Evaluate
\frac{2250}{19}\approx 118.421052632
Factor
\frac{2 \cdot 3 ^ {2} \cdot 5 ^ {3}}{19} = 118\frac{8}{19} = 118.42105263157895
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\begin{array}{l}\phantom{380)}\phantom{1}\\380\overline{)45000}\\\end{array}
Use the 1^{st} digit 4 from dividend 45000
\begin{array}{l}\phantom{380)}0\phantom{2}\\380\overline{)45000}\\\end{array}
Since 4 is less than 380, use the next digit 5 from dividend 45000 and add 0 to the quotient
\begin{array}{l}\phantom{380)}0\phantom{3}\\380\overline{)45000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 45000
\begin{array}{l}\phantom{380)}00\phantom{4}\\380\overline{)45000}\\\end{array}
Since 45 is less than 380, use the next digit 0 from dividend 45000 and add 0 to the quotient
\begin{array}{l}\phantom{380)}00\phantom{5}\\380\overline{)45000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 45000
\begin{array}{l}\phantom{380)}001\phantom{6}\\380\overline{)45000}\\\phantom{380)}\underline{\phantom{}380\phantom{99}}\\\phantom{380)9}70\\\end{array}
Find closest multiple of 380 to 450. We see that 1 \times 380 = 380 is the nearest. Now subtract 380 from 450 to get reminder 70. Add 1 to quotient.
\begin{array}{l}\phantom{380)}001\phantom{7}\\380\overline{)45000}\\\phantom{380)}\underline{\phantom{}380\phantom{99}}\\\phantom{380)9}700\\\end{array}
Use the 4^{th} digit 0 from dividend 45000
\begin{array}{l}\phantom{380)}0011\phantom{8}\\380\overline{)45000}\\\phantom{380)}\underline{\phantom{}380\phantom{99}}\\\phantom{380)9}700\\\phantom{380)}\underline{\phantom{9}380\phantom{9}}\\\phantom{380)9}320\\\end{array}
Find closest multiple of 380 to 700. We see that 1 \times 380 = 380 is the nearest. Now subtract 380 from 700 to get reminder 320. Add 1 to quotient.
\begin{array}{l}\phantom{380)}0011\phantom{9}\\380\overline{)45000}\\\phantom{380)}\underline{\phantom{}380\phantom{99}}\\\phantom{380)9}700\\\phantom{380)}\underline{\phantom{9}380\phantom{9}}\\\phantom{380)9}3200\\\end{array}
Use the 5^{th} digit 0 from dividend 45000
\begin{array}{l}\phantom{380)}00118\phantom{10}\\380\overline{)45000}\\\phantom{380)}\underline{\phantom{}380\phantom{99}}\\\phantom{380)9}700\\\phantom{380)}\underline{\phantom{9}380\phantom{9}}\\\phantom{380)9}3200\\\phantom{380)}\underline{\phantom{9}3040\phantom{}}\\\phantom{380)99}160\\\end{array}
Find closest multiple of 380 to 3200. We see that 8 \times 380 = 3040 is the nearest. Now subtract 3040 from 3200 to get reminder 160. Add 8 to quotient.
\text{Quotient: }118 \text{Reminder: }160
Since 160 is less than 380, stop the division. The reminder is 160. The topmost line 00118 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 118.
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}