8. Show 2 different ways you can use partial quotients to find $$ 632 \div 8 $$.

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To find $$ 632 \div 8 $$ using partial quotients, we can use two different approaches. Partial quotients involve estimating how many times the divisor can fit into the dividend and then subtracting the product from the dividend repeatedly until we reach zero or a remainder less than the divisor.

### Method 1: Using Larger Estimates

1. **Estimate**: Start with a larger estimate. Let's say $$ 8 \times 70 = 560 $$.
2. **Subtract**: 
   $$
   632 - 560 = 72
   $$
3. **Estimate Again**: Now, we can see how many times $$ 8 $$ fits into $$ 72 $$. We can estimate $$ 8 \times 9 = 72 $$.
4. **Subtract Again**: 
   $$
   72 - 72 = 0
   $$
5. **Combine the Quotients**: Now, we add the partial quotients:
   $$
   70 + 9 = 79
   $$
Thus, $$ 632 \div 8 = 79 $$.

### Method 2: Using Smaller Estimates

1. **Estimate**: Start with a smaller estimate. Let's say $$ 8 \times 60 = 480 $$.
2. **Subtract**: 
   $$
   632 - 480 = 152
   $$
3. **Estimate Again**: Now, we can see how many times $$ 8 $$ fits into $$ 152 $$. We can estimate $$ 8 \times 19 = 152 $$.
4. **Subtract Again**: 
   $$
   152 - 152 = 0
   $$
5. **Combine the Quotients**: Now, we add the partial quotients:
   $$
   60 + 19 = 79
   $$
Thus, $$ 632 \div 8 = 79 $$.

### Conclusion

In both methods, we arrive at the same result: 
$$
632 \div 8 = 79
$$

This demonstrates that partial quotients can be used flexibly with different estimates to achieve the same division result.
To find $$ 632 \div 8 $$ using partial quotients, you can: 1. **Method 1**: Estimate $$ 8 \times 70 = 560 $$, subtract to get 72, then estimate $$ 8 \times 9 = 72 $$, subtract to reach 0. Add the partial quotients: $$ 70 + 9 = 79 $$. 2. **Method 2**: Estimate $$ 8 \times 60 = 480 $$, subtract to get 152, then estimate $$ 8 \times 19 = 152 $$, subtract to reach 0. Add the partial quotients: $$ 60 + 19 = 79 $$. Both methods show that $$ 632 \div 8 = 79 $$.

8. Show 2 different ways you can use partial quotients to find \( 632 \div 8 \).

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