Solve 12 (3/5 * (- 15/21)) + (- 9/14 / (45/28)) - (2/3 * 30/12) | 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

$$( \frac { 3 } { 5 } \times \frac { - 15 } { 21 } ) + ( \frac { - 9 } { 14 } \div \frac { 45 } { 28 } ) - ( \frac { 2 } { 3 } \times \frac { 30 } { 12 } )$$

Evaluate

$-\frac{262}{105}\approx -2.495238095$

Solution Steps

Reduce the fraction $\frac{-15}{21}$ to lowest terms by extracting and canceling out $3$.

$$\frac{3}{5}\left(-\frac{5}{7}\right)+\frac{\frac{-9}{14}}{\frac{45}{28}}-\frac{2}{3}\times \frac{30}{12}$$

Multiply $\frac{3}{5}$ times $-\frac{5}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\left(-5\right)}{5\times 7}+\frac{\frac{-9}{14}}{\frac{45}{28}}-\frac{2}{3}\times \frac{30}{12}$$

Do the multiplications in the fraction $\frac{3\left(-5\right)}{5\times 7}$.

$$\frac{-15}{35}+\frac{\frac{-9}{14}}{\frac{45}{28}}-\frac{2}{3}\times \frac{30}{12}$$

Reduce the fraction $\frac{-15}{35}$ to lowest terms by extracting and canceling out $5$.

$$-\frac{3}{7}+\frac{\frac{-9}{14}}{\frac{45}{28}}-\frac{2}{3}\times \frac{30}{12}$$

Divide $\frac{-9}{14}$ by $\frac{45}{28}$ by multiplying $\frac{-9}{14}$ by the reciprocal of $\frac{45}{28}$.

$$-\frac{3}{7}+\frac{-9\times 28}{14\times 45}-\frac{2}{3}\times \frac{30}{12}$$

Cancel out $9\times 14$ in both numerator and denominator.

$$-\frac{3}{7}+\frac{-2}{5}-\frac{2}{3}\times \frac{30}{12}$$

Fraction $\frac{-2}{5}$ can be rewritten as $-\frac{2}{5}$ by extracting the negative sign.

$$-\frac{3}{7}-\frac{2}{5}-\frac{2}{3}\times \frac{30}{12}$$

Least common multiple of $7$ and $5$ is $35$. Convert $-\frac{3}{7}$ and $\frac{2}{5}$ to fractions with denominator $35$.

$$-\frac{15}{35}-\frac{14}{35}-\frac{2}{3}\times \frac{30}{12}$$

Since $-\frac{15}{35}$ and $\frac{14}{35}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-14}{35}-\frac{2}{3}\times \frac{30}{12}$$

Subtract $14$ from $-15$ to get $-29$.

$$-\frac{29}{35}-\frac{2}{3}\times \frac{30}{12}$$

Reduce the fraction $\frac{30}{12}$ to lowest terms by extracting and canceling out $6$.

$$-\frac{29}{35}-\frac{2}{3}\times \frac{5}{2}$$

Multiply $\frac{2}{3}$ times $\frac{5}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{29}{35}-\frac{2\times 5}{3\times 2}$$

Cancel out $2$ in both numerator and denominator.

$$-\frac{29}{35}-\frac{5}{3}$$

Least common multiple of $35$ and $3$ is $105$. Convert $-\frac{29}{35}$ and $\frac{5}{3}$ to fractions with denominator $105$.

$$-\frac{87}{105}-\frac{175}{105}$$

Since $-\frac{87}{105}$ and $\frac{175}{105}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-87-175}{105}$$

Subtract $175$ from $-87$ to get $-262$.

$$-\frac{262}{105}$$

Factor

$-\frac{262}{105} = -2\frac{52}{105} = -2.4952380952380953$