Solve 3/5*5/21+15/28:frac{5/84}{7frac{1}{2}+10}+frac{2:frac{1}{2}+3:frac{1}{3}}{frac{1}{2}:2+frac{1}{3}:3}*frac{1}{36}-frac{16}{35}

$$\frac { \frac { 3 } { 5 } \cdot \frac { 5 } { 21 } + \frac { 15 } { 28 } : \frac { 5 } { 84 } } { 7 \frac { 1 } { 2 } + 10 } + \frac { 2 : \frac { 1 } { 2 } + 3 : \frac { 1 } { 3 } } { \frac { 1 } { 2 } : 2 + \frac { 1 } { 3 } : 3 } \cdot \frac { 1 } { 36 } - \frac { 16 } { 35 }$$

Evaluate

$$\frac{261}{245}\approx 1.065306122$$

Solution Steps

Multiply \frac{3}{5} times \frac{5}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 5}{5\times 21}+\frac{\frac{15}{28}}{\frac{5}{84}}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{3}{21}+\frac{\frac{15}{28}}{\frac{5}{84}}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

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

$$\frac{\frac{1}{7}+\frac{\frac{15}{28}}{\frac{5}{84}}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Divide \frac{15}{28} by \frac{5}{84} by multiplying \frac{15}{28} by the reciprocal of \frac{5}{84}.

$$\frac{\frac{1}{7}+\frac{15}{28}\times \frac{84}{5}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Multiply \frac{15}{28} times \frac{84}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{7}+\frac{15\times 84}{28\times 5}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Do the multiplications in the fraction \frac{15\times 84}{28\times 5}.

$$\frac{\frac{1}{7}+\frac{1260}{140}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Divide 1260 by 140 to get 9.

$$\frac{\frac{1}{7}+9}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Convert 9 to fraction \frac{63}{7}.

$$\frac{\frac{1}{7}+\frac{63}{7}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Since \frac{1}{7} and \frac{63}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+63}{7}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Add 1 and 63 to get 64.

$$\frac{\frac{64}{7}}{\frac{7\times 2+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Multiply 7 and 2 to get 14.

$$\frac{\frac{64}{7}}{\frac{14+1}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Add 14 and 1 to get 15.

$$\frac{\frac{64}{7}}{\frac{15}{2}+10}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Convert 10 to fraction \frac{20}{2}.

$$\frac{\frac{64}{7}}{\frac{15}{2}+\frac{20}{2}}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Since \frac{15}{2} and \frac{20}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{64}{7}}{\frac{15+20}{2}}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Add 15 and 20 to get 35.

$$\frac{\frac{64}{7}}{\frac{35}{2}}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Divide \frac{64}{7} by \frac{35}{2} by multiplying \frac{64}{7} by the reciprocal of \frac{35}{2}.

$$\frac{64}{7}\times \frac{2}{35}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Multiply \frac{64}{7} times \frac{2}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64\times 2}{7\times 35}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Do the multiplications in the fraction \frac{64\times 2}{7\times 35}.

$$\frac{128}{245}+\frac{\frac{2}{\frac{1}{2}}+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Divide 2 by \frac{1}{2} by multiplying 2 by the reciprocal of \frac{1}{2}.

$$\frac{128}{245}+\frac{2\times 2+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Multiply 2 and 2 to get 4.

$$\frac{128}{245}+\frac{4+\frac{3}{\frac{1}{3}}}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Divide 3 by \frac{1}{3} by multiplying 3 by the reciprocal of \frac{1}{3}.

$$\frac{128}{245}+\frac{4+3\times 3}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Multiply 3 and 3 to get 9.

$$\frac{128}{245}+\frac{4+9}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Add 4 and 9 to get 13.

$$\frac{128}{245}+\frac{13}{\frac{\frac{1}{2}}{2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Express \frac{\frac{1}{2}}{2} as a single fraction.

$$\frac{128}{245}+\frac{13}{\frac{1}{2\times 2}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Multiply 2 and 2 to get 4.

$$\frac{128}{245}+\frac{13}{\frac{1}{4}+\frac{\frac{1}{3}}{3}}\times \frac{1}{36}-\frac{16}{35}$$

Express \frac{\frac{1}{3}}{3} as a single fraction.

$$\frac{128}{245}+\frac{13}{\frac{1}{4}+\frac{1}{3\times 3}}\times \frac{1}{36}-\frac{16}{35}$$

Multiply 3 and 3 to get 9.

$$\frac{128}{245}+\frac{13}{\frac{1}{4}+\frac{1}{9}}\times \frac{1}{36}-\frac{16}{35}$$

Least common multiple of 4 and 9 is 36. Convert \frac{1}{4} and \frac{1}{9} to fractions with denominator 36.

$$\frac{128}{245}+\frac{13}{\frac{9}{36}+\frac{4}{36}}\times \frac{1}{36}-\frac{16}{35}$$

Since \frac{9}{36} and \frac{4}{36} have the same denominator, add them by adding their numerators.

$$\frac{128}{245}+\frac{13}{\frac{9+4}{36}}\times \frac{1}{36}-\frac{16}{35}$$

Add 9 and 4 to get 13.

$$\frac{128}{245}+\frac{13}{\frac{13}{36}}\times \frac{1}{36}-\frac{16}{35}$$

Divide 13 by \frac{13}{36} by multiplying 13 by the reciprocal of \frac{13}{36}.

$$\frac{128}{245}+13\times \frac{36}{13}\times \frac{1}{36}-\frac{16}{35}$$

Cancel out 13 and 13.

$$\frac{128}{245}+36\times \frac{1}{36}-\frac{16}{35}$$

Cancel out 36 and 36.

$$\frac{128}{245}+1-\frac{16}{35}$$

Convert 1 to fraction \frac{245}{245}.

$$\frac{128}{245}+\frac{245}{245}-\frac{16}{35}$$

Since \frac{128}{245} and \frac{245}{245} have the same denominator, add them by adding their numerators.

$$\frac{128+245}{245}-\frac{16}{35}$$

Add 128 and 245 to get 373.

$$\frac{373}{245}-\frac{16}{35}$$

Least common multiple of 245 and 35 is 245. Convert \frac{373}{245} and \frac{16}{35} to fractions with denominator 245.

$$\frac{373}{245}-\frac{112}{245}$$

Since \frac{373}{245} and \frac{112}{245} have the same denominator, subtract them by subtracting their numerators.

$$\frac{373-112}{245}$$

Subtract 112 from 373 to get 261.

$$\frac{261}{245}$$

Factor

$$\frac{3 ^ {2} \cdot 29}{5 \cdot 7 ^ {2}} = 1\frac{16}{245} = 1.0653061224489795$$