Solve -(7)/(2)-6-(5)/(3)\times((2)/(5)-3+(6)/(3)\times(-2+(1)/(2)\times(-5+(3)/(5)))) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$- \frac{ 7 }{ 2 } -6- \frac{ 5 }{ 3 } \times ( \frac{ 2 }{ 5 } -3+ \frac{ 6 }{ 3 } \times (-2+ \frac{ 1 }{ 2 } \times (-5+ \frac{ 3 }{ 5 } )))$$

Evaluate

$\frac{53}{6}\approx 8.833333333$

Solution Steps

Convert $6$ to fraction $\frac{12}{2}$.

$$-\frac{7}{2}-\frac{12}{2}-\frac{5}{3}\left(\frac{2}{5}-3+\frac{6}{3}\left(-2+\frac{1}{2}\left(-5+\frac{3}{5}\right)\right)\right)$$

Since $-\frac{7}{2}$ and $\frac{12}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-12}{2}-\frac{5}{3}\left(\frac{2}{5}-3+\frac{6}{3}\left(-2+\frac{1}{2}\left(-5+\frac{3}{5}\right)\right)\right)$$

Subtract $12$ from $-7$ to get $-19$.

$$-\frac{19}{2}-\frac{5}{3}\left(\frac{2}{5}-3+\frac{6}{3}\left(-2+\frac{1}{2}\left(-5+\frac{3}{5}\right)\right)\right)$$

Convert $3$ to fraction $\frac{15}{5}$.

$$-\frac{19}{2}-\frac{5}{3}\left(\frac{2}{5}-\frac{15}{5}+\frac{6}{3}\left(-2+\frac{1}{2}\left(-5+\frac{3}{5}\right)\right)\right)$$

Since $\frac{2}{5}$ and $\frac{15}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{2}-\frac{5}{3}\left(\frac{2-15}{5}+\frac{6}{3}\left(-2+\frac{1}{2}\left(-5+\frac{3}{5}\right)\right)\right)$$

Subtract $15$ from $2$ to get $-13$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+\frac{6}{3}\left(-2+\frac{1}{2}\left(-5+\frac{3}{5}\right)\right)\right)$$

Divide $6$ by $3$ to get $2$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-2+\frac{1}{2}\left(-5+\frac{3}{5}\right)\right)\right)$$

Convert $-5$ to fraction $-\frac{25}{5}$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-2+\frac{1}{2}\left(-\frac{25}{5}+\frac{3}{5}\right)\right)\right)$$

Since $-\frac{25}{5}$ and $\frac{3}{5}$ have the same denominator, add them by adding their numerators.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-2+\frac{1}{2}\times \frac{-25+3}{5}\right)\right)$$

Add $-25$ and $3$ to get $-22$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-2+\frac{1}{2}\left(-\frac{22}{5}\right)\right)\right)$$

Multiply $\frac{1}{2}$ times $-\frac{22}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-2+\frac{1\left(-22\right)}{2\times 5}\right)\right)$$

Do the multiplications in the fraction $\frac{1\left(-22\right)}{2\times 5}$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-2+\frac{-22}{10}\right)\right)$$

Reduce the fraction $\frac{-22}{10}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-2-\frac{11}{5}\right)\right)$$

Convert $-2$ to fraction $-\frac{10}{5}$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-\frac{10}{5}-\frac{11}{5}\right)\right)$$

Since $-\frac{10}{5}$ and $\frac{11}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\times \frac{-10-11}{5}\right)$$

Subtract $11$ from $-10$ to get $-21$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+2\left(-\frac{21}{5}\right)\right)$$

Express $2\left(-\frac{21}{5}\right)$ as a single fraction.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+\frac{2\left(-21\right)}{5}\right)$$

Multiply $2$ and $-21$ to get $-42$.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}+\frac{-42}{5}\right)$$

Fraction $\frac{-42}{5}$ can be rewritten as $-\frac{42}{5}$ by extracting the negative sign.

$$-\frac{19}{2}-\frac{5}{3}\left(-\frac{13}{5}-\frac{42}{5}\right)$$

Since $-\frac{13}{5}$ and $\frac{42}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{2}-\frac{5}{3}\times \frac{-13-42}{5}$$

Subtract $42$ from $-13$ to get $-55$.

$$-\frac{19}{2}-\frac{5}{3}\times \frac{-55}{5}$$

Divide $-55$ by $5$ to get $-11$.

$$-\frac{19}{2}-\frac{5}{3}\left(-11\right)$$

Express $\frac{5}{3}\left(-11\right)$ as a single fraction.

$$-\frac{19}{2}-\frac{5\left(-11\right)}{3}$$

Multiply $5$ and $-11$ to get $-55$.

$$-\frac{19}{2}-\frac{-55}{3}$$

Fraction $\frac{-55}{3}$ can be rewritten as $-\frac{55}{3}$ by extracting the negative sign.

$$-\frac{19}{2}-\left(-\frac{55}{3}\right)$$

The opposite of $-\frac{55}{3}$ is $\frac{55}{3}$.

$$-\frac{19}{2}+\frac{55}{3}$$

Least common multiple of $2$ and $3$ is $6$. Convert $-\frac{19}{2}$ and $\frac{55}{3}$ to fractions with denominator $6$.

$$-\frac{57}{6}+\frac{110}{6}$$

Since $-\frac{57}{6}$ and $\frac{110}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{-57+110}{6}$$

Add $-57$ and $110$ to get $53$.

$$\frac{53}{6}$$

Factor

$\frac{53}{2 \cdot 3} = 8\frac{5}{6} = 8.833333333333334$