Solve {l}{3/45*7/8+21/45*6/8}{+frac{21}{45}*frac{5}{8}}

$$\left. \begin{array}{l}{ \frac { 3 } { 45 } \cdot \frac { 7 } { 8 } + \frac { 21 } { 45 } \cdot \frac { 6 } { 8 } }\\{ + \frac { 21 } { 45 } \cdot \frac { 5 } { 8 } }\end{array} \right.$$

Sort

$$\frac{7}{24},\frac{49}{120}$$

Solution Steps

Reduce the fraction \frac{3}{45} to lowest terms by extracting and canceling out 3.

$$sort(\frac{1}{15}\times \frac{7}{8}+\frac{21}{45}\times \frac{6}{8},\frac{21}{45}\times \frac{5}{8})$$

Multiply \frac{1}{15} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{1\times 7}{15\times 8}+\frac{21}{45}\times \frac{6}{8},\frac{21}{45}\times \frac{5}{8})$$

Do the multiplications in the fraction \frac{1\times 7}{15\times 8}.

$$sort(\frac{7}{120}+\frac{21}{45}\times \frac{6}{8},\frac{21}{45}\times \frac{5}{8})$$

Reduce the fraction \frac{21}{45} to lowest terms by extracting and canceling out 3.

$$sort(\frac{7}{120}+\frac{7}{15}\times \frac{6}{8},\frac{21}{45}\times \frac{5}{8})$$

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$sort(\frac{7}{120}+\frac{7}{15}\times \frac{3}{4},\frac{21}{45}\times \frac{5}{8})$$

Multiply \frac{7}{15} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{7}{120}+\frac{7\times 3}{15\times 4},\frac{21}{45}\times \frac{5}{8})$$

Do the multiplications in the fraction \frac{7\times 3}{15\times 4}.

$$sort(\frac{7}{120}+\frac{21}{60},\frac{21}{45}\times \frac{5}{8})$$

Reduce the fraction \frac{21}{60} to lowest terms by extracting and canceling out 3.

$$sort(\frac{7}{120}+\frac{7}{20},\frac{21}{45}\times \frac{5}{8})$$

Least common multiple of 120 and 20 is 120. Convert \frac{7}{120} and \frac{7}{20} to fractions with denominator 120.

$$sort(\frac{7}{120}+\frac{42}{120},\frac{21}{45}\times \frac{5}{8})$$

Since \frac{7}{120} and \frac{42}{120} have the same denominator, add them by adding their numerators.

$$sort(\frac{7+42}{120},\frac{21}{45}\times \frac{5}{8})$$

Add 7 and 42 to get 49.

$$sort(\frac{49}{120},\frac{21}{45}\times \frac{5}{8})$$

Reduce the fraction \frac{21}{45} to lowest terms by extracting and canceling out 3.

$$sort(\frac{49}{120},\frac{7}{15}\times \frac{5}{8})$$

Multiply \frac{7}{15} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$sort(\frac{49}{120},\frac{7\times 5}{15\times 8})$$

Do the multiplications in the fraction \frac{7\times 5}{15\times 8}.

$$sort(\frac{49}{120},\frac{35}{120})$$

Reduce the fraction \frac{35}{120} to lowest terms by extracting and canceling out 5.

$$sort(\frac{49}{120},\frac{7}{24})$$

Least common denominator of the numbers in the list \frac{49}{120},\frac{7}{24} is 120. Convert numbers in the list to fractions with denominator 120.

$$\frac{49}{120},\frac{35}{120}$$

To sort the list, start from a single element \frac{49}{120}.

$$\frac{49}{120}$$

Insert \frac{35}{120} to the appropriate location in the new list.

$$\frac{35}{120},\frac{49}{120}$$

Replace the obtained fractions with the initial values.

$$\frac{7}{24},\frac{49}{120}$$

Evaluate

$$\frac{49}{120},\ \frac{7}{24}$$