Solve 25/8+(72/3-25/2)-25/24

$$2 \frac{ 5 }{ 8 } +(7 \frac{ 2 }{ 3 } - \frac{ 25 }{ 2 } )-2 \frac{ 5 }{ 24 }$$

Evaluate

$$-\frac{53}{12}\approx -4.416666667$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\frac{16+5}{8}+\frac{7\times 3+2}{3}-\frac{25}{2}-\frac{2\times 24+5}{24}$$

Add 16 and 5 to get 21.

$$\frac{21}{8}+\frac{7\times 3+2}{3}-\frac{25}{2}-\frac{2\times 24+5}{24}$$

Multiply 7 and 3 to get 21.

$$\frac{21}{8}+\frac{21+2}{3}-\frac{25}{2}-\frac{2\times 24+5}{24}$$

Add 21 and 2 to get 23.

$$\frac{21}{8}+\frac{23}{3}-\frac{25}{2}-\frac{2\times 24+5}{24}$$

Least common multiple of 8 and 3 is 24. Convert \frac{21}{8} and \frac{23}{3} to fractions with denominator 24.

$$\frac{63}{24}+\frac{184}{24}-\frac{25}{2}-\frac{2\times 24+5}{24}$$

Since \frac{63}{24} and \frac{184}{24} have the same denominator, add them by adding their numerators.

$$\frac{63+184}{24}-\frac{25}{2}-\frac{2\times 24+5}{24}$$

Add 63 and 184 to get 247.

$$\frac{247}{24}-\frac{25}{2}-\frac{2\times 24+5}{24}$$

Least common multiple of 24 and 2 is 24. Convert \frac{247}{24} and \frac{25}{2} to fractions with denominator 24.

$$\frac{247}{24}-\frac{300}{24}-\frac{2\times 24+5}{24}$$

Since \frac{247}{24} and \frac{300}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{247-300}{24}-\frac{2\times 24+5}{24}$$

Subtract 300 from 247 to get -53.

$$-\frac{53}{24}-\frac{2\times 24+5}{24}$$

Multiply 2 and 24 to get 48.

$$-\frac{53}{24}-\frac{48+5}{24}$$

Add 48 and 5 to get 53.

$$-\frac{53}{24}-\frac{53}{24}$$

Since -\frac{53}{24} and \frac{53}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-53-53}{24}$$

Subtract 53 from -53 to get -106.

$$\frac{-106}{24}$$

Reduce the fraction \frac{-106}{24} to lowest terms by extracting and canceling out 2.

$$-\frac{53}{12}$$

Factor

$$-\frac{53}{12} = -4\frac{5}{12} = -4.416666666666667$$