Solve 147 (155 - 8)/31 ^ (- 147/31); 10 + 4/2 + (- 3 * 2 / 4) / 2 * 2 - 4 a) ( b) 1 | 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

$$\left. \begin{array} { l } { \frac { 155 - 8 } { 31 } \div \frac { 147 } { 31 } \div 147 } \\ { 10 + 4 \div 2 - 3 \times 2 \div 4 \div 2 \times 2 - 4 } \\ { 0 } \end{array} \right.$$

Sort

$0,\frac{1}{147},\frac{13}{2}$

Solution Steps

Express $\frac{\frac{\frac{155-8}{31}}{\frac{147}{31}}}{147}$ as a single fraction.

$$sort(\frac{\frac{155-8}{31}}{\frac{147}{31}\times 147},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Subtract $8$ from $155$ to get $147$.

$$sort(\frac{\frac{147}{31}}{\frac{147}{31}\times 147},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Express $\frac{147}{31}\times 147$ as a single fraction.

$$sort(\frac{\frac{147}{31}}{\frac{147\times 147}{31}},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Multiply $147$ and $147$ to get $21609$.

$$sort(\frac{\frac{147}{31}}{\frac{21609}{31}},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Divide $\frac{147}{31}$ by $\frac{21609}{31}$ by multiplying $\frac{147}{31}$ by the reciprocal of $\frac{21609}{31}$.

$$sort(\frac{147}{31}\times \frac{31}{21609},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Multiply $\frac{147}{31}$ times $\frac{31}{21609}$ by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{147\times 31}{31\times 21609},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Cancel out $31$ in both numerator and denominator.

$$sort(\frac{147}{21609},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Reduce the fraction $\frac{147}{21609}$ to lowest terms by extracting and canceling out $147$.

$$sort(\frac{1}{147},10+\frac{4}{2}-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Divide $4$ by $2$ to get $2$.

$$sort(\frac{1}{147},10+2-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Add $10$ and $2$ to get $12$.

$$sort(\frac{1}{147},12-\frac{\frac{3\times 2}{4}}{2}\times 2-4,0)$$

Express $\frac{\frac{3\times 2}{4}}{2}$ as a single fraction.

$$sort(\frac{1}{147},12-\frac{3\times 2}{4\times 2}\times 2-4,0)$$

Cancel out $2$ in both numerator and denominator.

$$sort(\frac{1}{147},12-\frac{3}{2\times 2}\times 2-4,0)$$

Multiply $2$ and $2$ to get $4$.

$$sort(\frac{1}{147},12-\frac{3}{4}\times 2-4,0)$$

Express $\frac{3}{4}\times 2$ as a single fraction.

$$sort(\frac{1}{147},12-\frac{3\times 2}{4}-4,0)$$

Multiply $3$ and $2$ to get $6$.

$$sort(\frac{1}{147},12-\frac{6}{4}-4,0)$$

Reduce the fraction $\frac{6}{4}$ to lowest terms by extracting and canceling out $2$.

$$sort(\frac{1}{147},12-\frac{3}{2}-4,0)$$

Convert $12$ to fraction $\frac{24}{2}$.

$$sort(\frac{1}{147},\frac{24}{2}-\frac{3}{2}-4,0)$$

Since $\frac{24}{2}$ and $\frac{3}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{1}{147},\frac{24-3}{2}-4,0)$$

Subtract $3$ from $24$ to get $21$.

$$sort(\frac{1}{147},\frac{21}{2}-4,0)$$

Convert $4$ to fraction $\frac{8}{2}$.

$$sort(\frac{1}{147},\frac{21}{2}-\frac{8}{2},0)$$

Since $\frac{21}{2}$ and $\frac{8}{2}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{1}{147},\frac{21-8}{2},0)$$

Subtract $8$ from $21$ to get $13$.

$$sort(\frac{1}{147},\frac{13}{2},0)$$

Convert decimal numbers in the list $\frac{1}{147},\frac{13}{2},0$ to fractions.

$$\frac{1}{147},\frac{13}{2},0$$

Least common denominator of the numbers in the list $\frac{1}{147},\frac{13}{2},0$ is $294$. Convert numbers in the list to fractions with denominator $294$.

$$\frac{2}{294},\frac{1911}{294},0$$

To sort the list, start from a single element $\frac{2}{294}$.

$$\frac{2}{294}$$

Insert $\frac{1911}{294}$ to the appropriate location in the new list.

$$\frac{2}{294},\frac{1911}{294}$$

Insert $0$ to the appropriate location in the new list.

$$0,\frac{2}{294},\frac{1911}{294}$$

Replace the obtained fractions with the initial values.

$$0,\frac{1}{147},\frac{13}{2}$$

Evaluate

$\frac{1}{147},\ \frac{13}{2},\ 0$