\frac { 45 } { 15 } = \frac { ? } { 1 } \quad \frac { 27 } { 9 } = \frac { ? } { 1 }
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false
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\frac{45}{15}=1\times \frac{27}{9}\text{ and }\frac{1}{1}\times \frac{27}{9}=\frac{1}{1}
Divide 1 by 1 to get 1.
\frac{45}{15}=1\times \frac{27}{9}\text{ and }1\times \frac{27}{9}=\frac{1}{1}
Divide 1 by 1 to get 1.
\frac{45}{15}=1\times \frac{27}{9}\text{ and }1\times \frac{27}{9}=1
Divide 1 by 1 to get 1.
3=1\times \frac{27}{9}\text{ and }1\times \frac{27}{9}=1
Divide 45 by 15 to get 3.
3=1\times 3\text{ and }1\times \frac{27}{9}=1
Divide 27 by 9 to get 3.
3=3\text{ and }1\times \frac{27}{9}=1
Multiply 1 and 3 to get 3.
\text{true}\text{ and }1\times \frac{27}{9}=1
Compare 3 and 3.
\text{true}\text{ and }1\times 3=1
Divide 27 by 9 to get 3.
\text{true}\text{ and }3=1
Multiply 1 and 3 to get 3.
\text{true}\text{ and }\text{false}
Compare 3 and 1.
\text{false}
The conjunction of \text{true} and \text{false} is \text{false}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}