Solve Which of the following are 75141 7 9 -; 5/3; 1/7; 1/12; 16/13; 12/11; 1/4 11 Fill in the blanks with | 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

$$\frac { 7 } { 9 } , \frac { 5 } { 3 } , \frac { 1 } { 7 } , \frac { 4 } { 11 } , \frac { 16 } { 12 } , \frac { 12 } { 13 } , \frac { 1 } { 11 } , \frac { 1 } { 4 } , \frac { 1 } { 4 }$$

Sort

$\frac{1}{11},\frac{1}{7},\frac{1}{4},\frac{1}{4},\frac{4}{11},\frac{7}{9},\frac{12}{13},\frac{4}{3},\frac{5}{3}$

Solution Steps

Reduce the fraction $\frac{16}{12}$ to lowest terms by extracting and canceling out $4$.

$$sort(\frac{7}{9},\frac{5}{3},\frac{1}{7},\frac{4}{11},\frac{4}{3},\frac{12}{13},\frac{1}{11},\frac{1}{4},\frac{1}{4})$$

Least common denominator of the numbers in the list $\frac{7}{9},\frac{5}{3},\frac{1}{7},\frac{4}{11},\frac{4}{3},\frac{12}{13},\frac{1}{11},\frac{1}{4},\frac{1}{4}$ is $36036$. Convert numbers in the list to fractions with denominator $36036$.

$$\frac{28028}{36036},\frac{60060}{36036},\frac{5148}{36036},\frac{13104}{36036},\frac{48048}{36036},\frac{33264}{36036},\frac{3276}{36036},\frac{9009}{36036},\frac{9009}{36036}$$

To sort the list, start from a single element $\frac{28028}{36036}$.

$$\frac{28028}{36036}$$

Insert $\frac{60060}{36036}$ to the appropriate location in the new list.

$$\frac{28028}{36036},\frac{60060}{36036}$$

Insert $\frac{5148}{36036}$ to the appropriate location in the new list.

$$\frac{5148}{36036},\frac{28028}{36036},\frac{60060}{36036}$$

Insert $\frac{13104}{36036}$ to the appropriate location in the new list.

$$\frac{5148}{36036},\frac{13104}{36036},\frac{28028}{36036},\frac{60060}{36036}$$

Insert $\frac{48048}{36036}$ to the appropriate location in the new list.

$$\frac{5148}{36036},\frac{13104}{36036},\frac{28028}{36036},\frac{48048}{36036},\frac{60060}{36036}$$

Insert $\frac{33264}{36036}$ to the appropriate location in the new list.

$$\frac{5148}{36036},\frac{13104}{36036},\frac{28028}{36036},\frac{33264}{36036},\frac{48048}{36036},\frac{60060}{36036}$$

Insert $\frac{3276}{36036}$ to the appropriate location in the new list.

$$\frac{3276}{36036},\frac{5148}{36036},\frac{13104}{36036},\frac{28028}{36036},\frac{33264}{36036},\frac{48048}{36036},\frac{60060}{36036}$$

Insert $\frac{9009}{36036}$ to the appropriate location in the new list.

$$\frac{3276}{36036},\frac{5148}{36036},\frac{9009}{36036},\frac{13104}{36036},\frac{28028}{36036},\frac{33264}{36036},\frac{48048}{36036},\frac{60060}{36036}$$

Insert $\frac{9009}{36036}$ to the appropriate location in the new list.

$$\frac{3276}{36036},\frac{5148}{36036},\frac{9009}{36036},\frac{9009}{36036},\frac{13104}{36036},\frac{28028}{36036},\frac{33264}{36036},\frac{48048}{36036},\frac{60060}{36036}$$

Replace the obtained fractions with the initial values.

$$\frac{1}{11},\frac{1}{7},\frac{1}{4},\frac{1}{4},\frac{4}{11},\frac{7}{9},\frac{12}{13},\frac{4}{3},\frac{5}{3}$$

Evaluate

$\frac{7}{9},\frac{5}{3},\frac{1}{7},\frac{4}{11},\frac{4}{3},\frac{12}{13},\frac{1}{11},\frac{1}{4},\frac{1}{4}$