.

*Make a plan*. Divide the total length of the chain link fence by the four equal sides of the square pen.

*Carry out the plan*. Divide by 4 equal sides. Be sure to change to improper fraction form and multiply by the reciprocal:

Each side of the pen is feet long.

*Check your answer*. Check your answer by working backward. Multiply the length of one side by 4 to find the total length.. This problem is checking.

*Make a plan*. Be careful of the extra information in the problem. The fact that there are 30 students in the class is not necessary to solve this problem. The key word *altogether*tells you to find the amount for each day and add the times together.

*Carry out the plan*. Find the amount for the first day. of an hour is equal to × 60 minutes = minutes. The second day is half this amount: of 36 = = 18 minutes. To find the total, add 36 + 18 = 54 minutes.

*Check your answer*. Check this answer by making sure the answer fits the details in the question. They worked three-fifths of an hour the first day, which was 36 minutes, then half that amount, or 18 minutes the second day. This was a total of 54 minutes, so this answer is checking.

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