Solve 8/37-4/29/frac{1{29}-2/37}-3

$$\frac { \frac { 8 } { 37 } - \frac { 4 } { 29 } } { \frac { 1 } { 29 } - \frac { 2 } { 37 } } - 3$$

Evaluate

$$-7$$

Solution Steps

Least common multiple of 37 and 29 is 1073. Convert \frac{8}{37} and \frac{4}{29} to fractions with denominator 1073.

$$\frac{\frac{232}{1073}-\frac{148}{1073}}{\frac{1}{29}-\frac{2}{37}}-3$$

Since \frac{232}{1073} and \frac{148}{1073} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{232-148}{1073}}{\frac{1}{29}-\frac{2}{37}}-3$$

Subtract 148 from 232 to get 84.

$$\frac{\frac{84}{1073}}{\frac{1}{29}-\frac{2}{37}}-3$$

Least common multiple of 29 and 37 is 1073. Convert \frac{1}{29} and \frac{2}{37} to fractions with denominator 1073.

$$\frac{\frac{84}{1073}}{\frac{37}{1073}-\frac{58}{1073}}-3$$

Since \frac{37}{1073} and \frac{58}{1073} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{84}{1073}}{\frac{37-58}{1073}}-3$$

Subtract 58 from 37 to get -21.

$$\frac{\frac{84}{1073}}{-\frac{21}{1073}}-3$$

Divide \frac{84}{1073} by -\frac{21}{1073} by multiplying \frac{84}{1073} by the reciprocal of -\frac{21}{1073}.

$$\frac{84}{1073}\left(-\frac{1073}{21}\right)-3$$

Multiply \frac{84}{1073} times -\frac{1073}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{84\left(-1073\right)}{1073\times 21}-3$$

Do the multiplications in the fraction \frac{84\left(-1073\right)}{1073\times 21}.

$$\frac{-90132}{22533}-3$$

Divide -90132 by 22533 to get -4.

$$-4-3$$

Subtract 3 from -4 to get -7.

$$-7$$

Factor

$$-7$$