Divide, and find out the quotient and remainder. Check your answer.
(i) `6971 divide 47`
(ii) `4178 divide 35`
(iii) `36195 divide 153`
(iv) `93575 divide 400`
(v) `23025 divide 1000`
(iv) `16135 divide 875`

Answer

Let's solve each division problem step by step, finding the quotient and remainder for each case, and then check our answers.

### (i) 6971 divided by 47

1. **Set up the division**: We have 6971 as the dividend and 47 as the divisor.
2. **Estimate how many times 47 fits into the first part of 6971**:
- 47 goes into 69 once (1).
- 1 × 47 = 47.
- Subtract: 69 - 47 = 22.
3. **Bring down the next digit (7)**: Now we have 227.
4. **Estimate how many times 47 fits into 227**:
- 47 goes into 227 four times (4).
- 4 × 47 = 188.
- Subtract: 227 - 188 = 39.
5. **Bring down the next digit (1)**: Now we have 391.
6. **Estimate how many times 47 fits into 391**:
- 47 goes into 391 eight times (8).
- 8 × 47 = 376.
- Subtract: 391 - 376 = 15.
7. **Final result**:
- Quotient = 148
- Remainder = 15

**Check**:
- \( 47 \times 148 + 15 = 6966 + 15 = 6971 \) (Correct)

### (ii) 4178 divided by 35

1. **Set up the division**: 4178 (dividend) and 35 (divisor).
2. **Estimate how many times 35 fits into 41**:
- 35 goes into 41 once (1).
- 1 × 35 = 35.
- Subtract: 41 - 35 = 6.
3. **Bring down the next digit (7)**: Now we have 67.
4. **Estimate how many times 35 fits into 67**:
- 35 goes into 67 once (1).
- 1 × 35 = 35.
- Subtract: 67 - 35 = 32.
5. **Bring down the next digit (8)**: Now we have 328.
6. **Estimate how many times 35 fits into 328**:
- 35 goes into 328 nine times (9).
- 9 × 35 = 315.
- Subtract: 328 - 315 = 13.
7. **Final result**:
- Quotient = 119
- Remainder = 13

**Check**:
- \( 35 \times 119 + 13 = 4165 + 13 = 4178 \) (Correct)

### (iii) 36195 divided by 153

1. **Set up the division**: 36195 (dividend) and 153 (divisor).
2. **Estimate how many times 153 fits into 361**:
- 153 goes into 361 twice (2).
- 2 × 153 = 306.
- Subtract: 361 - 306 = 55.
3. **Bring down the next digit (9)**: Now we have 559.
4. **Estimate how many times 153 fits into 559**:
- 153 goes into 559 three times (3).
- 3 × 153 = 459.
- Subtract: 559 - 459 = 100.
5. **Bring down the next digit (5)**: Now we have 1005.
6. **Estimate how many times 153 fits into 1005**:
- 153 goes into 1005 six times (6).
- 6 × 153 = 918.
- Subtract: 1005 - 918 = 87.
7. **Final result**:
- Quotient = 236
- Remainder = 87

**Check**:
- \( 153 \times 236 + 87 = 36108 + 87 = 36195 \) (Correct)

### (iv) 93575 divided by 400

1. **Set up the division**: 93575 (dividend) and 400 (divisor).
2. **Estimate how many times 400 fits into 935**:
- 400 goes into 935 twice (2).
- 2 × 400 = 800.
- Subtract: 935 - 800 = 135.
3. **Bring down the next digit (7)**: Now we have 1357.
4. **Estimate how many times 400 fits into 1357**:
- 400 goes into 1357 three times (3).
- 3 × 400 = 1200.
- Subtract: 1357 - 1200 = 157.
5. **Bring down the next digit (5)**: Now we have 1575.
6. **Estimate how many times 400 fits into 1575**:
- 400 goes into 1575 three times (3).
- 3 × 400 = 1200.
- Subtract: 1575 - 1200 = 375.
7. **Final result**:
- Quotient = 233
- Remainder = 375

**Check**:
- \( 400 \times 233 + 375 = 93200 + 375 = 93575 \) (Correct)

### (v) 23025 divided by 1000

1. **Set up the division**: 23025 (dividend) and 1000 (divisor).
2. **Estimate how many times 1000 fits into 2302**:
- 1000 goes into 2302 twice (2).
- 2 × 1000 = 2000.
- Subtract: 2302 - 2000 = 302.
3. **Bring down the next digit (5)**: Now we have 3025.
4. **Estimate how many times 1000 fits into 3025**:
- 1000 goes into 3025 three times (3).
- 3 × 1000 = 3000.
- Subtract: 3025 - 3000 = 25.
5. **Final result**:
- Quotient = 23
- Remainder = 25

**Check**:
- \( 1000 \times 23 + 25 = 23000 + 25 = 23025 \) (Correct)

### (vi) 16135 divided by 875

1. **Set up the division**: 16135 (dividend) and 875 (divisor).
2. **Estimate how many times 875 fits into 1613**:
- 875 goes into 1613 once (1).
- 1 × 875 = 875.
- Subtract: 1613 - 875 = 738.
3. **Bring down the next digit (5)**: Now we have 7385.
4. **Estimate how many times 875 fits into 7385**:
- 875 goes into 7385 eight times (8).
- 8 × 875 = 7000.
- Subtract: 7385 - 7000 = 385.
5. **Final result**:
- Quotient = 18
- Remainder = 385

**Check**:
- \( 875 \times 18 + 385 = 15750 + 385 = 16135 \) (Correct)

### Summary of Results:
1. **(i)** Quotient = 148, Remainder = 15
2. **(ii)** Quotient = 119, Remainder = 13
3. **(iii)** Quotient = 236, Remainder = 87
4. **(iv)** Quotient = 233, Remainder = 375
5. **(v)** Quotient = 23, Remainder = 25
6. **(vi)** Quotient = 18, Remainder = 385