Solve 15/2+5/4+8/7*1/2*frac{25}{15}

$$\frac { 15 } { 2 } + \frac { 5 } { 4 } + \frac { 8 } { 7 } \times \frac { 1 } { 2 } \times \frac { 25 } { 15 }$$

Evaluate

$$\frac{815}{84}\approx 9.702380952$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{15}{2} and \frac{5}{4} to fractions with denominator 4.

$$\frac{30}{4}+\frac{5}{4}+\frac{8}{7}\times \frac{1}{2}\times \frac{25}{15}$$

Since \frac{30}{4} and \frac{5}{4} have the same denominator, add them by adding their numerators.

$$\frac{30+5}{4}+\frac{8}{7}\times \frac{1}{2}\times \frac{25}{15}$$

Add 30 and 5 to get 35.

$$\frac{35}{4}+\frac{8}{7}\times \frac{1}{2}\times \frac{25}{15}$$

Multiply \frac{8}{7} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{4}+\frac{8\times 1}{7\times 2}\times \frac{25}{15}$$

Do the multiplications in the fraction \frac{8\times 1}{7\times 2}.

$$\frac{35}{4}+\frac{8}{14}\times \frac{25}{15}$$

Reduce the fraction \frac{8}{14} to lowest terms by extracting and canceling out 2.

$$\frac{35}{4}+\frac{4}{7}\times \frac{25}{15}$$

Reduce the fraction \frac{25}{15} to lowest terms by extracting and canceling out 5.

$$\frac{35}{4}+\frac{4}{7}\times \frac{5}{3}$$

Multiply \frac{4}{7} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35}{4}+\frac{4\times 5}{7\times 3}$$

Do the multiplications in the fraction \frac{4\times 5}{7\times 3}.

$$\frac{35}{4}+\frac{20}{21}$$

Least common multiple of 4 and 21 is 84. Convert \frac{35}{4} and \frac{20}{21} to fractions with denominator 84.

$$\frac{735}{84}+\frac{80}{84}$$

Since \frac{735}{84} and \frac{80}{84} have the same denominator, add them by adding their numerators.

$$\frac{735+80}{84}$$

Add 735 and 80 to get 815.

$$\frac{815}{84}$$

Factor

$$\frac{5 \cdot 163}{2 ^ {2} \cdot 3 \cdot 7} = 9\frac{59}{84} = 9.702380952380953$$