Solve -8/14*35/37+15/17*12/35*frac{35}{37}

$$\frac { - 8 } { 14 } \cdot \frac { 35 } { 37 } + \frac { 15 } { 17 } \cdot \frac { 12 } { 35 } \cdot \frac { 35 } { 37 }$$

Evaluate

$$-\frac{160}{629}\approx -0.254372019$$

Solution Steps

Reduce the fraction \frac{-8}{14} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{7}\times \frac{35}{37}+\frac{15}{17}\times \frac{12}{35}\times \frac{35}{37}$$

Multiply -\frac{4}{7} times \frac{35}{37} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4\times 35}{7\times 37}+\frac{15}{17}\times \frac{12}{35}\times \frac{35}{37}$$

Do the multiplications in the fraction \frac{-4\times 35}{7\times 37}.

$$\frac{-140}{259}+\frac{15}{17}\times \frac{12}{35}\times \frac{35}{37}$$

Reduce the fraction \frac{-140}{259} to lowest terms by extracting and canceling out 7.

$$-\frac{20}{37}+\frac{15}{17}\times \frac{12}{35}\times \frac{35}{37}$$

Multiply \frac{15}{17} times \frac{12}{35} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{20}{37}+\frac{15\times 12}{17\times 35}\times \frac{35}{37}$$

Do the multiplications in the fraction \frac{15\times 12}{17\times 35}.

$$-\frac{20}{37}+\frac{180}{595}\times \frac{35}{37}$$

Reduce the fraction \frac{180}{595} to lowest terms by extracting and canceling out 5.

$$-\frac{20}{37}+\frac{36}{119}\times \frac{35}{37}$$

Multiply \frac{36}{119} times \frac{35}{37} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{20}{37}+\frac{36\times 35}{119\times 37}$$

Do the multiplications in the fraction \frac{36\times 35}{119\times 37}.

$$-\frac{20}{37}+\frac{1260}{4403}$$

Reduce the fraction \frac{1260}{4403} to lowest terms by extracting and canceling out 7.

$$-\frac{20}{37}+\frac{180}{629}$$

Least common multiple of 37 and 629 is 629. Convert -\frac{20}{37} and \frac{180}{629} to fractions with denominator 629.

$$-\frac{340}{629}+\frac{180}{629}$$

Since -\frac{340}{629} and \frac{180}{629} have the same denominator, add them by adding their numerators.

$$\frac{-340+180}{629}$$

Add -340 and 180 to get -160.

$$-\frac{160}{629}$$

Factor

$$-\frac{160}{629} = -0.2543720190779014$$