Solve ( ii ) ((- 13/9) / (2/15))(7/3 / (5/8)) + (3/5 * 1/2); (1 1)(,1),( underline -7 - underline 7 ) | 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

$$( i i ) ( - \frac { 13 } { 9 } \div \frac { 2 } { 15 } ) \times ( \frac { 7 } { 3 } \div \frac { 5 } { 8 } ) + ( \frac { 3 } { 5 } \times \frac { 1 } { 2 } )$$

Evaluate

$\frac{3667}{90}\approx 40.744444444$

Solution Steps

Multiply $i$ and $i$ to get $-1$.

$$-\frac{-\frac{13}{9}}{\frac{2}{15}}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2}$$

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

$$-\left(-\frac{13}{9}\right)\times \frac{15}{2}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2}$$

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

$$-\frac{-13\times 15}{9\times 2}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2}$$

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

$$-\frac{-195}{18}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2}$$

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

$$-\left(-\frac{65}{6}\right)\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2}$$

Multiply $-1$ and $-\frac{65}{6}$ to get $\frac{65}{6}$.

$$\frac{65}{6}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2}$$

Divide $\frac{7}{3}$ by $\frac{5}{8}$ by multiplying $\frac{7}{3}$ by the reciprocal of $\frac{5}{8}$.

$$\frac{65}{6}\times \frac{7}{3}\times \frac{8}{5}+\frac{3}{5}\times \frac{1}{2}$$

Multiply $\frac{7}{3}$ times $\frac{8}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{65}{6}\times \frac{7\times 8}{3\times 5}+\frac{3}{5}\times \frac{1}{2}$$

Do the multiplications in the fraction $\frac{7\times 8}{3\times 5}$.

$$\frac{65}{6}\times \frac{56}{15}+\frac{3}{5}\times \frac{1}{2}$$

Multiply $\frac{65}{6}$ times $\frac{56}{15}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{65\times 56}{6\times 15}+\frac{3}{5}\times \frac{1}{2}$$

Do the multiplications in the fraction $\frac{65\times 56}{6\times 15}$.

$$\frac{3640}{90}+\frac{3}{5}\times \frac{1}{2}$$

Reduce the fraction $\frac{3640}{90}$ to lowest terms by extracting and canceling out $10$.

$$\frac{364}{9}+\frac{3}{5}\times \frac{1}{2}$$

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

$$\frac{364}{9}+\frac{3\times 1}{5\times 2}$$

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

$$\frac{364}{9}+\frac{3}{10}$$

Least common multiple of $9$ and $10$ is $90$. Convert $\frac{364}{9}$ and $\frac{3}{10}$ to fractions with denominator $90$.

$$\frac{3640}{90}+\frac{27}{90}$$

Since $\frac{3640}{90}$ and $\frac{27}{90}$ have the same denominator, add them by adding their numerators.

$$\frac{3640+27}{90}$$

Add $3640$ and $27$ to get $3667$.

$$\frac{3667}{90}$$

Real Part

$\frac{3667}{90} = 40\frac{67}{90} = 40.74444444444445$

Solution Steps

Multiply $i$ and $i$ to get $-1$.

$$Re(-\frac{-\frac{13}{9}}{\frac{2}{15}}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2})$$

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

$$Re(-\left(-\frac{13}{9}\right)\times \frac{15}{2}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2})$$

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

$$Re(-\frac{-13\times 15}{9\times 2}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2})$$

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

$$Re(-\frac{-195}{18}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2})$$

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

$$Re(-\left(-\frac{65}{6}\right)\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2})$$

Multiply $-1$ and $-\frac{65}{6}$ to get $\frac{65}{6}$.

$$Re(\frac{65}{6}\times \frac{\frac{7}{3}}{\frac{5}{8}}+\frac{3}{5}\times \frac{1}{2})$$

Divide $\frac{7}{3}$ by $\frac{5}{8}$ by multiplying $\frac{7}{3}$ by the reciprocal of $\frac{5}{8}$.

$$Re(\frac{65}{6}\times \frac{7}{3}\times \frac{8}{5}+\frac{3}{5}\times \frac{1}{2})$$

Multiply $\frac{7}{3}$ times $\frac{8}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$Re(\frac{65}{6}\times \frac{7\times 8}{3\times 5}+\frac{3}{5}\times \frac{1}{2})$$

Do the multiplications in the fraction $\frac{7\times 8}{3\times 5}$.

$$Re(\frac{65}{6}\times \frac{56}{15}+\frac{3}{5}\times \frac{1}{2})$$

Multiply $\frac{65}{6}$ times $\frac{56}{15}$ by multiplying numerator times numerator and denominator times denominator.

$$Re(\frac{65\times 56}{6\times 15}+\frac{3}{5}\times \frac{1}{2})$$

Do the multiplications in the fraction $\frac{65\times 56}{6\times 15}$.

$$Re(\frac{3640}{90}+\frac{3}{5}\times \frac{1}{2})$$

Reduce the fraction $\frac{3640}{90}$ to lowest terms by extracting and canceling out $10$.

$$Re(\frac{364}{9}+\frac{3}{5}\times \frac{1}{2})$$

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

$$Re(\frac{364}{9}+\frac{3\times 1}{5\times 2})$$

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

$$Re(\frac{364}{9}+\frac{3}{10})$$

Least common multiple of $9$ and $10$ is $90$. Convert $\frac{364}{9}$ and $\frac{3}{10}$ to fractions with denominator $90$.

$$Re(\frac{3640}{90}+\frac{27}{90})$$

Since $\frac{3640}{90}$ and $\frac{27}{90}$ have the same denominator, add them by adding their numerators.

$$Re(\frac{3640+27}{90})$$

Add $3640$ and $27$ to get $3667$.

$$Re(\frac{3667}{90})$$

The real part of $\frac{3667}{90}$ is $\frac{3667}{90}$.

$$\frac{3667}{90}$$