Solve 413/7-392/7/1frac{1{7}-1}

$$\frac { 41 \frac { 3 } { 7 } - 39 \frac { 2 } { 7 } } { 1 \frac { 1 } { 7 } - 1 }$$

Evaluate

$$15$$

Solution Steps

Multiply 41 and 7 to get 287.

$$\frac{\frac{287+3}{7}-\frac{39\times 7+2}{7}}{\frac{1\times 7+1}{7}-1}$$

Add 287 and 3 to get 290.

$$\frac{\frac{290}{7}-\frac{39\times 7+2}{7}}{\frac{1\times 7+1}{7}-1}$$

Multiply 39 and 7 to get 273.

$$\frac{\frac{290}{7}-\frac{273+2}{7}}{\frac{1\times 7+1}{7}-1}$$

Add 273 and 2 to get 275.

$$\frac{\frac{290}{7}-\frac{275}{7}}{\frac{1\times 7+1}{7}-1}$$

Since \frac{290}{7} and \frac{275}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{290-275}{7}}{\frac{1\times 7+1}{7}-1}$$

Subtract 275 from 290 to get 15.

$$\frac{\frac{15}{7}}{\frac{1\times 7+1}{7}-1}$$

Multiply 1 and 7 to get 7.

$$\frac{\frac{15}{7}}{\frac{7+1}{7}-1}$$

Add 7 and 1 to get 8.

$$\frac{\frac{15}{7}}{\frac{8}{7}-1}$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{\frac{15}{7}}{\frac{8}{7}-\frac{7}{7}}$$

Since \frac{8}{7} and \frac{7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15}{7}}{\frac{8-7}{7}}$$

Subtract 7 from 8 to get 1.

$$\frac{\frac{15}{7}}{\frac{1}{7}}$$

Divide \frac{15}{7} by \frac{1}{7} by multiplying \frac{15}{7} by the reciprocal of \frac{1}{7}.

$$\frac{15}{7}\times 7$$

Cancel out 7 and 7.

$$15$$

Factor

$$3\times 5$$