Solve 1/2 * 1/4 + 2/7 * (- 7/8) * 15/7 - 1/4 * 1/3 -3 -5 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

$$\left. \begin{array} { l } { \frac { 1 } { 2 } \times \frac { 1 } { 4 } + \frac { 2 } { 7 } \times \frac { - 7 } { 8 } \times \frac { 15 } { 7 } - \frac { 1 } { 4 } \times \frac { 1 } { 3 } } \\ { 7 \quad - 3 \quad - 5 \quad 7 } \end{array} \right.$$

Sort

$-53,-\frac{83}{168}$

Solution Steps

Multiply $\frac{1}{2}$ times $\frac{1}{4}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1\times 1}{2\times 4}+\frac{2}{7}\times \frac{-7}{8}\times \frac{15}{7}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Do the multiplications in the fraction $\frac{1\times 1}{2\times 4}$.

$$sort(\frac{1}{8}+\frac{2}{7}\times \frac{-7}{8}\times \frac{15}{7}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Fraction $\frac{-7}{8}$ can be rewritten as $-\frac{7}{8}$ by extracting the negative sign.

$$sort(\frac{1}{8}+\frac{2}{7}\left(-\frac{7}{8}\right)\times \frac{15}{7}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Multiply $\frac{2}{7}$ times $-\frac{7}{8}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1}{8}+\frac{2\left(-7\right)}{7\times 8}\times \frac{15}{7}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Do the multiplications in the fraction $\frac{2\left(-7\right)}{7\times 8}$.

$$sort(\frac{1}{8}+\frac{-14}{56}\times \frac{15}{7}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Reduce the fraction $\frac{-14}{56}$ to lowest terms by extracting and canceling out $14$.

$$sort(\frac{1}{8}-\frac{1}{4}\times \frac{15}{7}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Multiply $-\frac{1}{4}$ times $\frac{15}{7}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1}{8}+\frac{-15}{4\times 7}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Do the multiplications in the fraction $\frac{-15}{4\times 7}$.

$$sort(\frac{1}{8}+\frac{-15}{28}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Fraction $\frac{-15}{28}$ can be rewritten as $-\frac{15}{28}$ by extracting the negative sign.

$$sort(\frac{1}{8}-\frac{15}{28}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Least common multiple of $8$ and $28$ is $56$. Convert $\frac{1}{8}$ and $\frac{15}{28}$ to fractions with denominator $56$.

$$sort(\frac{7}{56}-\frac{30}{56}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Since $\frac{7}{56}$ and $\frac{30}{56}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{7-30}{56}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Subtract $30$ from $7$ to get $-23$.

$$sort(-\frac{23}{56}-\frac{1}{4}\times \frac{1}{3},7-3-57)$$

Multiply $\frac{1}{4}$ times $\frac{1}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(-\frac{23}{56}-\frac{1\times 1}{4\times 3},7-3-57)$$

Do the multiplications in the fraction $\frac{1\times 1}{4\times 3}$.

$$sort(-\frac{23}{56}-\frac{1}{12},7-3-57)$$

Least common multiple of $56$ and $12$ is $168$. Convert $-\frac{23}{56}$ and $\frac{1}{12}$ to fractions with denominator $168$.

$$sort(-\frac{69}{168}-\frac{14}{168},7-3-57)$$

Since $-\frac{69}{168}$ and $\frac{14}{168}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{-69-14}{168},7-3-57)$$

Subtract $14$ from $-69$ to get $-83$.

$$sort(-\frac{83}{168},7-3-57)$$

Subtract $3$ from $7$ to get $4$.

$$sort(-\frac{83}{168},4-57)$$

Subtract $57$ from $4$ to get $-53$.

$$sort(-\frac{83}{168},-53)$$

Convert decimal numbers in the list $-\frac{83}{168},-53$ to fractions.

$$-\frac{83}{168},-53$$

To sort the list, start from a single element $-\frac{83}{168}$.

$$-\frac{83}{168}$$

Insert $-53$ to the appropriate location in the new list.

$$-53,-\frac{83}{168}$$

Evaluate

$-\frac{83}{168},\ -53$