Evaluate
\frac{105}{74}\approx 1.418918919
Factor
\frac{3 \cdot 5 \cdot 7}{2 \cdot 37} = 1\frac{31}{74} = 1.4189189189189189
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\begin{array}{l}\phantom{148)}\phantom{1}\\148\overline{)210}\\\end{array}
Use the 1^{st} digit 2 from dividend 210
\begin{array}{l}\phantom{148)}0\phantom{2}\\148\overline{)210}\\\end{array}
Since 2 is less than 148, use the next digit 1 from dividend 210 and add 0 to the quotient
\begin{array}{l}\phantom{148)}0\phantom{3}\\148\overline{)210}\\\end{array}
Use the 2^{nd} digit 1 from dividend 210
\begin{array}{l}\phantom{148)}00\phantom{4}\\148\overline{)210}\\\end{array}
Since 21 is less than 148, use the next digit 0 from dividend 210 and add 0 to the quotient
\begin{array}{l}\phantom{148)}00\phantom{5}\\148\overline{)210}\\\end{array}
Use the 3^{rd} digit 0 from dividend 210
\begin{array}{l}\phantom{148)}001\phantom{6}\\148\overline{)210}\\\phantom{148)}\underline{\phantom{}148\phantom{}}\\\phantom{148)9}62\\\end{array}
Find closest multiple of 148 to 210. We see that 1 \times 148 = 148 is the nearest. Now subtract 148 from 210 to get reminder 62. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }62
Since 62 is less than 148, stop the division. The reminder is 62. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}