Math Problem Solver

\[\left( \left(-6 \cdot 7 + 5 \cdot 8\right) \cdot -18 \right) \:\%\: \left( 7 - 10 \right) + 7 \left(-8 + 13\right) + 14 = 49\]

\[\begin{aligned}\left( \left(-6 \cdot 7 + 5 \cdot 8\right) \cdot -18 \right) \:\%\: \left( 7 - 10 \right) + 7 \left(-8 + 13\right) + 14& = \left(\left(-6 \cdot 7 + 5 \cdot 8\right) \cdot -18 \:\%\: \left(7 - 10\right)\right) + 7 \cdot \left(-8 + 13\right) + 14\\& = \left(\left(-42 + 5 \cdot 8\right) \cdot -18 \:\%\: \left(7 - 10\right)\right) + 7 \cdot \left(-8 + 13\right) + 14\\& = \left(\left(-42 + 40\right) \cdot -18 \:\%\: \left(7 - 10\right)\right) + 7 \cdot \left(-8 + 13\right) + 14\\& = \left(-2 \cdot -18 \:\%\: \left(7 - 10\right)\right) + 7 \cdot \left(-8 + 13\right) + 14\\& = \left(36 \:\%\: \left(7 - 10\right)\right) + 7 \cdot \left(-8 + 13\right) + 14\\& = \left(36 \:\%\: \left(-3\right)\right) + 7 \cdot \left(-8 + 13\right) + 14\\& = 0 + 7 \cdot \left(-8 + 13\right) + 14\\& = 0 + 7 \cdot 5 + 14\\& = 0 + 35 + 14\\& = 35 + 14\\& = 49\end{aligned}\]

The notation \(m \% n\) denotes the remainder of the integer \(m\) divided by the integer \(n\). \(m \% n = r\) means that given integers \(m\) and \(n\), where \(n\) is non-zero, there exist integers \(q\) and \(r\), where \(\lvert r \rvert < \lvert n \rvert\), such that \(m = q n + r\). MathBot adopts the convention that the remainder \(r\) and the divisor \(n\) share the same sign. Alternate notations for \(m \% n\) are \(\operatorname{mod}(m, n)\) and \(m \bmod n\).