Solve 45/46*49/51-45/46-3/51

$$\frac { 45 } { 46 } \cdot \frac { 49 } { 51 } - \frac { 45 } { 46 } - \frac { 3 } { 51 }$$

Evaluate

$$-\frac{38}{391}\approx -0.097186701$$

Solution Steps

Multiply \frac{45}{46} times \frac{49}{51} by multiplying numerator times numerator and denominator times denominator.

$$\frac{45\times 49}{46\times 51}-\frac{45}{46}-\frac{3}{51}$$

Do the multiplications in the fraction \frac{45\times 49}{46\times 51}.

$$\frac{2205}{2346}-\frac{45}{46}-\frac{3}{51}$$

Reduce the fraction \frac{2205}{2346} to lowest terms by extracting and canceling out 3.

$$\frac{735}{782}-\frac{45}{46}-\frac{3}{51}$$

Least common multiple of 782 and 46 is 782. Convert \frac{735}{782} and \frac{45}{46} to fractions with denominator 782.

$$\frac{735}{782}-\frac{765}{782}-\frac{3}{51}$$

Since \frac{735}{782} and \frac{765}{782} have the same denominator, subtract them by subtracting their numerators.

$$\frac{735-765}{782}-\frac{3}{51}$$

Subtract 765 from 735 to get -30.

$$\frac{-30}{782}-\frac{3}{51}$$

Reduce the fraction \frac{-30}{782} to lowest terms by extracting and canceling out 2.

$$-\frac{15}{391}-\frac{3}{51}$$

Reduce the fraction \frac{3}{51} to lowest terms by extracting and canceling out 3.

$$-\frac{15}{391}-\frac{1}{17}$$

Least common multiple of 391 and 17 is 391. Convert -\frac{15}{391} and \frac{1}{17} to fractions with denominator 391.

$$-\frac{15}{391}-\frac{23}{391}$$

Since -\frac{15}{391} and \frac{23}{391} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-23}{391}$$

Subtract 23 from -15 to get -38.

$$-\frac{38}{391}$$

Factor

$$-\frac{38}{391} = -0.09718670076726342$$