Solve 3/48 - 0.5/27; Rightarrow7 39-10 34 729 54 | 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

$$\left. \begin{array} { l } { 7 \frac { 3 } { 18 } - \frac { 3 } { 27 } } \\ { 7 \frac { 39 - 10 } { 54 } } \\ { 7 \frac { 29 } { 54 } } \end{array} \right.$$

Sort

$\frac{203}{54},\frac{127}{18},\frac{407}{54}$

Solution Steps

Multiply $7$ and $18$ to get $126$.

$$sort(\frac{126+3}{18}-\frac{3}{27},7\times \frac{39-10}{54},\frac{7\times 54+29}{54})$$

Add $126$ and $3$ to get $129$.

$$sort(\frac{129}{18}-\frac{3}{27},7\times \frac{39-10}{54},\frac{7\times 54+29}{54})$$

Reduce the fraction $\frac{129}{18}$ to lowest terms by extracting and canceling out $3$.

$$sort(\frac{43}{6}-\frac{3}{27},7\times \frac{39-10}{54},\frac{7\times 54+29}{54})$$

Reduce the fraction $\frac{3}{27}$ to lowest terms by extracting and canceling out $3$.

$$sort(\frac{43}{6}-\frac{1}{9},7\times \frac{39-10}{54},\frac{7\times 54+29}{54})$$

Least common multiple of $6$ and $9$ is $18$. Convert $\frac{43}{6}$ and $\frac{1}{9}$ to fractions with denominator $18$.

$$sort(\frac{129}{18}-\frac{2}{18},7\times \frac{39-10}{54},\frac{7\times 54+29}{54})$$

Since $\frac{129}{18}$ and $\frac{2}{18}$ have the same denominator, subtract them by subtracting their numerators.

$$sort(\frac{129-2}{18},7\times \frac{39-10}{54},\frac{7\times 54+29}{54})$$

Subtract $2$ from $129$ to get $127$.

$$sort(\frac{127}{18},7\times \frac{39-10}{54},\frac{7\times 54+29}{54})$$

Subtract $10$ from $39$ to get $29$.

$$sort(\frac{127}{18},7\times \frac{29}{54},\frac{7\times 54+29}{54})$$

Express $7\times \frac{29}{54}$ as a single fraction.

$$sort(\frac{127}{18},\frac{7\times 29}{54},\frac{7\times 54+29}{54})$$

Multiply $7$ and $29$ to get $203$.

$$sort(\frac{127}{18},\frac{203}{54},\frac{7\times 54+29}{54})$$

Multiply $7$ and $54$ to get $378$.

$$sort(\frac{127}{18},\frac{203}{54},\frac{378+29}{54})$$

Add $378$ and $29$ to get $407$.

$$sort(\frac{127}{18},\frac{203}{54},\frac{407}{54})$$

Least common denominator of the numbers in the list $\frac{127}{18},\frac{203}{54},\frac{407}{54}$ is $54$. Convert numbers in the list to fractions with denominator $54$.

$$\frac{381}{54},\frac{203}{54},\frac{407}{54}$$

To sort the list, start from a single element $\frac{381}{54}$.

$$\frac{381}{54}$$

Insert $\frac{203}{54}$ to the appropriate location in the new list.

$$\frac{203}{54},\frac{381}{54}$$

Insert $\frac{407}{54}$ to the appropriate location in the new list.

$$\frac{203}{54},\frac{381}{54},\frac{407}{54}$$

Replace the obtained fractions with the initial values.

$$\frac{203}{54},\frac{127}{18},\frac{407}{54}$$

Evaluate

$\frac{127}{18},\ \frac{203}{54},\ \frac{407}{54}$