Instructions
- Read Carefully: Each section focuses on a different aspect of long division, from basic mechanics to complex real-world application.
- Show Your Work: Use the blank space provided under each question to show your long division steps (Estimate, Divide, Multiply, Subtract, Bring Down).
- Decimal Accuracy: Unless specified otherwise, carry out your division to two decimal places if there is a remainder.
- Interpret the Results: In word problems, think about whether a remainder means you need to round up, round down, or use a decimal.
- Challenge Yourself: Complete the final "Logistics Expert" challenge at the end for extra credit!
Section 1: The Mechanic's Warm-up
Solve these standard long division problems to sharpen your skills. Show every step of the process.
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546 ÷ 7
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2,496 ÷ 12
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8,142 ÷ 15
Section 2: The Logistics Warehouse
You are a manager at a global shipping hub. You need to organize inventory into equal containers. Fill out the table below to determine how many containers are needed and how much stock is left over.
| Total Items | Items per Container | Full Containers | Remaining Items (Remainder) |
|---|---|---|---|
| Example: 1,250 | 40 | 31 | 10 |
| 3,420 | 25 | ||
| 5,688 | 18 | ||
| 9,104 | 32 | ||
| 4,500 | 14 | ||
| 12,245 | 55 |
Section 3: Real-World Scenarios
Apply your division skills to solve these practical problems. Pay close attention to what the question is asking (e.g., do you need a whole number or a decimal?)
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The Concert Tour: A popular band is planning a tour. Their equipment weighs 14,350 pounds. If one shipping crate can hold 450 pounds, how many crates do they need to transport all of their equipment? (Hint: You cannot leave equipment behind!)
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The Fuel Efficiency Test: A hybrid delivery truck traveled 1,131 miles on 26 gallons of gas. Exactly how many miles did the truck travel per gallon? (Provide the answer as a decimal).\v
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The Charity Gala: A local charity raised $28,750. They want to divide the money equally among 12 different community programs. How much money will each program receive? (Round to the nearest cent).
Section 4: The Logic of Remainders
In 8th-grade math, knowing what to do with a remainder is just as important as the division itself. Circle the correct action for each scenario.
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You are buying boxes to hold 103 books. Each box holds 10 books. How many boxes do you buy?
- (A) Round Down: 10 boxes
- (B) Round Up: 11 boxes
- (C) Use Decimal: 10.3 boxes
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You are splitting $50.00 between 4 friends.
- (A) Round Down: $12.00 each
- (B) Use Remainder: $12 with $2 left over
- (C) Use Decimal: $12.50 each
Section 5: The Logistics Expert Challenge
A massive solar farm is being built. It requires 24,500 solar panels. The panels are delivered on trucks that can carry 115 panels each. Each truck costs $1,200 to hire.
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How many truck trips are required to deliver all the panels?
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What is the total cost of hiring the trucks?
Answer Key
Section 1: The Mechanic's Warm-up
- 78
- 208
- 542.8
Section 2: The Logistics Warehouse
- 3,420 ÷ 25: 136 containers, 20 remaining
- 5,688 ÷ 18: 316 containers, 0 remaining
- 9,104 ÷ 32: 284 containers, 16 remaining
- 4,500 ÷ 14: 321 containers, 6 remaining
- 12,245 ÷ 55: 222 containers, 35 remaining
Section 3: Real-World Scenarios
- 32 crates (14,350 / 450 = 31.88; you need a 32nd crate for the remaining weight).
- 43.5 miles per gallon.
- $2,395.83 per program.
Section 4: The Logic of Remainders
- (B) Round Up (You need a whole box for the last 3 books).
- (C) Use Decimal (Money is always expressed with decimals).
Section 5: The Logistics Expert Challenge
- 214 trips (24,500 / 115 = 213.04; you must round up to the next full truck).
- $256,800 (214 trips x $1,200).