Evaluate
34
Factor
2\times 17
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)340}\\\end{array}
Use the 1^{st} digit 3 from dividend 340
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)340}\\\end{array}
Since 3 is less than 10, use the next digit 4 from dividend 340 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)340}\\\end{array}
Use the 2^{nd} digit 4 from dividend 340
\begin{array}{l}\phantom{10)}03\phantom{4}\\10\overline{)340}\\\phantom{10)}\underline{\phantom{}30\phantom{9}}\\\phantom{10)9}4\\\end{array}
Find closest multiple of 10 to 34. We see that 3 \times 10 = 30 is the nearest. Now subtract 30 from 34 to get reminder 4. Add 3 to quotient.
\begin{array}{l}\phantom{10)}03\phantom{5}\\10\overline{)340}\\\phantom{10)}\underline{\phantom{}30\phantom{9}}\\\phantom{10)9}40\\\end{array}
Use the 3^{rd} digit 0 from dividend 340
\begin{array}{l}\phantom{10)}034\phantom{6}\\10\overline{)340}\\\phantom{10)}\underline{\phantom{}30\phantom{9}}\\\phantom{10)9}40\\\phantom{10)}\underline{\phantom{9}40\phantom{}}\\\phantom{10)999}0\\\end{array}
Find closest multiple of 10 to 40. We see that 4 \times 10 = 40 is the nearest. Now subtract 40 from 40 to get reminder 0. Add 4 to quotient.
\text{Quotient: }34 \text{Reminder: }0
Since 0 is less than 10, stop the division. The reminder is 0. The topmost line 034 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 34.
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}