Evaluate
35
Factor
5\times 7
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)525}\\\end{array}
Use the 1^{st} digit 5 from dividend 525
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)525}\\\end{array}
Since 5 is less than 15, use the next digit 2 from dividend 525 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)525}\\\end{array}
Use the 2^{nd} digit 2 from dividend 525
\begin{array}{l}\phantom{15)}03\phantom{4}\\15\overline{)525}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}7\\\end{array}
Find closest multiple of 15 to 52. We see that 3 \times 15 = 45 is the nearest. Now subtract 45 from 52 to get reminder 7. Add 3 to quotient.
\begin{array}{l}\phantom{15)}03\phantom{5}\\15\overline{)525}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}75\\\end{array}
Use the 3^{rd} digit 5 from dividend 525
\begin{array}{l}\phantom{15)}035\phantom{6}\\15\overline{)525}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}75\\\phantom{15)}\underline{\phantom{9}75\phantom{}}\\\phantom{15)999}0\\\end{array}
Find closest multiple of 15 to 75. We see that 5 \times 15 = 75 is the nearest. Now subtract 75 from 75 to get reminder 0. Add 5 to quotient.
\text{Quotient: }35 \text{Reminder: }0
Since 0 is less than 15, 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}