Solve 58.4*89/13+34/13*(-58.4)+58.4

$$58.4 \times 8 \frac { 9 } { 13 } + 3 \frac { 4 } { 13 } \times (-58.4)+58.4$$

Evaluate

$$\frac{24236}{65}\approx 372.861538462$$

Solution Steps

Multiply 8 and 13 to get 104.

$$58.4\times \frac{104+9}{13}+\frac{3\times 13+4}{13}\left(-58.4\right)+58.4$$

Add 104 and 9 to get 113.

$$58.4\times \frac{113}{13}+\frac{3\times 13+4}{13}\left(-58.4\right)+58.4$$

Convert decimal number 58.4 to fraction \frac{584}{10}. Reduce the fraction \frac{584}{10} to lowest terms by extracting and canceling out 2.

$$\frac{292}{5}\times \frac{113}{13}+\frac{3\times 13+4}{13}\left(-58.4\right)+58.4$$

Multiply \frac{292}{5} times \frac{113}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{292\times 113}{5\times 13}+\frac{3\times 13+4}{13}\left(-58.4\right)+58.4$$

Do the multiplications in the fraction \frac{292\times 113}{5\times 13}.

$$\frac{32996}{65}+\frac{3\times 13+4}{13}\left(-58.4\right)+58.4$$

Multiply 3 and 13 to get 39.

$$\frac{32996}{65}+\frac{39+4}{13}\left(-58.4\right)+58.4$$

Add 39 and 4 to get 43.

$$\frac{32996}{65}+\frac{43}{13}\left(-58.4\right)+58.4$$

Convert decimal number -58.4 to fraction -\frac{584}{10}. Reduce the fraction -\frac{584}{10} to lowest terms by extracting and canceling out 2.

$$\frac{32996}{65}+\frac{43}{13}\left(-\frac{292}{5}\right)+58.4$$

Multiply \frac{43}{13} times -\frac{292}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{32996}{65}+\frac{43\left(-292\right)}{13\times 5}+58.4$$

Do the multiplications in the fraction \frac{43\left(-292\right)}{13\times 5}.

$$\frac{32996}{65}+\frac{-12556}{65}+58.4$$

Fraction \frac{-12556}{65} can be rewritten as -\frac{12556}{65} by extracting the negative sign.

$$\frac{32996}{65}-\frac{12556}{65}+58.4$$

Since \frac{32996}{65} and \frac{12556}{65} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32996-12556}{65}+58.4$$

Subtract 12556 from 32996 to get 20440.

$$\frac{20440}{65}+58.4$$

Reduce the fraction \frac{20440}{65} to lowest terms by extracting and canceling out 5.

$$\frac{4088}{13}+58.4$$

Convert decimal number 58.4 to fraction \frac{584}{10}. Reduce the fraction \frac{584}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4088}{13}+\frac{292}{5}$$

Least common multiple of 13 and 5 is 65. Convert \frac{4088}{13} and \frac{292}{5} to fractions with denominator 65.

$$\frac{20440}{65}+\frac{3796}{65}$$

Since \frac{20440}{65} and \frac{3796}{65} have the same denominator, add them by adding their numerators.

$$\frac{20440+3796}{65}$$

Add 20440 and 3796 to get 24236.

$$\frac{24236}{65}$$

Factor

$$\frac{73 \cdot 83 \cdot 2 ^ {2}}{5 \cdot 13} = 372\frac{56}{65} = 372.8615384615385$$