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Unit 6 – Practice Problems

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UNIT 6 – PRACTICE PROBLEMS 1– 8: Use the diagrams given to represent the values in the addition problem and find the sum. Then

perform the operation and represent the sum using the symbolic representation of the algorithm.

1. Tom had 1

6 of a carrot cake last night and

2

6of a carrot cake today. How much of one whole carrot

cake did Tom have?

Symbolic Representation of Algorithm:

2. Ava walked 3

8 of a mile to the store and then ran another

7

8 of a mile to school. How far did she travel

in

total?


3. 3 2

4 4



2

4. 1 3

3 6


5. 1 2

6 9


6. 6 8

4 4



3

7. 1 1

2 43 2


8. 4 12

15 5


9– 15: Use the diagrams given to represent the values in the subtraction problem and find the difference.

Then perform the operation and represent the difference using the symbolic representation of the algorithm.

9. There was 3

5 of a cake left after a party. Joey ate

2

5 of the cake the next afternoon. How much of a

cake is leftover now?



4

10. Sara lives 12

8 of a mile from school. Ann live

3

8 of a mile. How much further does Sara live from

school?


11. 3 2

4 3


12. 5 1

8 4



5

13. 9 2

5 5


14. 2 1

4 23 2


15. 3 7

25 5



6

16. Add or subtract each of the following. Be sure to leave your answer in simplest (reduced) form. If

applicable, write your answer as both an improper fraction and a mixed number.

a. 5

8+

4

8 b. 4

3-

1

3 c. 2

10+

3

10

d. 7

22+

5

22 e. 12

17-

3

17

17. Add or subtract each of the following. State clearly what the common denominator is. Be sure to leave

your answer in simplest (reduced) form. If applicable, write your answer as both an improper fraction

and a mixed number.

a. 5

7+

4

9 b. 4

5-

1

3 c. 2

3+

3

5

d. 7

12+

5

24 e. 4

5-

3

7


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For 18 – 29: Use the diagrams given to represent the multiplication problem and find the product. Then

perform the operation and represent the product using the symbolic representation of the algorithm.

18. April’s guests ate 2

3 of an apple pie. The pie had 12 slices. How many slices did they eat?


19. Riley was 30 miles from home. He travelled 1

4 of this distance before stopping for gas. How many

miles did he travel before stopping for gas?


20. Javier has a 5 gallon bucket. If he fills it 1

3 of the way to the

top. How much water is in the bucket?

21. How much water is in the bucket if he fills it 2

3 of the way to

the top?


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22. Johnny’s gas tank holds 10 gallons. The gas gage says it is 2

5 full.

How many gallons of gas are in the tank?


23. Phil skated around a track 7 times. The distance around the track is 1

4 of a mile. How far did Phil

skate?

Picture:

Copies of Language:



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24. Chris is having a party with a total of 8 people. He bought enough cake for each person to have 2

4 of a

cake. How many cakes did he buy?

Picture:

Copies of Language:


.

25. Yesterday, Sharon walked 1

4 of a mile to school. Today, Sharon’s friend picked her up after she had

walked 1

2 of the way to school. How far to Sharon walk today?

Picture:

Copies of Language:


26. Maureen bought a rectangular piece of land to build a vacation home. The land is 2

5 of a mile long and

1

3 of a mile wide. How many square miles of land did Maureen buy?

Picture:

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10

27. Todd ordered a pizza. He ate 2

5 of the pizza that night. The next day, he ate

3

4 of what was left over.

How much of the whole pizza did Todd eat the next day?

Picture:

Copies of Language:


28. According to the Bureau of Labor Statistics, the buying power of the dollar is 4

15

times larger in 2016

when compared to 1991. Determine the comparable buying power in 2016 of $20 in 1991.

Picture:

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29. Kevin made a rectangular drink coaster. The coaster was 1

24

inches wide and 1

32

inches long. How

many square inches was the coaster?

Picture:

Copies of Language:



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30. Multiply and simplify. If applicable, write your answer as both an improper fraction and a mixed

number.

a. 1

6×3

5 b. 8

9×

9

12 c. 3

4× 0

d. 11

2×1

2 e. 3

1

3×2

2

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For 31 – 35: Use the diagrams given to represent the division problem and find the quotient.

31. Tia made 3 cakes for her guests. If each guest receives 1

4 of a cake, how many guests can Tia serve?

Picture:

Copies of Language:

Symbolic Representation:


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32. Greg ran 8 miles this month. If he ran 4

3 of a mile every day he ran, how many days did Greg run?

Picture:

Copies of Language:


33. 7 1

2 2

Copies of Language:


34. 9 3

5 5

Copies of Language:



13

35. 15 3

4 2

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36. Divide the fractions by multiplying the first fraction by the reciprocal of the second fraction. Simplify

your result if necessary. Write any answers greater than 1 as both an improper fraction and a mixed

number.

a) 11 22

12 7 b)

18 9

5 15 c)

12 5

5 6

37. Rewrite any mixed numbers as improper fractions. Then perform the division by multiplying the first

fraction by the reciprocal of the second fraction. Simplify your result if necessary and rewrite your

result as a mixed number when possible.

a) 1 5

43 7 b)

1 35 4

3 7 c)

1 21 4

3 3


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38. Perform the indicated operations. Write your answer in simplest form. If applicable, write your answer

as both an improper fraction and a mixed number.

a. 1

2-

1

3+

1

4 b. 2 -

8

5

c. 2

3+

1

3-

1

4 d.

1 5 7

3 3 3

39. Perform the indicated operations and simplify. If applicable, write your answer as both an improper

fraction and a mixed number.

a. 3

4¸

4

5×5

6 b.

1

2-

1

3×1

4

c. 2 -8

5

æ

èç

ö

ø÷

2

d. 1-1

2

æ

èç

ö

ø÷

2


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For 40 – 51: Solve the following problems. Show all of your work and write your final answer as a complete

sentence. When necessary, write your final answers as both mixed numbers and improper fractions.

40. If Josh ate 1

4of a pizza, what fraction of the pizza is left?

41. If I drove 102

3 miles one day and 12

1

4 miles the second day and 8

1

5 miles the third day, how far did I

drive?

42. Melody bought a 2-liter bottle of soda at the store. If she drank 1

8 of the bottle and her brother drank 2

7of the bottle, how much of the bottle is left?

43. James brought a small bag of carrots for lunch. There are 6 carrots in the bag. Is it possible for him to

eat 2

6of the bag for a morning snack and 5

6of the bag at lunch? Why or why not?


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44. Suppose that David is able to tile 1

4of his floor in 3 hours. How long would it take him to tile the rest

of the floor?

45. Maureen went on a 3 day, 50 mile biking trip. The first day she biked 2

213

miles. The second day she

biked 3

178

miles. How many miles did she bike on the 3rd day?

46. Scott bought a 5 lb bag of cookies at the bakery. He ate 2

5 of a bag and his sister ate

2

9 of a bag. What

fraction of the bag did they eat? What fraction of the bag remains?

47. Suppose your school costs for this term were $2500 and financial aid covered 3

4 of that amount. How

much did financial aid cover?


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48. If, on average, about 4

7 of the human body is water weight how much water weight is present in a

person weighing 182 pounds?

49. If, while training for a marathon, you ran 920 miles in 3 1

2 months, how many miles did you run each

month? (Assume you ran the same amount each month)

50. On your first math test, you earned 75 points. On your second math test, you earned 6

5 as many points

as your first test. How many points did you earn on your second math test?

51. You are serving cake at a party at your home. There are 12 people in total and 23

4 cakes. (You ate

some before they got there!). If the cakes are shared equally among the 12 guests, what fraction of a

cake will each guest receive?

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UNIT 6 PRACTICE PROBLEMS - WordPress.com 6 – Practice Problems 1 UNIT 6 ... 7 12 + 5 24 e. 4 5-3 7. Unit 6 – Practice Problems 7 For 18 ... some before they got there!)