Evaluate
\frac{300}{7}\approx 42.857142857
Factor
\frac{2 ^ {2} \cdot 3 \cdot 5 ^ {2}}{7} = 42\frac{6}{7} = 42.857142857142854
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\begin{array}{l}\phantom{35)}\phantom{1}\\35\overline{)1500}\\\end{array}
Use the 1^{st} digit 1 from dividend 1500
\begin{array}{l}\phantom{35)}0\phantom{2}\\35\overline{)1500}\\\end{array}
Since 1 is less than 35, use the next digit 5 from dividend 1500 and add 0 to the quotient
\begin{array}{l}\phantom{35)}0\phantom{3}\\35\overline{)1500}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1500
\begin{array}{l}\phantom{35)}00\phantom{4}\\35\overline{)1500}\\\end{array}
Since 15 is less than 35, use the next digit 0 from dividend 1500 and add 0 to the quotient
\begin{array}{l}\phantom{35)}00\phantom{5}\\35\overline{)1500}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1500
\begin{array}{l}\phantom{35)}004\phantom{6}\\35\overline{)1500}\\\phantom{35)}\underline{\phantom{}140\phantom{9}}\\\phantom{35)9}10\\\end{array}
Find closest multiple of 35 to 150. We see that 4 \times 35 = 140 is the nearest. Now subtract 140 from 150 to get reminder 10. Add 4 to quotient.
\begin{array}{l}\phantom{35)}004\phantom{7}\\35\overline{)1500}\\\phantom{35)}\underline{\phantom{}140\phantom{9}}\\\phantom{35)9}100\\\end{array}
Use the 4^{th} digit 0 from dividend 1500
\begin{array}{l}\phantom{35)}0042\phantom{8}\\35\overline{)1500}\\\phantom{35)}\underline{\phantom{}140\phantom{9}}\\\phantom{35)9}100\\\phantom{35)}\underline{\phantom{99}70\phantom{}}\\\phantom{35)99}30\\\end{array}
Find closest multiple of 35 to 100. We see that 2 \times 35 = 70 is the nearest. Now subtract 70 from 100 to get reminder 30. Add 2 to quotient.
\text{Quotient: }42 \text{Reminder: }30
Since 30 is less than 35, stop the division. The reminder is 30. The topmost line 0042 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 42.
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}