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Calculate the following with box method: a) 864 ext / 24 b) 945 ext / 27

Mathematics

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Answers

3 parts
a

36\text{36}

b

35\text{35}

c

9\text{9}

40\text{40}

Step-by-step solution

13 steps

Here are the calculations:

1. Calculate the following with box method:

Part a· 4 steps

864÷24864 \div 24

  1. Set up the division.

    0024)864‾\begin{array}{r} \phantom{00} \\ 24 \overline{\smash{)} 864} \\ \end{array}

  2. Determine how many times 24 goes into 864.

    We can start by finding a multiple of 24 that is close to 864.
    24×30=72024 \times 30 = 720.
    Subtract 720 from 864.

    3024)864‾−720144\begin{array}{r} 30 \\ 24 \overline{\smash{)} 864} \\ - 720 \\ \hline 144 \\ \end{array}

  3. Determine how many times 24 goes into the remainder, 144.

    24×6=14424 \times 6 = 144.
    Subtract 144 from 144.

    30+624)864‾−720144−1440\begin{array}{r} 30 + 6 \\ 24 \overline{\smash{)} 864} \\ - 720 \\ \hline 144 \\ - 144 \\ \hline 0 \\ \end{array}

  4. Add the partial quotients.

    30+6=3630 + 6 = 36.
    The remainder is 0.

    The answer is 36\boxed{\text{36}}.

Part b

35\text{35}

945÷27945 \div 27

  1. Set up the division.

    0027)945‾\begin{array}{r} \phantom{00} \\ 27 \overline{\smash{)} 945} \\ \end{array}

  2. Determine how many times 27 goes into 945.

    27×30=81027 \times 30 = 810.
    Subtract 810 from 945.

    3027)945‾−810135\begin{array}{r} 30 \\ 27 \overline{\smash{)} 945} \\ - 810 \\ \hline 135 \\ \end{array}

  3. Determine how many times 27 goes into the remainder, 135.

    27×5=13527 \times 5 = 135.
    Subtract 135 from 135.

    30+527)945‾−810135−1350\begin{array}{r} 30 + 5 \\ 27 \overline{\smash{)} 945} \\ - 810 \\ \hline 135 \\ - 135 \\ \hline 0 \\ \end{array}

  4. Add the partial quotients.

    30+5=3530 + 5 = 35.
    The remainder is 0.

    The answer is 35\boxed{\text{35}}.

Part c

9\text{9}

108÷12108 \div 12

  1. Set up the division.

    012)108‾\begin{array}{r} \phantom{0} \\ 12 \overline{\smash{)} 108} \\ \end{array}

  2. Determine how many times 12 goes into 108.

    12×9=10812 \times 9 = 108.
    Subtract 108 from 108.

    912)108‾−1080\begin{array}{r} 9 \\ 12 \overline{\smash{)} 108} \\ - 108 \\ \hline 0 \\ \end{array}

    The remainder is 0.

    The answer is 9\boxed{\text{9}}.

    2. Estimate 782÷20782 \div 20

  3. Round 782 to the nearest hundred that is easily divisible by 20.

    782 is close to 800.

  4. Perform the division with the rounded number.

    800÷20800 \div 20

  5. Simplify the division.

    800÷20=40800 \div 20 = 40

    The estimate is 40\boxed{\text{40}}.

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