Final answer:
The correct equations after verification are 1) 823 ÷ 6 = 137 r1 and 4) 267 ÷ 4 = 66 r3. The other options do not accurately represent the dividends and divisors provided.
Step-by-step explanation:
To select each correct equation from the given options, we can perform division and verify the results against the provided statements.
- For 823 ÷ 6, we should expect a quotient and a remainder. Calculating this, we get a quotient of 137 and a remainder of 1, which matches option 1) 823 ÷ 6 = 137 r1.
- Calculating 4,235 ÷ 7, the quotient should be whole, and the remainder should be less than 7. The correct quotient is 605 with a remainder of 0, which does not match option 2) 4,235 ÷ 7 = 600 r8.
- For 2,167 ÷ 3, we expect a whole number quotient with no remainder if the division is exact. The actual quotient is 722 with a remainder of 1, which does not match option 3) 2,167 ÷ 3 = 722.
- Calculating 267 ÷ 4 gives us a quotient of 66 and a remainder of 3. This matches option 4) 267 ÷ 4 = 66 r3.
- Finally, 6,552 ÷ 7 should also result in a whole number quotient with a remainder if it's not divisible. The actual quotient is 935 with a remainder of 7, which does not match option 5) 6,552 ÷ 7 = 936.
By verifying each equation, we determine the correct equations are option 1) 823 ÷ 6 = 137 r1 and option 4) 267 ÷ 4 = 66 r3.
After obtaining numerical solutions, it is crucial to check your answer to verify if the results are reasonable and make sense within the context of the problem presented.