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Calculate the following pairs: a) (328 ÷ 4) ÷ 2; 328 ÷ (4 ÷ 2) b) 144 ÷ (6 ÷ 3); (144 ÷ 6) ÷ 3

Mathematics

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Step-by-step solution

26 steps

1. Calculate the following pairs:

  • a) (328÷4)÷2(328 \div 4) \div 2 and 328÷(4÷2)328 \div (4 \div 2)
    • For (328÷4)÷2(328 \div 4) \div 2:
  1. Calculate the expression in the first parenthesis.

        $$
        328 \div 4 = 82
        $$
    
  2. Divide the result by 2.

        $$
        82 \div 2 = 41
        $$
        The first expression equals $\boxed{41}$.
    
    *   For $328 \div (4 \div 2)$:
    
  3. Calculate the expression in the second parenthesis.

        $$
        4 \div 2 = 2
        $$
    
  4. Divide 328 by the result.

        $$
        328 \div 2 = 164
        $$
        The second expression equals $\boxed{164}$.
    
    • b) 144÷(6÷3)144 \div (6 \div 3) and (144÷6)÷3(144 \div 6) \div 3
      • For 144÷(6÷3)144 \div (6 \div 3):
  5. Calculate the expression in the first parenthesis.

        $$
        6 \div 3 = 2
        $$
    
  6. Divide 144 by the result.

        $$
        144 \div 2 = 72
        $$
        The first expression equals $\boxed{72}$.
    
    *   For $(144 \div 6) \div 3$:
    
  7. Calculate the expression in the second parenthesis.

        $$
        144 \div 6 = 24
        $$
    
  8. Divide the result by 3.

        $$
        24 \div 3 = 8
        $$
        The second expression equals $\boxed{8}$.
    

    2. Divide these numbers by 4. Check your answers by multiplying.

    • a) 118÷4118 \div 4
  9. Perform the division.

    $$
    118 \div 4 = 29 \text{ remainder } 2
    $$
    
  10. Check the answer by multiplying.

    $$
    29 \times 4 + 2 = 116 + 2 = 118
    $$
    The answer is $\boxed{\text{29 remainder 2}}$.
    
    • b) 85÷485 \div 4
  11. Perform the division.

    $$
    85 \div 4 = 21 \text{ remainder } 1
    $$
    
  12. Check the answer by multiplying.

    $$
    21 \times 4 + 1 = 84 + 1 = 85
    $$
    The answer is $\boxed{\text{21 remainder 1}}$.
    
    • c) 261÷4261 \div 4
  13. Perform the division.

    $$
    261 \div 4 = 65 \text{ remainder } 1
    $$
    
  14. Check the answer by multiplying.

    $$
    65 \times 4 + 1 = 260 + 1 = 261
    $$
    The answer is $\boxed{\text{65 remainder 1}}$.
    

    3. Divide these numbers by 9. Use rounding to decide whether the answers are reasonable.

    • a) 475÷9475 \div 9
  15. Perform the division.

    $$
    475 \div 9 = 52 \text{ remainder } 7
    $$
    
  16. Round 475 to the nearest multiple of 9.

    475≈450475 \approx 450.

  17. Estimate the division.

    $$
    450 \div 9 = 50
    $$
    The answer 52 is close to the estimate 50, so it is $\boxed{\text{reasonable}}$.
    
    • b) 234÷9234 \div 9
  18. Perform the division.

    $$
    234 \div 9 = 26
    $$
    
  19. Round 234 to the nearest multiple of 9.

    234≈230234 \approx 230 (not a multiple of 9). 234≈270234 \approx 270 (multiple of 9). Or 234≈225234 \approx 225 (multiple of 9). Let's use 234≈230234 \approx 230.

  20. Estimate the division.

    $$
    230 \div 9 \approx 25.5
    $$
    The answer 26 is close to the estimate 25.5, so it is $\boxed{\text{reasonable}}$.
    
    • c) 701÷9701 \div 9
  21. Perform the division.

    $$
    701 \div 9 = 77 \text{ remainder } 8
    $$
    
  22. Round 701 to the nearest multiple of 9.

    701≈720701 \approx 720.

  23. Estimate the division.

    $$
    720 \div 9 = 80
    $$
    The answer 77 is close to the estimate 80, so it is $\boxed{\text{reasonable}}$.
    
    • d) 511÷9511 \div 9
  24. Perform the division.

    $$
    511 \div 9 = 56 \text{ remainder } 7
    $$
    
  25. Round 511 to the nearest multiple of 9.

    511≈540511 \approx 540.

  26. Estimate the division.

    $$
    540 \div 9 = 60
    $$
    The answer 56 is close to the estimate 60, so it is $\boxed{\text{reasonable}}$.
    

    4. Fill in the missing numbers:

    • a) 630÷□=7630 \div \square = 7 To find the missing number, divide 630 by 7.

      630÷7=90630 \div 7 = 90

      The missing number is 90\boxed{90}.

    • b) 560÷□=7560 \div \square = 7 To find the missing number, divide 560 by 7.

      560÷7=80560 \div 7 = 80

      The missing number is 80\boxed{80}.

    • c) 720÷□=60720 \div \square = 60 To find the missing number, divide 720 by 60.

      720÷60=12720 \div 60 = 12

      The missing number is 12\boxed{12}.

    • d) 360÷□=9360 \div \square = 9 To find the missing number, divide 360 by 9.

      360÷9=40360 \div 9 = 40

      The missing number is 40\boxed{40}.

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