Solve (-3)/(8)[3-(3)/(5)-((17)/(20)-1)\times((1)/(3)-3)] | 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

$$\frac{ -3 }{ 8 } [3- \frac{ 3 }{ 5 } -( \frac{ 17 }{ 20 } -1) \times ( \frac{ 1 }{ 3 } -3)]$$

Evaluate

$-\frac{3}{4}=-0.75$

Solution Steps

Fraction $\frac{-3}{8}$ can be rewritten as $-\frac{3}{8}$ by extracting the negative sign.

$$-\frac{3}{8}\left(3-\frac{3}{5}-\left(\frac{17}{20}-1\right)\left(\frac{1}{3}-3\right)\right)$$

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

$$-\frac{3}{8}\left(\frac{15}{5}-\frac{3}{5}-\left(\frac{17}{20}-1\right)\left(\frac{1}{3}-3\right)\right)$$

Since $\frac{15}{5}$ and $\frac{3}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{8}\left(\frac{15-3}{5}-\left(\frac{17}{20}-1\right)\left(\frac{1}{3}-3\right)\right)$$

Subtract $3$ from $15$ to get $12$.

$$-\frac{3}{8}\left(\frac{12}{5}-\left(\frac{17}{20}-1\right)\left(\frac{1}{3}-3\right)\right)$$

Convert $1$ to fraction $\frac{20}{20}$.

$$-\frac{3}{8}\left(\frac{12}{5}-\left(\frac{17}{20}-\frac{20}{20}\right)\left(\frac{1}{3}-3\right)\right)$$

Since $\frac{17}{20}$ and $\frac{20}{20}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{8}\left(\frac{12}{5}-\frac{17-20}{20}\left(\frac{1}{3}-3\right)\right)$$

Subtract $20$ from $17$ to get $-3$.

$$-\frac{3}{8}\left(\frac{12}{5}-\left(-\frac{3}{20}\left(\frac{1}{3}-3\right)\right)\right)$$

Convert $3$ to fraction $\frac{9}{3}$.

$$-\frac{3}{8}\left(\frac{12}{5}-\left(-\frac{3}{20}\left(\frac{1}{3}-\frac{9}{3}\right)\right)\right)$$

Since $\frac{1}{3}$ and $\frac{9}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{8}\left(\frac{12}{5}-\left(-\frac{3}{20}\times \frac{1-9}{3}\right)\right)$$

Subtract $9$ from $1$ to get $-8$.

$$-\frac{3}{8}\left(\frac{12}{5}-\left(-\frac{3}{20}\left(-\frac{8}{3}\right)\right)\right)$$

Multiply $-\frac{3}{20}$ times $-\frac{8}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{3}{8}\left(\frac{12}{5}-\frac{-3\left(-8\right)}{20\times 3}\right)$$

Do the multiplications in the fraction $\frac{-3\left(-8\right)}{20\times 3}$.

$$-\frac{3}{8}\left(\frac{12}{5}-\frac{24}{60}\right)$$

Reduce the fraction $\frac{24}{60}$ to lowest terms by extracting and canceling out $12$.

$$-\frac{3}{8}\left(\frac{12}{5}-\frac{2}{5}\right)$$

Since $\frac{12}{5}$ and $\frac{2}{5}$ have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{8}\times \frac{12-2}{5}$$

Subtract $2$ from $12$ to get $10$.

$$-\frac{3}{8}\times \frac{10}{5}$$

Divide $10$ by $5$ to get $2$.

$$-\frac{3}{8}\times 2$$

Express $-\frac{3}{8}\times 2$ as a single fraction.

$$\frac{-3\times 2}{8}$$

Multiply $-3$ and $2$ to get $-6$.

$$\frac{-6}{8}$$

Reduce the fraction $\frac{-6}{8}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{3}{4}$$

Factor

$-\frac{3}{4} = -0.75$