To find the difference between the quotients obtained from dividing 32,456 by 24 and 46,951 by 83, we will follow these steps:
### Step 1: Divide 32,456 by 24
1. **Calculate the quotient**:
- 24 goes into 32 once (1), so we write down 1 and subtract \(24 \times 1 = 24\) from 32.
- \(32 - 24 = 8\). Bring down the next digit (4), making it 84.
- 24 goes into 84 three times (3), so we write down 3 and subtract \(24 \times 3 = 72\) from 84.
- \(84 - 72 = 12\). Bring down the next digit (5), making it 125.
- 24 goes into 125 five times (5), so we write down 5 and subtract \(24 \times 5 = 120\) from 125.
- \(125 - 120 = 5\). Bring down the next digit (6), making it 56.
- 24 goes into 56 two times (2), so we write down 2 and subtract \(24 \times 2 = 48\) from 56.
- \(56 - 48 = 8\).
Thus, the quotient \(q_1\) is **1352** with a remainder of 8.
### Step 2: Divide 46,951 by 83
2. **Calculate the quotient**:
- 83 goes into 469 five times (5), so we write down 5 and subtract \(83 \times 5 = 415\) from 469.
- \(469 - 415 = 54\). Bring down the next digit (1), making it 541.
- 83 goes into 541 six times (6), so we write down 6 and subtract \(83 \times 6 = 498\) from 541.
- \(541 - 498 = 43\). Bring down the next digit (5), making it 435.
- 83 goes into 435 five times (5), so we write down 5 and subtract \(83 \times 5 = 415\) from 435.
- \(435 - 415 = 20\). Bring down the next digit (1), making it 201.
- 83 goes into 201 two times (2), so we write down 2 and subtract \(83 \times 2 = 166\) from 201.
- \(201 - 166 = 35\).
Thus, the quotient \(q_2\) is **565** with a remainder of 35.
### Step 3: Find the difference between the two quotients
3. **Calculate the difference**:
- The difference is given by \(q_1 - q_2\).
- \(1352 - 565 = 787\).
### Final Answer
The difference between the quotients is **787**.
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