Solve (11/4*2/5+33/7:9/14):frac{5}{12}-10frac{1}{5}

$$( 1 \frac { 1 } { 4 } \cdot \frac { 2 } { 5 } + 3 \frac { 3 } { 7 } : \frac { 9 } { 14 } ) : \frac { 5 } { 12 } - 10 \frac { 1 } { 5 }$$

Evaluate

$$\frac{19}{5}=3.8$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{\frac{4+1}{4}\times \frac{2}{5}+\frac{\frac{3\times 7+3}{7}}{\frac{9}{14}}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Add 4 and 1 to get 5.

$$\frac{\frac{5}{4}\times \frac{2}{5}+\frac{\frac{3\times 7+3}{7}}{\frac{9}{14}}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Multiply \frac{5}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 2}{4\times 5}+\frac{\frac{3\times 7+3}{7}}{\frac{9}{14}}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{\frac{2}{4}+\frac{\frac{3\times 7+3}{7}}{\frac{9}{14}}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{2}+\frac{\frac{3\times 7+3}{7}}{\frac{9}{14}}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Divide \frac{3\times 7+3}{7} by \frac{9}{14} by multiplying \frac{3\times 7+3}{7} by the reciprocal of \frac{9}{14}.

$$\frac{\frac{1}{2}+\frac{\left(3\times 7+3\right)\times 14}{7\times 9}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Cancel out 7 in both numerator and denominator.

$$\frac{\frac{1}{2}+\frac{2\left(3+3\times 7\right)}{9}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Multiply 3 and 7 to get 21.

$$\frac{\frac{1}{2}+\frac{2\left(3+21\right)}{9}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Add 3 and 21 to get 24.

$$\frac{\frac{1}{2}+\frac{2\times 24}{9}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Multiply 2 and 24 to get 48.

$$\frac{\frac{1}{2}+\frac{48}{9}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Reduce the fraction \frac{48}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{2}+\frac{16}{3}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{16}{3} to fractions with denominator 6.

$$\frac{\frac{3}{6}+\frac{32}{6}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Since \frac{3}{6} and \frac{32}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+32}{6}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Add 3 and 32 to get 35.

$$\frac{\frac{35}{6}}{\frac{5}{12}}-\frac{10\times 5+1}{5}$$

Divide \frac{35}{6} by \frac{5}{12} by multiplying \frac{35}{6} by the reciprocal of \frac{5}{12}.

$$\frac{35}{6}\times \frac{12}{5}-\frac{10\times 5+1}{5}$$

Multiply \frac{35}{6} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35\times 12}{6\times 5}-\frac{10\times 5+1}{5}$$

Do the multiplications in the fraction \frac{35\times 12}{6\times 5}.

$$\frac{420}{30}-\frac{10\times 5+1}{5}$$

Divide 420 by 30 to get 14.

$$14-\frac{10\times 5+1}{5}$$

Multiply 10 and 5 to get 50.

$$14-\frac{50+1}{5}$$

Add 50 and 1 to get 51.

$$14-\frac{51}{5}$$

Convert 14 to fraction \frac{70}{5}.

$$\frac{70}{5}-\frac{51}{5}$$

Since \frac{70}{5} and \frac{51}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{70-51}{5}$$

Subtract 51 from 70 to get 19.

$$\frac{19}{5}$$

Factor

$$\frac{19}{5} = 3\frac{4}{5} = 3.8$$