Evaluate
78
Factor
2\times 3\times 13
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\begin{array}{l}\phantom{20)}\phantom{1}\\20\overline{)1560}\\\end{array}
Use the 1^{st} digit 1 from dividend 1560
\begin{array}{l}\phantom{20)}0\phantom{2}\\20\overline{)1560}\\\end{array}
Since 1 is less than 20, use the next digit 5 from dividend 1560 and add 0 to the quotient
\begin{array}{l}\phantom{20)}0\phantom{3}\\20\overline{)1560}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1560
\begin{array}{l}\phantom{20)}00\phantom{4}\\20\overline{)1560}\\\end{array}
Since 15 is less than 20, use the next digit 6 from dividend 1560 and add 0 to the quotient
\begin{array}{l}\phantom{20)}00\phantom{5}\\20\overline{)1560}\\\end{array}
Use the 3^{rd} digit 6 from dividend 1560
\begin{array}{l}\phantom{20)}007\phantom{6}\\20\overline{)1560}\\\phantom{20)}\underline{\phantom{}140\phantom{9}}\\\phantom{20)9}16\\\end{array}
Find closest multiple of 20 to 156. We see that 7 \times 20 = 140 is the nearest. Now subtract 140 from 156 to get reminder 16. Add 7 to quotient.
\begin{array}{l}\phantom{20)}007\phantom{7}\\20\overline{)1560}\\\phantom{20)}\underline{\phantom{}140\phantom{9}}\\\phantom{20)9}160\\\end{array}
Use the 4^{th} digit 0 from dividend 1560
\begin{array}{l}\phantom{20)}0078\phantom{8}\\20\overline{)1560}\\\phantom{20)}\underline{\phantom{}140\phantom{9}}\\\phantom{20)9}160\\\phantom{20)}\underline{\phantom{9}160\phantom{}}\\\phantom{20)9999}0\\\end{array}
Find closest multiple of 20 to 160. We see that 8 \times 20 = 160 is the nearest. Now subtract 160 from 160 to get reminder 0. Add 8 to quotient.
\text{Quotient: }78 \text{Reminder: }0
Since 0 is less than 20, stop the division. The reminder is 0. The topmost line 0078 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 78.
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}