Evaluate
35
Factor
5\times 7
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)945}\\\end{array}
Use the 1^{st} digit 9 from dividend 945
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)945}\\\end{array}
Since 9 is less than 27, use the next digit 4 from dividend 945 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)945}\\\end{array}
Use the 2^{nd} digit 4 from dividend 945
\begin{array}{l}\phantom{27)}03\phantom{4}\\27\overline{)945}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}13\\\end{array}
Find closest multiple of 27 to 94. We see that 3 \times 27 = 81 is the nearest. Now subtract 81 from 94 to get reminder 13. Add 3 to quotient.
\begin{array}{l}\phantom{27)}03\phantom{5}\\27\overline{)945}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}135\\\end{array}
Use the 3^{rd} digit 5 from dividend 945
\begin{array}{l}\phantom{27)}035\phantom{6}\\27\overline{)945}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}135\\\phantom{27)}\underline{\phantom{}135\phantom{}}\\\phantom{27)999}0\\\end{array}
Find closest multiple of 27 to 135. We see that 5 \times 27 = 135 is the nearest. Now subtract 135 from 135 to get reminder 0. Add 5 to quotient.
\text{Quotient: }35 \text{Reminder: }0
Since 0 is less than 27, stop the division. The reminder is 0. The topmost line 035 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 35.
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}