Evaluate
75
Factor
3\times 5^{2}
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\begin{array}{l}\phantom{50)}\phantom{1}\\50\overline{)3750}\\\end{array}
Use the 1^{st} digit 3 from dividend 3750
\begin{array}{l}\phantom{50)}0\phantom{2}\\50\overline{)3750}\\\end{array}
Since 3 is less than 50, use the next digit 7 from dividend 3750 and add 0 to the quotient
\begin{array}{l}\phantom{50)}0\phantom{3}\\50\overline{)3750}\\\end{array}
Use the 2^{nd} digit 7 from dividend 3750
\begin{array}{l}\phantom{50)}00\phantom{4}\\50\overline{)3750}\\\end{array}
Since 37 is less than 50, use the next digit 5 from dividend 3750 and add 0 to the quotient
\begin{array}{l}\phantom{50)}00\phantom{5}\\50\overline{)3750}\\\end{array}
Use the 3^{rd} digit 5 from dividend 3750
\begin{array}{l}\phantom{50)}007\phantom{6}\\50\overline{)3750}\\\phantom{50)}\underline{\phantom{}350\phantom{9}}\\\phantom{50)9}25\\\end{array}
Find closest multiple of 50 to 375. We see that 7 \times 50 = 350 is the nearest. Now subtract 350 from 375 to get reminder 25. Add 7 to quotient.
\begin{array}{l}\phantom{50)}007\phantom{7}\\50\overline{)3750}\\\phantom{50)}\underline{\phantom{}350\phantom{9}}\\\phantom{50)9}250\\\end{array}
Use the 4^{th} digit 0 from dividend 3750
\begin{array}{l}\phantom{50)}0075\phantom{8}\\50\overline{)3750}\\\phantom{50)}\underline{\phantom{}350\phantom{9}}\\\phantom{50)9}250\\\phantom{50)}\underline{\phantom{9}250\phantom{}}\\\phantom{50)9999}0\\\end{array}
Find closest multiple of 50 to 250. We see that 5 \times 50 = 250 is the nearest. Now subtract 250 from 250 to get reminder 0. Add 5 to quotient.
\text{Quotient: }75 \text{Reminder: }0
Since 0 is less than 50, stop the division. The reminder is 0. The topmost line 0075 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 75.
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}