Solve ((-5/21)+(-38/35))+-123/70

$$(( - \frac { 5 } { 21 } )+( -3 \frac { 8 } { 35 } ))+ -1 \frac { 23 } { 70 }$$

Evaluate

$$-\frac{1007}{210}\approx -4.795238095$$

Solution Steps

Multiply 3 and 35 to get 105.

$$-\frac{5}{21}-\frac{105+8}{35}-\frac{1\times 70+23}{70}$$

Add 105 and 8 to get 113.

$$-\frac{5}{21}-\frac{113}{35}-\frac{1\times 70+23}{70}$$

Least common multiple of 21 and 35 is 105. Convert -\frac{5}{21} and \frac{113}{35} to fractions with denominator 105.

$$-\frac{25}{105}-\frac{339}{105}-\frac{1\times 70+23}{70}$$

Since -\frac{25}{105} and \frac{339}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-25-339}{105}-\frac{1\times 70+23}{70}$$

Subtract 339 from -25 to get -364.

$$\frac{-364}{105}-\frac{1\times 70+23}{70}$$

Reduce the fraction \frac{-364}{105} to lowest terms by extracting and canceling out 7.

$$-\frac{52}{15}-\frac{1\times 70+23}{70}$$

Multiply 1 and 70 to get 70.

$$-\frac{52}{15}-\frac{70+23}{70}$$

Add 70 and 23 to get 93.

$$-\frac{52}{15}-\frac{93}{70}$$

Least common multiple of 15 and 70 is 210. Convert -\frac{52}{15} and \frac{93}{70} to fractions with denominator 210.

$$-\frac{728}{210}-\frac{279}{210}$$

Since -\frac{728}{210} and \frac{279}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-728-279}{210}$$

Subtract 279 from -728 to get -1007.

$$-\frac{1007}{210}$$

Factor

$$-\frac{1007}{210} = -4\frac{167}{210} = -4.795238095238095$$