Evaluate
\frac{1586}{35}\approx 45.314285714
Factor
\frac{2 \cdot 13 \cdot 61}{5 \cdot 7} = 45\frac{11}{35} = 45.31428571428572
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\begin{array}{l}\phantom{70)}\phantom{1}\\70\overline{)3172}\\\end{array}
Use the 1^{st} digit 3 from dividend 3172
\begin{array}{l}\phantom{70)}0\phantom{2}\\70\overline{)3172}\\\end{array}
Since 3 is less than 70, use the next digit 1 from dividend 3172 and add 0 to the quotient
\begin{array}{l}\phantom{70)}0\phantom{3}\\70\overline{)3172}\\\end{array}
Use the 2^{nd} digit 1 from dividend 3172
\begin{array}{l}\phantom{70)}00\phantom{4}\\70\overline{)3172}\\\end{array}
Since 31 is less than 70, use the next digit 7 from dividend 3172 and add 0 to the quotient
\begin{array}{l}\phantom{70)}00\phantom{5}\\70\overline{)3172}\\\end{array}
Use the 3^{rd} digit 7 from dividend 3172
\begin{array}{l}\phantom{70)}004\phantom{6}\\70\overline{)3172}\\\phantom{70)}\underline{\phantom{}280\phantom{9}}\\\phantom{70)9}37\\\end{array}
Find closest multiple of 70 to 317. We see that 4 \times 70 = 280 is the nearest. Now subtract 280 from 317 to get reminder 37. Add 4 to quotient.
\begin{array}{l}\phantom{70)}004\phantom{7}\\70\overline{)3172}\\\phantom{70)}\underline{\phantom{}280\phantom{9}}\\\phantom{70)9}372\\\end{array}
Use the 4^{th} digit 2 from dividend 3172
\begin{array}{l}\phantom{70)}0045\phantom{8}\\70\overline{)3172}\\\phantom{70)}\underline{\phantom{}280\phantom{9}}\\\phantom{70)9}372\\\phantom{70)}\underline{\phantom{9}350\phantom{}}\\\phantom{70)99}22\\\end{array}
Find closest multiple of 70 to 372. We see that 5 \times 70 = 350 is the nearest. Now subtract 350 from 372 to get reminder 22. Add 5 to quotient.
\text{Quotient: }45 \text{Reminder: }22
Since 22 is less than 70, stop the division. The reminder is 22. The topmost line 0045 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 45.
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}