Solve 63/4/4frac{1{2}}+22/5/1frac{5{7}}-1frac{2}{5}

$$\frac { 6 \frac { 3 } { 4 } } { 4 \frac { 1 } { 2 } } + \frac { 2 \frac { 2 } { 5 } } { 1 \frac { 5 } { 7 } } - 1 \frac { 2 } { 5 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Divide \frac{6\times 4+3}{4} by \frac{4\times 2+1}{2} by multiplying \frac{6\times 4+3}{4} by the reciprocal of \frac{4\times 2+1}{2}.

$$\frac{\left(6\times 4+3\right)\times 2}{4\left(4\times 2+1\right)}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3+4\times 6}{2\left(1+2\times 4\right)}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Multiply 4 and 6 to get 24.

$$\frac{3+24}{2\left(1+2\times 4\right)}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Add 3 and 24 to get 27.

$$\frac{27}{2\left(1+2\times 4\right)}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Multiply 2 and 4 to get 8.

$$\frac{27}{2\left(1+8\right)}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Add 1 and 8 to get 9.

$$\frac{27}{2\times 9}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Multiply 2 and 9 to get 18.

$$\frac{27}{18}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Reduce the fraction \frac{27}{18} to lowest terms by extracting and canceling out 9.

$$\frac{3}{2}+\frac{\frac{2\times 5+2}{5}}{\frac{1\times 7+5}{7}}-\frac{1\times 5+2}{5}$$

Divide \frac{2\times 5+2}{5} by \frac{1\times 7+5}{7} by multiplying \frac{2\times 5+2}{5} by the reciprocal of \frac{1\times 7+5}{7}.

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

Multiply 2 and 5 to get 10.

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

Add 10 and 2 to get 12.

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

Multiply 12 and 7 to get 84.

$$\frac{3}{2}+\frac{84}{5\left(1\times 7+5\right)}-\frac{1\times 5+2}{5}$$

Multiply 1 and 7 to get 7.

$$\frac{3}{2}+\frac{84}{5\left(7+5\right)}-\frac{1\times 5+2}{5}$$

Add 7 and 5 to get 12.

$$\frac{3}{2}+\frac{84}{5\times 12}-\frac{1\times 5+2}{5}$$

Multiply 5 and 12 to get 60.

$$\frac{3}{2}+\frac{84}{60}-\frac{1\times 5+2}{5}$$

Reduce the fraction \frac{84}{60} to lowest terms by extracting and canceling out 12.

$$\frac{3}{2}+\frac{7}{5}-\frac{1\times 5+2}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{7}{5} to fractions with denominator 10.

$$\frac{15}{10}+\frac{14}{10}-\frac{1\times 5+2}{5}$$

Since \frac{15}{10} and \frac{14}{10} have the same denominator, add them by adding their numerators.

$$\frac{15+14}{10}-\frac{1\times 5+2}{5}$$

Add 15 and 14 to get 29.

$$\frac{29}{10}-\frac{1\times 5+2}{5}$$

Multiply 1 and 5 to get 5.

$$\frac{29}{10}-\frac{5+2}{5}$$

Add 5 and 2 to get 7.

$$\frac{29}{10}-\frac{7}{5}$$

Least common multiple of 10 and 5 is 10. Convert \frac{29}{10} and \frac{7}{5} to fractions with denominator 10.

$$\frac{29}{10}-\frac{14}{10}$$

Since \frac{29}{10} and \frac{14}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29-14}{10}$$

Subtract 14 from 29 to get 15.

$$\frac{15}{10}$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$