To solve the given problems, we will rearrange the numbers in such a way that it makes it easier to add them. Let's break down each part step by step.
### Part (a): Find the sum of `837 + 208 + 363`
1. **Identify pairs that make 10**:
- Look at the units place of the numbers: 7 (from 837), 8 (from 208), and 3 (from 363).
- Notice that 7 + 3 = 10.
2. **Rearranging the numbers**:
- We can rearrange the numbers as follows: `837 + 363 + 208`.
3. **Add the first pair (837 and 363)**:
- 837 + 363
- Units place: 7 + 3 = 10 (write down 0, carry over 1)
- Tens place: 3 + 6 + 1 (carry) = 10 (write down 0, carry over 1)
- Hundreds place: 8 + 3 + 1 (carry) = 12
- So, 837 + 363 = 1200.
4. **Now add the result to 208**:
- 1200 + 208
- Units place: 0 + 8 = 8
- Tens place: 0 + 0 = 0
- Hundreds place: 2 + 1 = 2
- So, 1200 + 208 = 1408.
### Final answer for part (a):
**The sum is 1408.**
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### Part (b): Find the sum of `1962 + 453 + 1538 + 647`
1. **Identify pairs that make 10**:
- Look at the units place: 2 (from 1962), 8 (from 1538), 3 (from 453), and 7 (from 647).
- Notice that 2 + 8 = 10 and 3 + 7 = 10.
2. **Rearranging the numbers**:
- We can rearrange the numbers as follows: `1962 + 1538 + 453 + 647`.
3. **Add the first pair (1962 and 1538)**:
- 1962 + 1538
- Units place: 2 + 8 = 10 (write down 0, carry over 1)
- Tens place: 6 + 3 + 1 (carry) = 10 (write down 0, carry over 1)
- Hundreds place: 9 + 5 + 1 (carry) = 15 (write down 5, carry over 1)
- Thousands place: 1 + 1 (carry) = 2
- So, 1962 + 1538 = 3500.
4. **Now add the second pair (453 and 647)**:
- 453 + 647
- Units place: 3 + 7 = 10 (write down 0, carry over 1)
- Tens place: 5 + 4 + 1 (carry) = 10 (write down 0, carry over 1)
- Hundreds place: 4 + 6 + 1 (carry) = 11 (write down 1, carry over 1)
- So, 453 + 647 = 1100.
5. **Finally, add the two results together**:
- 3500 + 1100
- Units place: 0 + 0 = 0
- Tens place: 0 + 0 = 0
- Hundreds place: 5 + 1 = 6
- Thousands place: 3 + 1 = 4
- So, 3500 + 1100 = 4600.
### Final answer for part (b):
**The sum is 4600.**
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