Solve -2+(1)/(5)-(5)/(2)\times(-5+(2)/(3)\times(-1+4(-5+(3)/(2))) | 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

$$-2+ \frac{ 1 }{ 5 } - \frac{ 5 }{ 2 } \times (-5+ \frac{ 2 }{ 3 } \times (-1+4(-5+ \frac{ 3 }{ 2 } ))$$

Evaluate

$\frac{357}{10}=35.7$

Solution Steps

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

$$-\frac{10}{5}+\frac{1}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+4\left(-5+\frac{3}{2}\right)\right)\right)$$

Since $-\frac{10}{5}$ and $\frac{1}{5}$ have the same denominator, add them by adding their numerators.

$$\frac{-10+1}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+4\left(-5+\frac{3}{2}\right)\right)\right)$$

Add $-10$ and $1$ to get $-9$.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+4\left(-5+\frac{3}{2}\right)\right)\right)$$

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

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+4\left(-\frac{10}{2}+\frac{3}{2}\right)\right)\right)$$

Since $-\frac{10}{2}$ and $\frac{3}{2}$ have the same denominator, add them by adding their numerators.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+4\times \frac{-10+3}{2}\right)\right)$$

Add $-10$ and $3$ to get $-7$.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+4\left(-\frac{7}{2}\right)\right)\right)$$

Express $4\left(-\frac{7}{2}\right)$ as a single fraction.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+\frac{4\left(-7\right)}{2}\right)\right)$$

Multiply $4$ and $-7$ to get $-28$.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1+\frac{-28}{2}\right)\right)$$

Divide $-28$ by $2$ to get $-14$.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-1-14\right)\right)$$

Subtract $14$ from $-1$ to get $-15$.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2}{3}\left(-15\right)\right)$$

Express $\frac{2}{3}\left(-15\right)$ as a single fraction.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{2\left(-15\right)}{3}\right)$$

Multiply $2$ and $-15$ to get $-30$.

$$-\frac{9}{5}-\frac{5}{2}\left(-5+\frac{-30}{3}\right)$$

Divide $-30$ by $3$ to get $-10$.

$$-\frac{9}{5}-\frac{5}{2}\left(-5-10\right)$$

Subtract $10$ from $-5$ to get $-15$.

$$-\frac{9}{5}-\frac{5}{2}\left(-15\right)$$

Express $\frac{5}{2}\left(-15\right)$ as a single fraction.

$$-\frac{9}{5}-\frac{5\left(-15\right)}{2}$$

Multiply $5$ and $-15$ to get $-75$.

$$-\frac{9}{5}-\frac{-75}{2}$$

Fraction $\frac{-75}{2}$ can be rewritten as $-\frac{75}{2}$ by extracting the negative sign.

$$-\frac{9}{5}-\left(-\frac{75}{2}\right)$$

The opposite of $-\frac{75}{2}$ is $\frac{75}{2}$.

$$-\frac{9}{5}+\frac{75}{2}$$

Least common multiple of $5$ and $2$ is $10$. Convert $-\frac{9}{5}$ and $\frac{75}{2}$ to fractions with denominator $10$.

$$-\frac{18}{10}+\frac{375}{10}$$

Since $-\frac{18}{10}$ and $\frac{375}{10}$ have the same denominator, add them by adding their numerators.

$$\frac{-18+375}{10}$$

Add $-18$ and $375$ to get $357$.

$$\frac{357}{10}$$

Factor

$\frac{3 \cdot 7 \cdot 17}{2 \cdot 5} = 35\frac{7}{10} = 35.7$