Solve 13 that ) and ( -4 7 + 14 3 )+; (- 4/7 * 34/18) | 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

$$\left. \begin{array} { l } { \frac { 15 } { ( 10.0214 ) ( 41 + 1 \times 11 + 31 ) } 40 , 40 ( - \frac { 1.414 } { 211 } ) } \\ { 78.24 \times 2 2410 } \end{array} \right.$$

Sort

$-\frac{1414}{5275},\frac{3000000}{4158881},1753358.4$

Solution Steps

Multiply $1$ and $11$ to get $11$.

$$sort(\frac{15}{10.0214\left(41+11+31\right)}\times 40,40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Add $41$ and $11$ to get $52$.

$$sort(\frac{15}{10.0214\left(52+31\right)}\times 40,40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Add $52$ and $31$ to get $83$.

$$sort(\frac{15}{10.0214\times 83}\times 40,40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Multiply $10.0214$ and $83$ to get $831.7762$.

$$sort(\frac{15}{831.7762}\times 40,40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Expand $\frac{15}{831.7762}$ by multiplying both numerator and the denominator by $10000$.

$$sort(\frac{150000}{8317762}\times 40,40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Reduce the fraction $\frac{150000}{8317762}$ to lowest terms by extracting and canceling out $2$.

$$sort(\frac{75000}{4158881}\times 40,40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Express $\frac{75000}{4158881}\times 40$ as a single fraction.

$$sort(\frac{75000\times 40}{4158881},40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Multiply $75000$ and $40$ to get $3000000$.

$$sort(\frac{3000000}{4158881},40\left(-\frac{1.414}{211}\right),78.24\times 22410)$$

Expand $\frac{1.414}{211}$ by multiplying both numerator and the denominator by $1000$.

$$sort(\frac{3000000}{4158881},40\left(-\frac{1414}{211000}\right),78.24\times 22410)$$

Reduce the fraction $\frac{1414}{211000}$ to lowest terms by extracting and canceling out $2$.

$$sort(\frac{3000000}{4158881},40\left(-\frac{707}{105500}\right),78.24\times 22410)$$

Express $40\left(-\frac{707}{105500}\right)$ as a single fraction.

$$sort(\frac{3000000}{4158881},\frac{40\left(-707\right)}{105500},78.24\times 22410)$$

Multiply $40$ and $-707$ to get $-28280$.

$$sort(\frac{3000000}{4158881},\frac{-28280}{105500},78.24\times 22410)$$

Reduce the fraction $\frac{-28280}{105500}$ to lowest terms by extracting and canceling out $20$.

$$sort(\frac{3000000}{4158881},-\frac{1414}{5275},78.24\times 22410)$$

Multiply $78.24$ and $22410$ to get $1753358.4$.

$$sort(\frac{3000000}{4158881},-\frac{1414}{5275},1753358.4)$$

Convert decimal numbers in the list $\frac{3000000}{4158881},-\frac{1414}{5275},1753358.4$ to fractions.

$$\frac{3000000}{4158881},-\frac{1414}{5275},\frac{8766792}{5}$$

Least common denominator of the numbers in the list $\frac{3000000}{4158881},-\frac{1414}{5275},\frac{8766792}{5}$ is $21938097275$. Convert numbers in the list to fractions with denominator $21938097275$.

$$\frac{15825000000}{21938097275},-\frac{5880657734}{21938097275},\frac{38465347137138360}{21938097275}$$

To sort the list, start from a single element $\frac{15825000000}{21938097275}$.

$$\frac{15825000000}{21938097275}$$

Insert $-\frac{5880657734}{21938097275}$ to the appropriate location in the new list.

$$-\frac{5880657734}{21938097275},\frac{15825000000}{21938097275}$$

Insert $\frac{38465347137138360}{21938097275}$ to the appropriate location in the new list.

$$-\frac{5880657734}{21938097275},\frac{15825000000}{21938097275},\frac{38465347137138360}{21938097275}$$

Replace the obtained fractions with the initial values.

$$-\frac{1414}{5275},\frac{3000000}{4158881},1753358.4$$

Evaluate

$\frac{3000000}{4158881},\ -\frac{1414}{5275},\ 1753358.4$