1. A Charity worker has 240 books, 200 pens, 80 pencils and 45 chocolates.  He wants to distribute them with a group of children equally. a) Find the largest number of children he can distribute, so that each  student gets an equal number of books, pens, pencils, and chocolates. b) Write down how many books, pens, pencils, and chocolates will be  given to each child.
c) What is the most appropriate mathematical technique to solve this  type of problem?
d) Why cannot the technique mentioned in part (c) be directly used to solve part (a)?
e) Briefly explain how you overcome the obstacle state in part (d).

To solve this problem, we need to find the largest number of children such that each child receives an equal number of books, pens, pencils, and chocolates. Here are the detailed steps:

### a) Find the largest number of children he can distribute to, so that each student gets an equal number of books, pens, pencils, and chocolates.

The key to solving this part of the problem is to find the greatest common divisor (GCD) of the numbers of each type of item. The GCD will give us the largest number of children such that each child gets the same number of books, pens, pencils, and chocolates.

- Books: 240
- Pens: 200
- Pencils: 80
- Chocolates: 45

First, we find the GCD of these numbers. 

To find the GCD of more than two numbers, we can use the following method:

1. Find the GCD of the first two numbers.
2. Use the result to find the GCD with the next number.
3. Repeat the process until all numbers have been included.

Let's find the GCD step-by-step:

1. GCD of 240 and 200:
   \[
   \text{GCD}(240, 200) = 40
   \]

2. GCD of the result with 80:
   \[
   \text{GCD}(40, 80) = 40
   \]

3. GCD of the result with 45:
   \[
   \text{GCD}(40, 45) = 5
   \]

Thus, the largest number of children is 5.

### b) Write down how many books, pens, pencils, and chocolates will be given to each child.

Each child will receive:
- Books: \(\frac{240}{5} = 48\)
- Pens: \(\frac{200}{5} = 40\)
- Pencils: \(\frac{80}{5} = 16\)
- Chocolates: \(\frac{45}{5} = 9\)

### c) What is the most appropriate mathematical technique to solve this type of problem?

The most appropriate mathematical technique to solve this type of problem is finding the Greatest Common Divisor (GCD).

### d) Why cannot the technique mentioned in part (c) be directly used to solve part (a)?

The technique of finding the GCD is directly applicable to solve part (a). The GCD helps determine the largest number of groups into which the items can be equally divided.

### e) Briefly explain how you overcome the obstacle stated in part (d).

Since there is no obstacle in directly using the GCD to solve part (a), the process is straightforward. By applying the Euclidean algorithm or using a function to compute the GCD, we can determine the largest number of children that can evenly receive all types of items.

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Do you want details or have any questions? Here are 5 more questions you can ask:

1. How is the Euclidean algorithm used to find the GCD of two numbers?
2. Can you explain the steps of finding the GCD with an example?
3. What is the Least Common Multiple (LCM), and how is it different from the GCD?
4. How can we find the GCD of more than two numbers efficiently?
5. Can you show how to distribute different items to a different number of children?

**Tip:** When dealing with problems that involve distributing items evenly, always consider the GCD to determine the largest possible equal distribution.

Learn how to distribute 240 books, 200 pens, 80 pencils, and 45 chocolates equally among children using the Greatest Common Divisor (GCD) method. Step-by-step solution included. Suitable for students in Grades 5-7.

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