Understanding of Concept
1. Mr. Dodd filled the gas tank on his lawn mower with 3.8 gallons of gas. He mowed his yard 10 times on the same tank of gas. He used the same amount of gas each time. How much gas did he use each time? Write an equation to show your work. Explain how the decimal point moves.
0.38 gallons
3.8 / 10 = 0.38 gallons
The decimal point moves 1 place to the left.
6. Kathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same amount.
A. Estimate the cost of each ticket. Write an equation to show your work.
B. Find the exact cost of each ticket. Compare your answer to your estimate to check for reasonableness.
A. $20 ; $240 / 12 = 20
B. $19.25 ; My answer is close to my estimate, so my answer is reasonable.
13. Choose the correct quotient for each expression.
0.78 / 10 = ___
7,080 / 103 = ___
70.8 / 102 = ___
780 / 103 = ___
0.78 / 10 = 0.078
7,080 / 103 = 7.08
70.8 / 102 = 0.708
780 / 103 = 0.78
3. Choose the correct quotient for each expression. Use number sense and estimation to help.
21.6 / 1.8 =
10.23 / 0.55 =
78.75 / 3.5 =
29.67 / 4.6 =
21.6 / 1.8 = 12
10.23 / 0.55 = 18.6
78.75 / 3.5 = 22.5
29.67 / 4.6 = 6.45
14. Diego is making a large mural. He draws a hexagon with a perimeter of 10.5 meters. Each side of the hexagon is the same length.
A. How many meters long is each side of Diego's hexagon? Write an equation to model your work.
B. The total cost of supplies to paint the mural is $38.70. Diego and 9 friends divide the total cost equally. How much does each person pay?
A. 1.75m / 10.5 / 6 = 1.75
B. $3.87
11. Eileen bought 8 roses for $45.50. Which is the best way to estimate the cost of one rose?
B. $48 / 8 = $6.00
17. How many quarters are there in $30. Solve the equation 30 / 0.25 to help you.
C. 120 quarters
9. If 8 ounces of canned pumpkin has 82 calories, how many calories are in 1 ounce? Use your answer to find how many calories are in 6 ounces of pumpkin.
10.25 calories are in one ounce.
10.25 x 6 = 61.5 calories in 6 ounces
18. When solving 6.1 / 102, how is the decimal point moved?
D. 2 places to the left
4. What is the value of the missing exponent in the equation?
B. 2
16. Lou's Diner spent $12.80 on 8 pounds of potatoes. What was the cost of one pound of potatoes? What would be the total cost if the cost per pound remained the same and the diner bought 7 pounds? Show your work.
A pound costs $1.60.
12.80 / 8 = 1.60. If there were 7 pounds, the cost would be $11.20.
1.60 x 7 = 11.2
7. Select all of the following equations that are true when 12.5 is used. Use number sense to help.
A. ___ / 10 = 1.25
B. ___ / 1 = 1.25
C. ___ / 1 = 12.5
D. ___ / 100 = 1.25
E. ___ / 100 = 0.125
A. 12.5 / 10 = 1.25
C. 12.5 / 1 = 12.5
E. 12.5 / 100 = 0.125
15. Select all of the following equations that are true when 40.3 is used. Use number sense to help.
A. ___ / 101 = 403
B. ___ / 102 = 0.403
C. ___ / 100 = 40.3
D. ___ / 103 = 4.03
E. ___ / 102 = 4.03
B. 40.3 / 102 = 0.403
C. 40.3 / 100 = 40.3
22. Three coworkers decided to buy fruit to share at lunchtime. Antonio spent $1.47 on bananas. Laura spent $2.88 on apples. Suzanne spent $2.85 on oranges.
A. Complete the bar diagram to find out how much they spent in all on fruit.
B. They evenly divided the cost of 3 types of fruit. How much did each person pay? Complete the bar diagram to help you.
C. If Laura bought 2.1 pounds of apples, is the price per pound of apples greater than or less than $1? How can you tell?
A. $7.20 (bananas $1.47, apples $2.88, oranges $2.85)
B. $2.40 (2.40 x 3)
C. Greater than ; Since 2.88 is greater than 2.1, the quotient 2.88 / 2.1 will be greater than 1.
10. Use the equation 1.6 / n = 0.016.
A. What value of n makes the equation true? Write your answer using an exponent.
B. Explain how you know your answer is correct.
B. Since the decimal point moved two places between the dividend and the quotient, the divisor is 102
2. Kimberly scored a total of 35.08 points in four events for her gymnastic competition. If she scored the same number of points in each event, how many points did she score in each event? Write an equation to show your work.
8.77 points
35.08 / 4 = 8.77
12. Toby's faucet dripped a total of 1.92 liters of water in 24 hours. The faucet dripped the same amount of water each hour.
A. Estimate how many liters his faucet dripped each hour. Write an equation to model your work.
B. Find the exact amount of water that dripped each hour.
C. Compare your estimate to your answer. Is your answer reasonable? Explain.
A. 0.1 liters ; 2 / 20 = 0.1
B. 0.08 liters ; 1.92 / 24 = 0.08
C. 0.1 is close to 0.08, so my answer is reasonable.
8. Which division problem does the model Tess made represent?
D. 1.62 / 3 = 0.54
19. A group of 5 friends bought a bag of grapes to share equally. If the bag of grapes weighs 11.25 pounds, how much is each person's share? How many friends could share the grapes if each person's share was 1.25 pounds? Write an equation to model your work.
2.25 lb ; 11.25 / 5 = 2.25
9 friends ; 11.25 / 1.25 = 9
21. June says that there should be a decimal point in the quotient below after the 4. Is she correct? Use number sense to explain your answer.
43.94 / 5.2 = 845
June is not correct. I used compatible numbers to estimate 40 / 5 = 8 and 84.5 is not close to 8. The decimal point belongs after the 8.
20. When dividing 560.9 by 100, how should the decimal point be moved?
Since the divisor is 102, the decimal point is moved 2 places to the left to find the quotient.
5. The chef at a restaurant bought 37 pounds of salad for $46.25. How much did she pay for each pound of salad?
B. $1.25