Solve {l}{text{(2)}126/7}{text{100585}}{text{(2)}0.02}{text{0.}785+0.03*0.785+0}

$$\left. \begin{array} { l } { \text { (2) } 12 \frac { 6 } { 7 } } \\ { \text { 100585 } } \\ { \text { (2) } 0.02 } \\ { \text { 0. } 785 + 0.03 \times 0.785 + 0 } \end{array} \right.$$

Sort

$$0.02355,0.04,\frac{180}{7},100585$$

Solution Steps

Multiply 12 and 7 to get 84.

$$sort(2\times \frac{84+6}{7},100585,2\times 0.02,0\times 785+0.03\times 0.785+0)$$

Add 84 and 6 to get 90.

$$sort(2\times \frac{90}{7},100585,2\times 0.02,0\times 785+0.03\times 0.785+0)$$

Express 2\times \frac{90}{7} as a single fraction.

$$sort(\frac{2\times 90}{7},100585,2\times 0.02,0\times 785+0.03\times 0.785+0)$$

Multiply 2 and 90 to get 180.

$$sort(\frac{180}{7},100585,2\times 0.02,0\times 785+0.03\times 0.785+0)$$

Multiply 2 and 0.02 to get 0.04.

$$sort(\frac{180}{7},100585,0.04,0\times 785+0.03\times 0.785+0)$$

Multiply 0 and 785 to get 0.

$$sort(\frac{180}{7},100585,0.04,0+0.03\times 0.785+0)$$

Multiply 0.03 and 0.785 to get 0.02355.

$$sort(\frac{180}{7},100585,0.04,0+0.02355+0)$$

Add 0 and 0.02355 to get 0.02355.

$$sort(\frac{180}{7},100585,0.04,0.02355+0)$$

Add 0.02355 and 0 to get 0.02355.

$$sort(\frac{180}{7},100585,0.04,0.02355)$$

Convert decimal numbers in the list \frac{180}{7},100585,0.04,0.02355 to fractions.

$$\frac{180}{7},100585,\frac{1}{25},\frac{471}{20000}$$

Least common denominator of the numbers in the list \frac{180}{7},100585,\frac{1}{25},\frac{471}{20000} is 140000. Convert numbers in the list to fractions with denominator 140000.

$$\frac{3600000}{140000},\frac{14081900000}{140000},\frac{5600}{140000},\frac{3297}{140000}$$

To sort the list, start from a single element \frac{3600000}{140000}.

$$\frac{3600000}{140000}$$

Insert \frac{14081900000}{140000} to the appropriate location in the new list.

$$\frac{3600000}{140000},\frac{14081900000}{140000}$$

Insert \frac{5600}{140000} to the appropriate location in the new list.

$$\frac{5600}{140000},\frac{3600000}{140000},\frac{14081900000}{140000}$$

Insert \frac{3297}{140000} to the appropriate location in the new list.

$$\frac{3297}{140000},\frac{5600}{140000},\frac{3600000}{140000},\frac{14081900000}{140000}$$

Replace the obtained fractions with the initial values.

$$0.02355,0.04,\frac{180}{7},100585$$

Evaluate

$$\frac{180}{7},\ 100585,\ 0.04,\ 0.02355$$