Solve 35/15+3-5/4+2/515/2-12*5

$$\frac{ 35 }{ 15 } +3- \frac{ 5 }{ 4 } + \frac{ 2 }{ 5 } \frac{ 15 }{ 2 } -12 \cdot 5$$

Evaluate

$$-\frac{635}{12}\approx -52.916666667$$

Solution Steps

Reduce the fraction \frac{35}{15} to lowest terms by extracting and canceling out 5.

$$\frac{7}{3}+3-\frac{5}{4}+\frac{2}{5}\times \frac{15}{2}-12\times 5$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{7}{3}+\frac{9}{3}-\frac{5}{4}+\frac{2}{5}\times \frac{15}{2}-12\times 5$$

Since \frac{7}{3} and \frac{9}{3} have the same denominator, add them by adding their numerators.

$$\frac{7+9}{3}-\frac{5}{4}+\frac{2}{5}\times \frac{15}{2}-12\times 5$$

Add 7 and 9 to get 16.

$$\frac{16}{3}-\frac{5}{4}+\frac{2}{5}\times \frac{15}{2}-12\times 5$$

Least common multiple of 3 and 4 is 12. Convert \frac{16}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{64}{12}-\frac{15}{12}+\frac{2}{5}\times \frac{15}{2}-12\times 5$$

Since \frac{64}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-15}{12}+\frac{2}{5}\times \frac{15}{2}-12\times 5$$

Subtract 15 from 64 to get 49.

$$\frac{49}{12}+\frac{2}{5}\times \frac{15}{2}-12\times 5$$

Multiply \frac{2}{5} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49}{12}+\frac{2\times 15}{5\times 2}-12\times 5$$

Cancel out 2 in both numerator and denominator.

$$\frac{49}{12}+\frac{15}{5}-12\times 5$$

Divide 15 by 5 to get 3.

$$\frac{49}{12}+3-12\times 5$$

Convert 3 to fraction \frac{36}{12}.

$$\frac{49}{12}+\frac{36}{12}-12\times 5$$

Since \frac{49}{12} and \frac{36}{12} have the same denominator, add them by adding their numerators.

$$\frac{49+36}{12}-12\times 5$$

Add 49 and 36 to get 85.

$$\frac{85}{12}-12\times 5$$

Multiply 12 and 5 to get 60.

$$\frac{85}{12}-60$$

Convert 60 to fraction \frac{720}{12}.

$$\frac{85}{12}-\frac{720}{12}$$

Since \frac{85}{12} and \frac{720}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{85-720}{12}$$

Subtract 720 from 85 to get -635.

$$-\frac{635}{12}$$

Factor

$$-\frac{635}{12} = -52\frac{11}{12} = -52.916666666666664$$