Evaluate
278
Factor
2\times 139
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)4170}\\\end{array}
Use the 1^{st} digit 4 from dividend 4170
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)4170}\\\end{array}
Since 4 is less than 15, use the next digit 1 from dividend 4170 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)4170}\\\end{array}
Use the 2^{nd} digit 1 from dividend 4170
\begin{array}{l}\phantom{15)}02\phantom{4}\\15\overline{)4170}\\\phantom{15)}\underline{\phantom{}30\phantom{99}}\\\phantom{15)}11\\\end{array}
Find closest multiple of 15 to 41. We see that 2 \times 15 = 30 is the nearest. Now subtract 30 from 41 to get reminder 11. Add 2 to quotient.
\begin{array}{l}\phantom{15)}02\phantom{5}\\15\overline{)4170}\\\phantom{15)}\underline{\phantom{}30\phantom{99}}\\\phantom{15)}117\\\end{array}
Use the 3^{rd} digit 7 from dividend 4170
\begin{array}{l}\phantom{15)}027\phantom{6}\\15\overline{)4170}\\\phantom{15)}\underline{\phantom{}30\phantom{99}}\\\phantom{15)}117\\\phantom{15)}\underline{\phantom{}105\phantom{9}}\\\phantom{15)9}12\\\end{array}
Find closest multiple of 15 to 117. We see that 7 \times 15 = 105 is the nearest. Now subtract 105 from 117 to get reminder 12. Add 7 to quotient.
\begin{array}{l}\phantom{15)}027\phantom{7}\\15\overline{)4170}\\\phantom{15)}\underline{\phantom{}30\phantom{99}}\\\phantom{15)}117\\\phantom{15)}\underline{\phantom{}105\phantom{9}}\\\phantom{15)9}120\\\end{array}
Use the 4^{th} digit 0 from dividend 4170
\begin{array}{l}\phantom{15)}0278\phantom{8}\\15\overline{)4170}\\\phantom{15)}\underline{\phantom{}30\phantom{99}}\\\phantom{15)}117\\\phantom{15)}\underline{\phantom{}105\phantom{9}}\\\phantom{15)9}120\\\phantom{15)}\underline{\phantom{9}120\phantom{}}\\\phantom{15)9999}0\\\end{array}
Find closest multiple of 15 to 120. We see that 8 \times 15 = 120 is the nearest. Now subtract 120 from 120 to get reminder 0. Add 8 to quotient.
\text{Quotient: }278 \text{Reminder: }0
Since 0 is less than 15, stop the division. The reminder is 0. The topmost line 0278 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 278.
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}