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Answer :
Sure! Let's work through this problem step-by-step.
### Problem Analysis
John performed the subtraction [tex]\(345 - 182\)[/tex] and got the result [tex]\(163\)[/tex]. We want to find the correct number sentence that John could use to check his work.
### Understanding Number Sentences
To check a subtraction, we can use addition. The idea is to add the subtracted number and the result to see if we get the original number back.
### Steps to Verify
1. Subtraction Result: John calculated [tex]\(345 - 182 = 163\)[/tex].
2. Checking the Choices:
- Choice A: [tex]\(182 + 163\)[/tex]
- Choice B: [tex]\(345 + 163\)[/tex]
- Choice C: [tex]\(345 + 182\)[/tex]
- Choice D: [tex]\(182 - 163\)[/tex]
3. Evaluating Choice A:
[tex]\[
182 + 163 = 345
\][/tex]
This correctly adds up to the original number [tex]\(345\)[/tex], so this is the correct way to check the subtraction result.
4. Evaluating Other Choices:
- Choice B: [tex]\(345 + 163\)[/tex] gives a number much larger than [tex]\(345\)[/tex]. This one doesn't help in checking the subtraction.
- Choice C: [tex]\(345 + 182\)[/tex] gives a number much larger than [tex]\(345\)[/tex]. This one also doesn't help.
- Choice D: [tex]\(182 - 163\)[/tex] gives a number smaller than [tex]\(182\)[/tex]. This one doesn't help in checking the subtraction.
Since Choice A is the correct one, John can write:
[tex]\[
182 + 163 = 345
\][/tex]
This confirms his subtraction.
### Conclusion
The correct number sentence John should write to check his work is:
[tex]\[
\boxed{182 + 163 = 345}
\][/tex]
This verifies that his subtraction [tex]\(345 - 182 = 163\)[/tex] is indeed correct.
### Problem Analysis
John performed the subtraction [tex]\(345 - 182\)[/tex] and got the result [tex]\(163\)[/tex]. We want to find the correct number sentence that John could use to check his work.
### Understanding Number Sentences
To check a subtraction, we can use addition. The idea is to add the subtracted number and the result to see if we get the original number back.
### Steps to Verify
1. Subtraction Result: John calculated [tex]\(345 - 182 = 163\)[/tex].
2. Checking the Choices:
- Choice A: [tex]\(182 + 163\)[/tex]
- Choice B: [tex]\(345 + 163\)[/tex]
- Choice C: [tex]\(345 + 182\)[/tex]
- Choice D: [tex]\(182 - 163\)[/tex]
3. Evaluating Choice A:
[tex]\[
182 + 163 = 345
\][/tex]
This correctly adds up to the original number [tex]\(345\)[/tex], so this is the correct way to check the subtraction result.
4. Evaluating Other Choices:
- Choice B: [tex]\(345 + 163\)[/tex] gives a number much larger than [tex]\(345\)[/tex]. This one doesn't help in checking the subtraction.
- Choice C: [tex]\(345 + 182\)[/tex] gives a number much larger than [tex]\(345\)[/tex]. This one also doesn't help.
- Choice D: [tex]\(182 - 163\)[/tex] gives a number smaller than [tex]\(182\)[/tex]. This one doesn't help in checking the subtraction.
Since Choice A is the correct one, John can write:
[tex]\[
182 + 163 = 345
\][/tex]
This confirms his subtraction.
### Conclusion
The correct number sentence John should write to check his work is:
[tex]\[
\boxed{182 + 163 = 345}
\][/tex]
This verifies that his subtraction [tex]\(345 - 182 = 163\)[/tex] is indeed correct.
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