Solve -5/14-(-8/3-3/70)=

$$- \frac { 5 } { 14 } - ( - \frac { 8 } { 3 } - \frac { 3 } { 70 } ) =$$

Evaluate

$$\frac{247}{105}\approx 2.352380952$$

Solution Steps

Least common multiple of 3 and 70 is 210. Convert -\frac{8}{3} and \frac{3}{70} to fractions with denominator 210.

$$-\frac{5}{14}-\left(-\frac{560}{210}-\frac{9}{210}\right)$$

Since -\frac{560}{210} and \frac{9}{210} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{14}-\frac{-560-9}{210}$$

Subtract 9 from -560 to get -569.

$$-\frac{5}{14}-\left(-\frac{569}{210}\right)$$

The opposite of -\frac{569}{210} is \frac{569}{210}.

$$-\frac{5}{14}+\frac{569}{210}$$

Least common multiple of 14 and 210 is 210. Convert -\frac{5}{14} and \frac{569}{210} to fractions with denominator 210.

$$-\frac{75}{210}+\frac{569}{210}$$

Since -\frac{75}{210} and \frac{569}{210} have the same denominator, add them by adding their numerators.

$$\frac{-75+569}{210}$$

Add -75 and 569 to get 494.

$$\frac{494}{210}$$

Reduce the fraction \frac{494}{210} to lowest terms by extracting and canceling out 2.

$$\frac{247}{105}$$

Factor

$$\frac{13 \cdot 19}{3 \cdot 5 \cdot 7} = 2\frac{37}{105} = 2.3523809523809525$$