Solve 6*101/4:132/3-5/7*3/5=

$$6 \cdot 10 \frac { 1 } { 4 } : 13 \frac { 2 } { 3 } - \frac { 5 } { 7 } \cdot \frac { 3 } { 5 } =$$

Evaluate

$$\frac{57}{14}\approx 4.071428571$$

Solution Steps

Multiply 10 and 4 to get 40.

$$\frac{6\times \frac{40+1}{4}}{\frac{13\times 3+2}{3}}-\frac{5}{7}\times \frac{3}{5}$$

Add 40 and 1 to get 41.

$$\frac{6\times \frac{41}{4}}{\frac{13\times 3+2}{3}}-\frac{5}{7}\times \frac{3}{5}$$

Express 6\times \frac{41}{4} as a single fraction.

$$\frac{\frac{6\times 41}{4}}{\frac{13\times 3+2}{3}}-\frac{5}{7}\times \frac{3}{5}$$

Multiply 6 and 41 to get 246.

$$\frac{\frac{246}{4}}{\frac{13\times 3+2}{3}}-\frac{5}{7}\times \frac{3}{5}$$

Reduce the fraction \frac{246}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{123}{2}}{\frac{13\times 3+2}{3}}-\frac{5}{7}\times \frac{3}{5}$$

Multiply 13 and 3 to get 39.

$$\frac{\frac{123}{2}}{\frac{39+2}{3}}-\frac{5}{7}\times \frac{3}{5}$$

Add 39 and 2 to get 41.

$$\frac{\frac{123}{2}}{\frac{41}{3}}-\frac{5}{7}\times \frac{3}{5}$$

Divide \frac{123}{2} by \frac{41}{3} by multiplying \frac{123}{2} by the reciprocal of \frac{41}{3}.

$$\frac{123}{2}\times \frac{3}{41}-\frac{5}{7}\times \frac{3}{5}$$

Multiply \frac{123}{2} times \frac{3}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{123\times 3}{2\times 41}-\frac{5}{7}\times \frac{3}{5}$$

Do the multiplications in the fraction \frac{123\times 3}{2\times 41}.

$$\frac{369}{82}-\frac{5}{7}\times \frac{3}{5}$$

Reduce the fraction \frac{369}{82} to lowest terms by extracting and canceling out 41.

$$\frac{9}{2}-\frac{5}{7}\times \frac{3}{5}$$

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

$$\frac{9}{2}-\frac{5\times 3}{7\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{9}{2}-\frac{3}{7}$$

Least common multiple of 2 and 7 is 14. Convert \frac{9}{2} and \frac{3}{7} to fractions with denominator 14.

$$\frac{63}{14}-\frac{6}{14}$$

Since \frac{63}{14} and \frac{6}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{63-6}{14}$$

Subtract 6 from 63 to get 57.

$$\frac{57}{14}$$

Factor

$$\frac{3 \cdot 19}{2 \cdot 7} = 4\frac{1}{14} = 4.071428571428571$$