Evaluate
\frac{157}{10}=15.7
Factor
\frac{157}{2 \cdot 5} = 15\frac{7}{10} = 15.7
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)471}\\\end{array}
Use the 1^{st} digit 4 from dividend 471
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)471}\\\end{array}
Since 4 is less than 30, use the next digit 7 from dividend 471 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)471}\\\end{array}
Use the 2^{nd} digit 7 from dividend 471
\begin{array}{l}\phantom{30)}01\phantom{4}\\30\overline{)471}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}17\\\end{array}
Find closest multiple of 30 to 47. We see that 1 \times 30 = 30 is the nearest. Now subtract 30 from 47 to get reminder 17. Add 1 to quotient.
\begin{array}{l}\phantom{30)}01\phantom{5}\\30\overline{)471}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}171\\\end{array}
Use the 3^{rd} digit 1 from dividend 471
\begin{array}{l}\phantom{30)}015\phantom{6}\\30\overline{)471}\\\phantom{30)}\underline{\phantom{}30\phantom{9}}\\\phantom{30)}171\\\phantom{30)}\underline{\phantom{}150\phantom{}}\\\phantom{30)9}21\\\end{array}
Find closest multiple of 30 to 171. We see that 5 \times 30 = 150 is the nearest. Now subtract 150 from 171 to get reminder 21. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }21
Since 21 is less than 30, stop the division. The reminder is 21. The topmost line 015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}