Solve 23/24+1/3-(3/4+1/7)

$$\frac { 23 } { 24 } + \frac { 1 } { 3 } - ( \frac { 3 } { 4 } + \frac { 1 } { 7 } )$$

Evaluate

$$\frac{67}{168}\approx 0.398809524$$

Solution Steps

Least common multiple of 24 and 3 is 24. Convert \frac{23}{24} and \frac{1}{3} to fractions with denominator 24.

$$\frac{23}{24}+\frac{8}{24}-\left(\frac{3}{4}+\frac{1}{7}\right)$$

Since \frac{23}{24} and \frac{8}{24} have the same denominator, add them by adding their numerators.

$$\frac{23+8}{24}-\left(\frac{3}{4}+\frac{1}{7}\right)$$

Add 23 and 8 to get 31.

$$\frac{31}{24}-\left(\frac{3}{4}+\frac{1}{7}\right)$$

Least common multiple of 4 and 7 is 28. Convert \frac{3}{4} and \frac{1}{7} to fractions with denominator 28.

$$\frac{31}{24}-\left(\frac{21}{28}+\frac{4}{28}\right)$$

Since \frac{21}{28} and \frac{4}{28} have the same denominator, add them by adding their numerators.

$$\frac{31}{24}-\frac{21+4}{28}$$

Add 21 and 4 to get 25.

$$\frac{31}{24}-\frac{25}{28}$$

Least common multiple of 24 and 28 is 168. Convert \frac{31}{24} and \frac{25}{28} to fractions with denominator 168.

$$\frac{217}{168}-\frac{150}{168}$$

Since \frac{217}{168} and \frac{150}{168} have the same denominator, subtract them by subtracting their numerators.

$$\frac{217-150}{168}$$

Subtract 150 from 217 to get 67.

$$\frac{67}{168}$$

Factor

$$\frac{67}{2 ^ {3} \cdot 3 \cdot 7} = 0.39880952380952384$$