Evaluate
\frac{500000}{7}\approx 71428.571428571
Factor
\frac{2 ^ {5} \cdot 5 ^ {6}}{7} = 71428\frac{4}{7} = 71428.57142857143
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)1000000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1000000
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)1000000}\\\end{array}
Since 1 is less than 14, use the next digit 0 from dividend 1000000 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)1000000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1000000
\begin{array}{l}\phantom{14)}00\phantom{4}\\14\overline{)1000000}\\\end{array}
Since 10 is less than 14, use the next digit 0 from dividend 1000000 and add 0 to the quotient
\begin{array}{l}\phantom{14)}00\phantom{5}\\14\overline{)1000000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1000000
\begin{array}{l}\phantom{14)}007\phantom{6}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}2\\\end{array}
Find closest multiple of 14 to 100. We see that 7 \times 14 = 98 is the nearest. Now subtract 98 from 100 to get reminder 2. Add 7 to quotient.
\begin{array}{l}\phantom{14)}007\phantom{7}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\end{array}
Use the 4^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{14)}0071\phantom{8}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\phantom{14)}\underline{\phantom{99}14\phantom{999}}\\\phantom{14)999}6\\\end{array}
Find closest multiple of 14 to 20. We see that 1 \times 14 = 14 is the nearest. Now subtract 14 from 20 to get reminder 6. Add 1 to quotient.
\begin{array}{l}\phantom{14)}0071\phantom{9}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\phantom{14)}\underline{\phantom{99}14\phantom{999}}\\\phantom{14)999}60\\\end{array}
Use the 5^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{14)}00714\phantom{10}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\phantom{14)}\underline{\phantom{99}14\phantom{999}}\\\phantom{14)999}60\\\phantom{14)}\underline{\phantom{999}56\phantom{99}}\\\phantom{14)9999}4\\\end{array}
Find closest multiple of 14 to 60. We see that 4 \times 14 = 56 is the nearest. Now subtract 56 from 60 to get reminder 4. Add 4 to quotient.
\begin{array}{l}\phantom{14)}00714\phantom{11}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\phantom{14)}\underline{\phantom{99}14\phantom{999}}\\\phantom{14)999}60\\\phantom{14)}\underline{\phantom{999}56\phantom{99}}\\\phantom{14)9999}40\\\end{array}
Use the 6^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{14)}007142\phantom{12}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\phantom{14)}\underline{\phantom{99}14\phantom{999}}\\\phantom{14)999}60\\\phantom{14)}\underline{\phantom{999}56\phantom{99}}\\\phantom{14)9999}40\\\phantom{14)}\underline{\phantom{9999}28\phantom{9}}\\\phantom{14)9999}12\\\end{array}
Find closest multiple of 14 to 40. We see that 2 \times 14 = 28 is the nearest. Now subtract 28 from 40 to get reminder 12. Add 2 to quotient.
\begin{array}{l}\phantom{14)}007142\phantom{13}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\phantom{14)}\underline{\phantom{99}14\phantom{999}}\\\phantom{14)999}60\\\phantom{14)}\underline{\phantom{999}56\phantom{99}}\\\phantom{14)9999}40\\\phantom{14)}\underline{\phantom{9999}28\phantom{9}}\\\phantom{14)9999}120\\\end{array}
Use the 7^{th} digit 0 from dividend 1000000
\begin{array}{l}\phantom{14)}0071428\phantom{14}\\14\overline{)1000000}\\\phantom{14)}\underline{\phantom{9}98\phantom{9999}}\\\phantom{14)99}20\\\phantom{14)}\underline{\phantom{99}14\phantom{999}}\\\phantom{14)999}60\\\phantom{14)}\underline{\phantom{999}56\phantom{99}}\\\phantom{14)9999}40\\\phantom{14)}\underline{\phantom{9999}28\phantom{9}}\\\phantom{14)9999}120\\\phantom{14)}\underline{\phantom{9999}112\phantom{}}\\\phantom{14)999999}8\\\end{array}
Find closest multiple of 14 to 120. We see that 8 \times 14 = 112 is the nearest. Now subtract 112 from 120 to get reminder 8. Add 8 to quotient.
\text{Quotient: }71428 \text{Reminder: }8
Since 8 is less than 14, stop the division. The reminder is 8. The topmost line 0071428 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 71428.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}