using\:multiples\:of\:\:10_5\:,\:50_5\:,\:100_5,\:and\:200_5\:to\:model\::\left[A\right]3,\:890,\:\left[B\right]\:872,\:550,\:\left[C\right]3.798,\:440\:,\:and\:\:\left[D\right]63,\:990 . solve  this for me

The given problem asks to model the values \([A]\), \([B]\), \([C]\), and \([D]\) using multiples of 10, 50, 100, and 200. Let's break this down step by step and solve each one.

### Values to be modeled:

- \( A = 3,890 \)
- \( B = 872,550 \)
- \( C = 3,798,440 \)
- \( D = 63,990 \)

### Multiples Available:

- \( 10_5 \) : Represents multiples of 10.
- \( 50_5 \) : Represents multiples of 50.
- \( 100_5 \) : Represents multiples of 100.
- \( 200_5 \) : Represents multiples of 200.

We'll aim to model each value as a combination of these multiples.

---

### **For \( A = 3,890 \):**

We will break down \( A = 3,890 \) using the multiples of 10, 50, 100, and 200.

Start by using \( 200_5 \) multiples to cover the large part of \( A \).

\[
200_5 \times 19 = 3,800
\]

This leaves a remainder of \( 3,890 - 3,800 = 90 \).

Now we can model 90 using multiples of 10:

\[
10_5 \times 9 = 90
\]

Thus, \( A = 3,890 \) is modeled as:

\[
A = 200_5 \times 19 + 10_5 \times 9
\]

---

### **For \( B = 872,550 \):**

We start with the largest multiple \( 200_5 \):

\[
200_5 \times 4,362 = 872,400
\]

This leaves a remainder of \( 872,550 - 872,400 = 150 \).

Now, we can model 150 using \( 50_5 \):

\[
50_5 \times 3 = 150
\]

Thus, \( B = 872,550 \) is modeled as:

\[
B = 200_5 \times 4,362 + 50_5 \times 3
\]

---

### **For \( C = 3,798,440 \):**

Again, start with the largest multiple \( 200_5 \):

\[
200_5 \times 18,992 = 3,798,400
\]

This leaves a remainder of \( 3,798,440 - 3,798,400 = 40 \).

Now, we can model 40 using \( 10_5 \):

\[
10_5 \times 4 = 40
\]

Thus, \( C = 3,798,440 \) is modeled as:

\[
C = 200_5 \times 18,992 + 10_5 \times 4
\]

---

### **For \( D = 63,990 \):**

We will use \( 200_5 \):

\[
200_5 \times 319 = 63,800
\]

This leaves a remainder of \( 63,990 - 63,800 = 190 \).

Now we model 190 as:

\[
100_5 \times 1 = 100 \quad \text{and} \quad 50_5 \times 1 = 50 \quad \text{and} \quad 10_5 \times 4 = 40
\]

Thus, \( D = 63,990 \) is modeled as:

\[
D = 200_5 \times 319 + 100_5 \times 1 + 50_5 \times 1 + 10_5 \times 4
\]

---

### Summary of the Models:

- \( A = 200_5 \times 19 + 10_5 \times 9 \)
- \( B = 200_5 \times 4,362 + 50_5 \times 3 \)
- \( C = 200_5 \times 18,992 + 10_5 \times 4 \)
- \( D = 200_5 \times 319 + 100_5 \times 1 + 50_5 \times 1 + 10_5 \times 4 \)

Would you like more details on any step? Let me know if you have any questions.

### Relative Questions:

1. How can we optimize these multiples for larger numbers?
2. What are the advantages of using multiples in mathematical modeling?
3. Can you express the models without using certain multiples?
4. How do the multiples change when modeling with different base numbers?
5. What are other examples where multiples are used in practical scenarios?

### Tip: 
When breaking down large numbers, always start with the largest multiple to reduce the number of smaller components needed.

using multiples of 10_5, 50_5, 100_5, and 200_5 to model: [A]3,890, [B]872,550, [C]3,798,440, and [D]63,990. solve this for me

Learn how to model numbers like 3,890, 872,550, 3,798,440, and 63,990 using multiples of 10, 50, 100, and 200. This problem involves number breakdowns, multiplication, and remainder calculation. Suitable for Grades 6-8.

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