Solve ((- 13/9) / (2/15))(7/3 / (5/5)) + (3/5 * 1/2) of rational | 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

$$( - \frac { 13 } { 9 } \div \frac { 2 } { 15 } ) \times ( \frac { 7 } { 3 } \div \frac { 5 } { 5 } ) + ( \frac { 3 } { 5 } \times \frac { 1 } { 2 } )$$

Evaluate

$-\frac{1124}{45}\approx -24.977777778$

Solution Steps

Divide $5$ by $5$ to get $1$.

$$\frac{-\frac{13}{9}}{\frac{2}{15}}\times \frac{\frac{7}{3}}{1}+\frac{3}{5}\times \frac{1}{2}$$

Divide $-\frac{13}{9}$ by $\frac{2}{15}$ by multiplying $-\frac{13}{9}$ by the reciprocal of $\frac{2}{15}$.

$$-\frac{13}{9}\times \frac{15}{2}\times \frac{\frac{7}{3}}{1}+\frac{3}{5}\times \frac{1}{2}$$

Multiply $-\frac{13}{9}$ times $\frac{15}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13\times 15}{9\times 2}\times \frac{\frac{7}{3}}{1}+\frac{3}{5}\times \frac{1}{2}$$

Do the multiplications in the fraction $\frac{-13\times 15}{9\times 2}$.

$$\frac{-195}{18}\times \frac{\frac{7}{3}}{1}+\frac{3}{5}\times \frac{1}{2}$$

Reduce the fraction $\frac{-195}{18}$ to lowest terms by extracting and canceling out $3$.

$$-\frac{65}{6}\times \frac{\frac{7}{3}}{1}+\frac{3}{5}\times \frac{1}{2}$$

Anything divided by one gives itself.

$$-\frac{65}{6}\times \frac{7}{3}+\frac{3}{5}\times \frac{1}{2}$$

Multiply $-\frac{65}{6}$ times $\frac{7}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-65\times 7}{6\times 3}+\frac{3}{5}\times \frac{1}{2}$$

Do the multiplications in the fraction $\frac{-65\times 7}{6\times 3}$.

$$\frac{-455}{18}+\frac{3}{5}\times \frac{1}{2}$$

Fraction $\frac{-455}{18}$ can be rewritten as $-\frac{455}{18}$ by extracting the negative sign.

$$-\frac{455}{18}+\frac{3}{5}\times \frac{1}{2}$$

Multiply $\frac{3}{5}$ times $\frac{1}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{455}{18}+\frac{3\times 1}{5\times 2}$$

Do the multiplications in the fraction $\frac{3\times 1}{5\times 2}$.

$$-\frac{455}{18}+\frac{3}{10}$$

Least common multiple of $18$ and $10$ is $90$. Convert $-\frac{455}{18}$ and $\frac{3}{10}$ to fractions with denominator $90$.

$$-\frac{2275}{90}+\frac{27}{90}$$

Since $-\frac{2275}{90}$ and $\frac{27}{90}$ have the same denominator, add them by adding their numerators.

$$\frac{-2275+27}{90}$$

Add $-2275$ and $27$ to get $-2248$.

$$\frac{-2248}{90}$$

Reduce the fraction $\frac{-2248}{90}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{1124}{45}$$

Factor

$-\frac{1124}{45} = -24\frac{44}{45} = -24.977777777777778$