Evaluate
\frac{1075}{3}\approx 358.333333333
Factor
\frac{5 ^ {2} \cdot 43}{3} = 358\frac{1}{3} = 358.3333333333333
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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)43000}\\\end{array}
Use the 1^{st} digit 4 from dividend 43000
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)43000}\\\end{array}
Since 4 is less than 120, use the next digit 3 from dividend 43000 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)43000}\\\end{array}
Use the 2^{nd} digit 3 from dividend 43000
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)43000}\\\end{array}
Since 43 is less than 120, use the next digit 0 from dividend 43000 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)43000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 43000
\begin{array}{l}\phantom{120)}003\phantom{6}\\120\overline{)43000}\\\phantom{120)}\underline{\phantom{}360\phantom{99}}\\\phantom{120)9}70\\\end{array}
Find closest multiple of 120 to 430. We see that 3 \times 120 = 360 is the nearest. Now subtract 360 from 430 to get reminder 70. Add 3 to quotient.
\begin{array}{l}\phantom{120)}003\phantom{7}\\120\overline{)43000}\\\phantom{120)}\underline{\phantom{}360\phantom{99}}\\\phantom{120)9}700\\\end{array}
Use the 4^{th} digit 0 from dividend 43000
\begin{array}{l}\phantom{120)}0035\phantom{8}\\120\overline{)43000}\\\phantom{120)}\underline{\phantom{}360\phantom{99}}\\\phantom{120)9}700\\\phantom{120)}\underline{\phantom{9}600\phantom{9}}\\\phantom{120)9}100\\\end{array}
Find closest multiple of 120 to 700. We see that 5 \times 120 = 600 is the nearest. Now subtract 600 from 700 to get reminder 100. Add 5 to quotient.
\begin{array}{l}\phantom{120)}0035\phantom{9}\\120\overline{)43000}\\\phantom{120)}\underline{\phantom{}360\phantom{99}}\\\phantom{120)9}700\\\phantom{120)}\underline{\phantom{9}600\phantom{9}}\\\phantom{120)9}1000\\\end{array}
Use the 5^{th} digit 0 from dividend 43000
\begin{array}{l}\phantom{120)}00358\phantom{10}\\120\overline{)43000}\\\phantom{120)}\underline{\phantom{}360\phantom{99}}\\\phantom{120)9}700\\\phantom{120)}\underline{\phantom{9}600\phantom{9}}\\\phantom{120)9}1000\\\phantom{120)}\underline{\phantom{99}960\phantom{}}\\\phantom{120)999}40\\\end{array}
Find closest multiple of 120 to 1000. We see that 8 \times 120 = 960 is the nearest. Now subtract 960 from 1000 to get reminder 40. Add 8 to quotient.
\text{Quotient: }358 \text{Reminder: }40
Since 40 is less than 120, stop the division. The reminder is 40. The topmost line 00358 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 358.
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}