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Problem Solving: Division Word Problems (3÷1) w/ Remainder

Below, I will solve each problem step by step and explain the solution.

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#### 1. At the carnival, nine friends bought two hundred fourteen tickets. If they wanted to split all the tickets so each friend got the same amount, how many tickets would they need to buy?

- Total tickets: 214
- Number of friends: 9
- Tickets per friend: \( \frac{214}{9} \)

Perform the division:
\[
214 \div 9 = 23 \text{ R } 7
\]
This means each friend gets 23 tickets, and there are 7 tickets left over.

To ensure no tickets are left over, they need to buy enough tickets so that the total is divisible by 9. The next multiple of 9 after 214 is:
\[
216 \quad (\text{since } 9 \times 24 = 216)
\]

Thus, they need to buy:
\[
216 - 214 = 2 \text{ more tickets}
\]

Answer: 2

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#### 2. A clown needed two hundred seventy-five balloons for a party he was going to, but the balloons only came in packs of 2. How many packs of balloons would he need to buy?

- Total balloons needed: 275
- Balloons per pack: 2

Perform the division:
\[
275 \div 2 = 137 \text{ R } 1
\]
This means 137 packs give 274 balloons, and there is a remainder of 1 balloon needed.

Since the clown needs 275 balloons, he must buy one additional pack to cover the remaining balloon.

Thus, the total number of packs needed is:
\[
137 + 1 = 138
\]

Answer: 138

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#### 3. A vase can hold ten flowers. If a florist had eight hundred seventy-eight flowers she wanted to put equally into vases, how many flowers would be in the last vase that isn't full?

- Total flowers: 878
- Flowers per vase: 10

Perform the division:
\[
878 \div 10 = 87 \text{ R } 8
\]
This means 87 vases are completely filled with 10 flowers each, and there are 8 flowers left over.

The last vase will contain the remaining 8 flowers.

Answer: 8

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#### 4. An industrial machine can make four hundred seventy-nine crayons a day. If each box of crayons has two crayons in it, how many full boxes does the machine make a day?

- Total crayons made per day: 479
- Crayons per box: 2

Perform the division:
\[
479 \div 2 = 239 \text{ R } 1
\]
This means the machine can fill 239 full boxes, with 1 crayon left over.

Answer: 239

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#### 5. A movie theater needed nine hundred eighty popcorn buckets. If each package has nine buckets in it, how many packages will they need to buy?

- Total buckets needed: 980
- Buckets per package: 9

Perform the division:
\[
980 \div 9 = 108 \text{ R } 8
\]
This means 108 packages provide 972 buckets, and there are 8 buckets still needed.

To cover the remaining 8 buckets, they need to buy one additional package.

Thus, the total number of packages needed is:
\[
108 + 1 = 109
\]

Answer: 109

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#### 6. Debby is making head necklaces. She wants to use seven hundred twenty-three beads to make seven necklaces. If she wants each necklace to have the same number of beads, how many beads will she have left over?

- Total beads: 723
- Number of necklaces: 7

Perform the division:
\[
723 \div 7 = 103 \text{ R } 2
\]
This means each necklace can have 103 beads, and there will be 2 beads left over.

Answer: 2

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#### 7. A restaurant needs to buy six hundred fifty-eight new plates. If each box has five plates in it, how many boxes will they need to buy?

- Total plates needed: 658
- Plates per box: 5

Perform the division:
\[
658 \div 5 = 131 \text{ R } 3
\]
This means 131 boxes provide 655 plates, and there are 3 plates still needed.

To cover the remaining 3 plates, they need to buy one additional box.

Thus, the total number of boxes needed is:
\[
131 + 1 = 132
\]

Answer: 132

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#### 8. A school had six hundred ninety students sign up for the trivia teams. If they wanted to have nine teams, with the same number of students on each team, how many more students would they need to sign up?

- Total students signed up: 690
- Number of teams: 9

Perform the division:
\[
690 \div 9 = 76 \text{ R } 6
\]
This means each team can have 76 students, and there are 6 students left over.

To ensure an equal distribution, the school needs enough students so that the total is divisible by 9. The next multiple of 9 after 690 is:
\[
693 \quad (\text{since } 9 \times 77 = 693)
\]

Thus, the school needs:
\[
693 - 690 = 3 \text{ more students}
\]

Answer: 3

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#### 9. A cafeteria was putting milk cartons into stacks. They had five hundred twenty-five cartons and were putting them into stacks with two cartons in each stack. How many full stacks could they make?

- Total cartons: 525
- Cartons per stack: 2

Perform the division:
\[
525 \div 2 = 262 \text{ R } 1
\]
This means 262 full stacks can be made, with 1 carton left over.

Answer: 262

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#### 10. A botanist picked eight hundred fifteen flowers. She wanted to put them into four bouquets with the same number of flowers in each. How many more should she pick so she doesn’t have any extra?

- Total flowers picked: 815
- Number of bouquets: 4

Perform the division:
\[
815 \div 4 = 203 \text{ R } 3
\]
This means each bouquet can have 203 flowers, and there are 3 flowers left over.

To ensure no flowers are left over, the botanist needs enough flowers so that the total is divisible by 4. The next multiple of 4 after 815 is:
\[
816 \quad (\text{since } 4 \times 204 = 816)
\]

Thus, the botanist needs:
\[
816 - 815 = 1 \text{ more flower}
\]

Answer: 1

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Final Answers:

1. 2
2. 138
3. 8
4. 239
5. 109
6. 2
7. 132
8. 3
9. 262
10. 1

Boxed Final Answer:
\[
\boxed{2, 138, 8, 239, 109, 2, 132, 3, 262, 1}
\]