Solve (iii) (- 5 * 2/15) - (- 6 * 2/9); (8/5 * (- 3/2)) + (- 3/10 * 9/16) (iv) | 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

$$\left. \begin{array} { l } { ( - 5 \times \frac { 2 } { 15 } ) - ( - 6 \times \frac { 2 } { 9 } ) } \\ { ( \frac { 8 } { 5 } \times \frac { - 3 } { 2 } ) + ( \frac { - 3 } { 10 } \times \frac { 9 } { 16 } ) } \end{array} \right.$$

Sort

$-\frac{411}{160},\frac{2}{3}$

Solution Steps

Express $-5\times \frac{2}{15}$ as a single fraction.

$$sort(\frac{-5\times 2}{15}-\left(-6\times \frac{2}{9}\right),\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Multiply $-5$ and $2$ to get $-10$.

$$sort(\frac{-10}{15}-\left(-6\times \frac{2}{9}\right),\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Reduce the fraction $\frac{-10}{15}$ to lowest terms by extracting and canceling out $5$.

$$sort(-\frac{2}{3}-\left(-6\times \frac{2}{9}\right),\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Express $-6\times \frac{2}{9}$ as a single fraction.

$$sort(-\frac{2}{3}-\frac{-6\times 2}{9},\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Multiply $-6$ and $2$ to get $-12$.

$$sort(-\frac{2}{3}-\frac{-12}{9},\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Reduce the fraction $\frac{-12}{9}$ to lowest terms by extracting and canceling out $3$.

$$sort(-\frac{2}{3}-\left(-\frac{4}{3}\right),\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

The opposite of $-\frac{4}{3}$ is $\frac{4}{3}$.

$$sort(-\frac{2}{3}+\frac{4}{3},\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Since $-\frac{2}{3}$ and $\frac{4}{3}$ have the same denominator, add them by adding their numerators.

$$sort(\frac{-2+4}{3},\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Add $-2$ and $4$ to get $2$.

$$sort(\frac{2}{3},\frac{8}{5}\times \frac{-3}{2}+\frac{-3}{10}\times \frac{9}{16})$$

Fraction $\frac{-3}{2}$ can be rewritten as $-\frac{3}{2}$ by extracting the negative sign.

$$sort(\frac{2}{3},\frac{8}{5}\left(-\frac{3}{2}\right)+\frac{-3}{10}\times \frac{9}{16})$$

Multiply $\frac{8}{5}$ times $-\frac{3}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{2}{3},\frac{8\left(-3\right)}{5\times 2}+\frac{-3}{10}\times \frac{9}{16})$$

Do the multiplications in the fraction $\frac{8\left(-3\right)}{5\times 2}$.

$$sort(\frac{2}{3},\frac{-24}{10}+\frac{-3}{10}\times \frac{9}{16})$$

Reduce the fraction $\frac{-24}{10}$ to lowest terms by extracting and canceling out $2$.

$$sort(\frac{2}{3},-\frac{12}{5}+\frac{-3}{10}\times \frac{9}{16})$$

Fraction $\frac{-3}{10}$ can be rewritten as $-\frac{3}{10}$ by extracting the negative sign.

$$sort(\frac{2}{3},-\frac{12}{5}-\frac{3}{10}\times \frac{9}{16})$$

Multiply $-\frac{3}{10}$ times $\frac{9}{16}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{2}{3},-\frac{12}{5}+\frac{-3\times 9}{10\times 16})$$

Do the multiplications in the fraction $\frac{-3\times 9}{10\times 16}$.

$$sort(\frac{2}{3},-\frac{12}{5}+\frac{-27}{160})$$

Fraction $\frac{-27}{160}$ can be rewritten as $-\frac{27}{160}$ by extracting the negative sign.

$$sort(\frac{2}{3},-\frac{12}{5}-\frac{27}{160})$$

Least common multiple of $5$ and $160$ is $160$. Convert $-\frac{12}{5}$ and $\frac{27}{160}$ to fractions with denominator $160$.

$$sort(\frac{2}{3},-\frac{384}{160}-\frac{27}{160})$$

Since $-\frac{384}{160}$ and $\frac{27}{160}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{2}{3},\frac{-384-27}{160})$$

Subtract $27$ from $-384$ to get $-411$.

$$sort(\frac{2}{3},-\frac{411}{160})$$

Least common denominator of the numbers in the list $\frac{2}{3},-\frac{411}{160}$ is $480$. Convert numbers in the list to fractions with denominator $480$.

$$\frac{320}{480},-\frac{1233}{480}$$

To sort the list, start from a single element $\frac{320}{480}$.

$$\frac{320}{480}$$

Insert $-\frac{1233}{480}$ to the appropriate location in the new list.

$$-\frac{1233}{480},\frac{320}{480}$$

Replace the obtained fractions with the initial values.

$$-\frac{411}{160},\frac{2}{3}$$

Evaluate

$\frac{2}{3},\ -\frac{411}{160}$