Match each expression on the left with its equivalent on the right. Some answer choices on the right will not be used.

1. [tex]8,200 \times 100[/tex]
2. [tex]820,000 \div 10[/tex]
3. [tex]820 \times 10[/tex]
4. [tex]82,000 \div 1,000[/tex]

Options:
A. 820
B. 8,200
C. 82
D. 82,000
E. 820,000
F. 8,200,000

Let's match the expressions step-by-step by simplifying each one.

1. For the expression
[tex]$$8,200 \times 100,$$[/tex]
we multiply. Multiplying gives:
[tex]$$8,200 \times 100 = 820,000.$$[/tex]
Thus, [tex]$$8,200 \times 100$$[/tex] is matched with [tex]$$820,000.$$[/tex]

2. Next, consider the expression
[tex]$$820,000 \div 10.$$[/tex]
Dividing by 10 moves the decimal one place to the left, so:
[tex]$$820,000 \div 10 = 82,000.$$[/tex]
Therefore, [tex]$$820,000 \div 10$$[/tex] is matched with [tex]$$82,000.$$[/tex]

3. Now, look at
[tex]$$820 \times 10.$$[/tex]
Multiplying by 10 shifts the digits one place to the left:
[tex]$$820 \times 10 = 8,200.$$[/tex]
This means [tex]$$820 \times 10$$[/tex] is matched with [tex]$$8,200.$$[/tex]

4. Finally, for
[tex]$$82,000 \div 1,000,$$[/tex]
dividing by 1,000 shifts the decimal three places to the left:
[tex]$$82,000 \div 1,000 = 82.$$[/tex]
Hence, [tex]$$82,000 \div 1,000$$[/tex] is matched with [tex]$$82.$$[/tex]

To summarize, the matches are:

- [tex]$$8,200 \times 100 = 820,000$$[/tex]
- [tex]$$820,000 \div 10 = 82,000$$[/tex]
- [tex]$$820 \times 10 = 8,200$$[/tex]
- [tex]$$82,000 \div 1,000 = 82$$[/tex]