Evaluate
\frac{105}{2}=52.5
Factor
\frac{3 \cdot 5 \cdot 7}{2} = 52\frac{1}{2} = 52.5
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\begin{array}{l}\phantom{60)}\phantom{1}\\60\overline{)3150}\\\end{array}
Use the 1^{st} digit 3 from dividend 3150
\begin{array}{l}\phantom{60)}0\phantom{2}\\60\overline{)3150}\\\end{array}
Since 3 is less than 60, use the next digit 1 from dividend 3150 and add 0 to the quotient
\begin{array}{l}\phantom{60)}0\phantom{3}\\60\overline{)3150}\\\end{array}
Use the 2^{nd} digit 1 from dividend 3150
\begin{array}{l}\phantom{60)}00\phantom{4}\\60\overline{)3150}\\\end{array}
Since 31 is less than 60, use the next digit 5 from dividend 3150 and add 0 to the quotient
\begin{array}{l}\phantom{60)}00\phantom{5}\\60\overline{)3150}\\\end{array}
Use the 3^{rd} digit 5 from dividend 3150
\begin{array}{l}\phantom{60)}005\phantom{6}\\60\overline{)3150}\\\phantom{60)}\underline{\phantom{}300\phantom{9}}\\\phantom{60)9}15\\\end{array}
Find closest multiple of 60 to 315. We see that 5 \times 60 = 300 is the nearest. Now subtract 300 from 315 to get reminder 15. Add 5 to quotient.
\begin{array}{l}\phantom{60)}005\phantom{7}\\60\overline{)3150}\\\phantom{60)}\underline{\phantom{}300\phantom{9}}\\\phantom{60)9}150\\\end{array}
Use the 4^{th} digit 0 from dividend 3150
\begin{array}{l}\phantom{60)}0052\phantom{8}\\60\overline{)3150}\\\phantom{60)}\underline{\phantom{}300\phantom{9}}\\\phantom{60)9}150\\\phantom{60)}\underline{\phantom{9}120\phantom{}}\\\phantom{60)99}30\\\end{array}
Find closest multiple of 60 to 150. We see that 2 \times 60 = 120 is the nearest. Now subtract 120 from 150 to get reminder 30. Add 2 to quotient.
\text{Quotient: }52 \text{Reminder: }30
Since 30 is less than 60, stop the division. The reminder is 30. The topmost line 0052 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 52.
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}