Students can practice long division skills by solving real-world scenarios involving jewelry making and inventory management.

Let's solve each of the division word problems step by step.

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Problem 1:

A necklace has 34 beads. How many necklaces can be made from 45,730 beads?

#### Step 1: Understand what is being asked
We need to find how many complete necklaces can be made if each necklace uses 34 beads and we have a total of 45,730 beads.

This is a division problem:
> Total beads ÷ Beads per necklace = Number of necklaces

So,
$$
\frac{45,\!730}{34}
$$

#### Step 2: Perform the division

Let’s divide 45,730 by 34.

We can do this using long division:

1. 34 goes into 45 once (34 × 1 = 34), subtract: 45 - 34 = 11
2. Bring down 7 → 117
3. 34 goes into 117 three times (34 × 3 = 102), subtract: 117 - 102 = 15
4. Bring down 3 → 153
5. 34 goes into 153 four times (34 × 4 = 136), subtract: 153 - 136 = 17
6. Bring down 0 → 170
7. 34 goes into 170 exactly five times (34 × 5 = 170), subtract: 170 - 170 = 0

So,
$$
\frac{45,\!730}{34} = 1,\!345
$$

✔ Answer: 1,345 necklaces can be made.

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Problem 2:

A salesman of a handicraft shop keeps 100 key chains in a container. He has 77,809 key chains. Calculate the number of containers needed.

#### Step 1: Understand what is being asked
Each container holds 100 key chains. We need to find how many containers are required to hold 77,809 key chains.

Again, this is a division problem:
> Total key chains ÷ Key chains per container = Number of containers

So,
$$
\frac{77,\!809}{100}
$$

#### Step 2: Perform the division

Dividing by 100 is easy — just move the decimal point two places to the left:
$$
77,\!809 ÷ 100 = 778.09
$$

But since we're dealing with containers, and you can't have a fraction of a container, we need to round up if there's any remainder (because even one extra key chain needs an additional container).

So:
- 778 full containers can hold $ 778 \times 100 = 77,\!800 $ key chains
- Remaining key chains: $ 77,\!809 - 77,\!800 = 9 $

These 9 key chains still need one more container

Therefore, total containers needed = 778 + 1 = 779

✔ Answer: 779 containers are needed.

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✔ Final Answers:

1. 1,345 necklaces
2. 779 containers

Let me know if you'd like these explained visually or with diagrams!