Solve 3/7+(-35/26)-(-19/114)

$$\frac { 3 } { 7 } + ( - 3 \frac { 5 } { 26 } ) - ( - 1 \frac { 9 } { 114 } )$$

Evaluate

$$-\frac{2913}{1729}\approx -1.684788895$$

Solution Steps

Multiply 3 and 26 to get 78.

$$\frac{3}{7}-\frac{78+5}{26}-\left(-\frac{1\times 114+9}{114}\right)$$

Add 78 and 5 to get 83.

$$\frac{3}{7}-\frac{83}{26}-\left(-\frac{1\times 114+9}{114}\right)$$

Least common multiple of 7 and 26 is 182. Convert \frac{3}{7} and \frac{83}{26} to fractions with denominator 182.

$$\frac{78}{182}-\frac{581}{182}-\left(-\frac{1\times 114+9}{114}\right)$$

Since \frac{78}{182} and \frac{581}{182} have the same denominator, subtract them by subtracting their numerators.

$$\frac{78-581}{182}-\left(-\frac{1\times 114+9}{114}\right)$$

Subtract 581 from 78 to get -503.

$$-\frac{503}{182}-\left(-\frac{1\times 114+9}{114}\right)$$

Multiply 1 and 114 to get 114.

$$-\frac{503}{182}-\left(-\frac{114+9}{114}\right)$$

Add 114 and 9 to get 123.

$$-\frac{503}{182}-\left(-\frac{123}{114}\right)$$

Reduce the fraction \frac{123}{114} to lowest terms by extracting and canceling out 3.

$$-\frac{503}{182}-\left(-\frac{41}{38}\right)$$

The opposite of -\frac{41}{38} is \frac{41}{38}.

$$-\frac{503}{182}+\frac{41}{38}$$

Least common multiple of 182 and 38 is 3458. Convert -\frac{503}{182} and \frac{41}{38} to fractions with denominator 3458.

$$-\frac{9557}{3458}+\frac{3731}{3458}$$

Since -\frac{9557}{3458} and \frac{3731}{3458} have the same denominator, add them by adding their numerators.

$$\frac{-9557+3731}{3458}$$

Add -9557 and 3731 to get -5826.

$$\frac{-5826}{3458}$$

Reduce the fraction \frac{-5826}{3458} to lowest terms by extracting and canceling out 2.

$$-\frac{2913}{1729}$$

Factor

$$-\frac{2913}{1729} = -1\frac{1184}{1729} = -1.684788895315211$$