Evaluate
805
Factor
5\times 7\times 23
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\begin{array}{l}\phantom{75)}\phantom{1}\\75\overline{)60375}\\\end{array}
Use the 1^{st} digit 6 from dividend 60375
\begin{array}{l}\phantom{75)}0\phantom{2}\\75\overline{)60375}\\\end{array}
Since 6 is less than 75, use the next digit 0 from dividend 60375 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0\phantom{3}\\75\overline{)60375}\\\end{array}
Use the 2^{nd} digit 0 from dividend 60375
\begin{array}{l}\phantom{75)}00\phantom{4}\\75\overline{)60375}\\\end{array}
Since 60 is less than 75, use the next digit 3 from dividend 60375 and add 0 to the quotient
\begin{array}{l}\phantom{75)}00\phantom{5}\\75\overline{)60375}\\\end{array}
Use the 3^{rd} digit 3 from dividend 60375
\begin{array}{l}\phantom{75)}008\phantom{6}\\75\overline{)60375}\\\phantom{75)}\underline{\phantom{}600\phantom{99}}\\\phantom{75)99}3\\\end{array}
Find closest multiple of 75 to 603. We see that 8 \times 75 = 600 is the nearest. Now subtract 600 from 603 to get reminder 3. Add 8 to quotient.
\begin{array}{l}\phantom{75)}008\phantom{7}\\75\overline{)60375}\\\phantom{75)}\underline{\phantom{}600\phantom{99}}\\\phantom{75)99}37\\\end{array}
Use the 4^{th} digit 7 from dividend 60375
\begin{array}{l}\phantom{75)}0080\phantom{8}\\75\overline{)60375}\\\phantom{75)}\underline{\phantom{}600\phantom{99}}\\\phantom{75)99}37\\\end{array}
Since 37 is less than 75, use the next digit 5 from dividend 60375 and add 0 to the quotient
\begin{array}{l}\phantom{75)}0080\phantom{9}\\75\overline{)60375}\\\phantom{75)}\underline{\phantom{}600\phantom{99}}\\\phantom{75)99}375\\\end{array}
Use the 5^{th} digit 5 from dividend 60375
\begin{array}{l}\phantom{75)}00805\phantom{10}\\75\overline{)60375}\\\phantom{75)}\underline{\phantom{}600\phantom{99}}\\\phantom{75)99}375\\\phantom{75)}\underline{\phantom{99}375\phantom{}}\\\phantom{75)99999}0\\\end{array}
Find closest multiple of 75 to 375. We see that 5 \times 75 = 375 is the nearest. Now subtract 375 from 375 to get reminder 0. Add 5 to quotient.
\text{Quotient: }805 \text{Reminder: }0
Since 0 is less than 75, stop the division. The reminder is 0. The topmost line 00805 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 805.
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}