Solve 5/8+4/6-8/9+2/3-frac{3}{24}

$$\frac{ 5 }{ 8 } + \frac{ 4 }{ 6 } - \frac{ 8 }{ 9 } + \frac{ 2 }{ 3 } - \frac{ 3 }{ 24 }$$

Evaluate

$$\frac{17}{18}\approx 0.944444444$$

Solution Steps

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{5}{8}+\frac{2}{3}-\frac{8}{9}+\frac{2}{3}-\frac{3}{24}$$

Least common multiple of 8 and 3 is 24. Convert \frac{5}{8} and \frac{2}{3} to fractions with denominator 24.

$$\frac{15}{24}+\frac{16}{24}-\frac{8}{9}+\frac{2}{3}-\frac{3}{24}$$

Since \frac{15}{24} and \frac{16}{24} have the same denominator, add them by adding their numerators.

$$\frac{15+16}{24}-\frac{8}{9}+\frac{2}{3}-\frac{3}{24}$$

Add 15 and 16 to get 31.

$$\frac{31}{24}-\frac{8}{9}+\frac{2}{3}-\frac{3}{24}$$

Least common multiple of 24 and 9 is 72. Convert \frac{31}{24} and \frac{8}{9} to fractions with denominator 72.

$$\frac{93}{72}-\frac{64}{72}+\frac{2}{3}-\frac{3}{24}$$

Since \frac{93}{72} and \frac{64}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{93-64}{72}+\frac{2}{3}-\frac{3}{24}$$

Subtract 64 from 93 to get 29.

$$\frac{29}{72}+\frac{2}{3}-\frac{3}{24}$$

Least common multiple of 72 and 3 is 72. Convert \frac{29}{72} and \frac{2}{3} to fractions with denominator 72.

$$\frac{29}{72}+\frac{48}{72}-\frac{3}{24}$$

Since \frac{29}{72} and \frac{48}{72} have the same denominator, add them by adding their numerators.

$$\frac{29+48}{72}-\frac{3}{24}$$

Add 29 and 48 to get 77.

$$\frac{77}{72}-\frac{3}{24}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{77}{72}-\frac{1}{8}$$

Least common multiple of 72 and 8 is 72. Convert \frac{77}{72} and \frac{1}{8} to fractions with denominator 72.

$$\frac{77}{72}-\frac{9}{72}$$

Since \frac{77}{72} and \frac{9}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{77-9}{72}$$

Subtract 9 from 77 to get 68.

$$\frac{68}{72}$$

Reduce the fraction \frac{68}{72} to lowest terms by extracting and canceling out 4.

$$\frac{17}{18}$$

Factor

$$\frac{17}{2 \cdot 3 ^ {2}} = 0.9444444444444444$$