How do I divide 4 over 7 in a easier way

Mathematics

ScanSolve AI Answer

Answer

0.571428‾0.\overline{571428}

Step-by-step solution

7 steps

To divide 4 by 7, we perform long division. Since 4 is smaller than 7, the result will be a decimal.

  1. Set up the long division.

    7)4.0000...‾7 \overline{\smash{)} 4.0000...}

  2. Divide 40 by 7.

    The largest multiple of 7 less than or equal to 40 is 7×5=357 \times 5 = 35.
    Write 5 above the 0, and subtract 35 from 40.

    0.57)4.0000‾−35↓50\begin{array}{r} 0.5 \\ 7 \overline{\smash{)} 4.0000} \\ -35 \downarrow \\ \hline 50 \end{array}

  3. Bring down the next 0 to make 50.

    Divide 50 by 7. The largest multiple of 7 less than or equal to 50 is 7×7=497 \times 7 = 49.
    Write 7 above the next 0, and subtract 49 from 50.

    0.577)4.0000‾−35↓50−49↓10\begin{array}{r} 0.57 \\ 7 \overline{\smash{)} 4.0000} \\ -35 \downarrow \\ \hline 50 \\ -49 \downarrow \\ \hline 10 \end{array}

  4. Bring down the next 0 to make 10.

    Divide 10 by 7. The largest multiple of 7 less than or equal to 10 is 7×1=77 \times 1 = 7.
    Write 1 above the next 0, and subtract 7 from 10.

    0.5717)4.0000‾−35↓50−49↓10−7↓30\begin{array}{r} 0.571 \\ 7 \overline{\smash{)} 4.0000} \\ -35 \downarrow \\ \hline 50 \\ -49 \downarrow \\ \hline 10 \\ -7 \downarrow \\ \hline 30 \end{array}

  5. Bring down the next 0 to make 30.

    Divide 30 by 7. The largest multiple of 7 less than or equal to 30 is 7×4=287 \times 4 = 28.
    Write 4 above the next 0, and subtract 28 from 30.

    0.57147)4.0000‾−35↓50−49↓10−7↓30−28↓20\begin{array}{r} 0.5714 \\ 7 \overline{\smash{)} 4.0000} \\ -35 \downarrow \\ \hline 50 \\ -49 \downarrow \\ \hline 10 \\ -7 \downarrow \\ \hline 30 \\ -28 \downarrow \\ \hline 20 \end{array}

  6. Bring down the next 0 to make 20.

    Divide 20 by 7. The largest multiple of 7 less than or equal to 20 is 7×2=147 \times 2 = 14.
    Write 2 above the next 0, and subtract 14 from 20.

    0.571427)4.00000‾−35↓50−49↓10−7↓30−28↓20−14↓60\begin{array}{r} 0.57142 \\ 7 \overline{\smash{)} 4.00000} \\ -35 \downarrow \\ \hline 50 \\ -49 \downarrow \\ \hline 10 \\ -7 \downarrow \\ \hline 30 \\ -28 \downarrow \\ \hline 20 \\ -14 \downarrow \\ \hline 60 \end{array}

  7. Bring down the next 0 to make 60.

    Divide 60 by 7. The largest multiple of 7 less than or equal to 60 is 7×8=567 \times 8 = 56.
    Write 8 above the next 0, and subtract 56 from 60.

    0.5714287)4.000000‾−35↓50−49↓10−7↓30−28↓20−14↓60−56↓4\begin{array}{r} 0.571428 \\ 7 \overline{\smash{)} 4.000000} \\ -35 \downarrow \\ \hline 50 \\ -49 \downarrow \\ \hline 10 \\ -7 \downarrow \\ \hline 30 \\ -28 \downarrow \\ \hline 20 \\ -14 \downarrow \\ \hline 60 \\ -56 \downarrow \\ \hline 4 \end{array}

    At this point, we have a remainder of 4, which is the same as our starting number. This means the decimal will repeat. The repeating block is 571428.

    So, 47\frac{4}{7} as a decimal is approximately 0.571428... or 0.571428‾0.\overline{571428}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QSimplify the following expression: −4 of [2 ÷ 84 ÷ 7 − 1]QHow do you divide 126 by 4, showing the steps and the remainder?QSimplify the following expression: (3)/(4) + (12)/(7) / (4)/(7) of (7)/(3)((10)/(7) − (5)/(8))…QSolve the following division problems: 64/4, 96/8, 55/5, 72/6, 84/7.QConvert (3)/(4) to an equivalent fraction with a denominator of 8.
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.