Solve 13/30-16/35-9/40

$$\frac { 13 } { 30 } - \frac { 16 } { 35 } - \frac { 9 } { 40 }$$

Evaluate

$$-\frac{209}{840}\approx -0.248809524$$

Solution Steps

Least common multiple of 30 and 35 is 210. Convert \frac{13}{30} and \frac{16}{35} to fractions with denominator 210.

$$\frac{91}{210}-\frac{96}{210}-\frac{9}{40}$$

Since \frac{91}{210} and \frac{96}{210} have the same denominator, subtract them by subtracting their numerators.

$$\frac{91-96}{210}-\frac{9}{40}$$

Subtract 96 from 91 to get -5.

$$\frac{-5}{210}-\frac{9}{40}$$

Reduce the fraction \frac{-5}{210} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{42}-\frac{9}{40}$$

Least common multiple of 42 and 40 is 840. Convert -\frac{1}{42} and \frac{9}{40} to fractions with denominator 840.

$$-\frac{20}{840}-\frac{189}{840}$$

Since -\frac{20}{840} and \frac{189}{840} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-20-189}{840}$$

Subtract 189 from -20 to get -209.

$$-\frac{209}{840}$$

Factor

$$-\frac{209}{840} = -0.2488095238095238$$