Solve 17/12-5/12-7/4-4/3+frac{5}{4}-frac{4}{9}

$$\frac{ 17 }{ 12 } - \frac{ 5 }{ 12 } - \frac{ 7 }{ 4 } - \frac{ 4 }{ 3 } + \frac{ 5 }{ 4 } - \frac{ 4 }{ 9 }$$

Evaluate

$$-\frac{23}{18}\approx -1.277777778$$

Solution Steps

Since \frac{17}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17-5}{12}-\frac{7}{4}-\frac{4}{3}+\frac{5}{4}-\frac{4}{9}$$

Subtract 5 from 17 to get 12.

$$\frac{12}{12}-\frac{7}{4}-\frac{4}{3}+\frac{5}{4}-\frac{4}{9}$$

Divide 12 by 12 to get 1.

$$1-\frac{7}{4}-\frac{4}{3}+\frac{5}{4}-\frac{4}{9}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{4}-\frac{7}{4}-\frac{4}{3}+\frac{5}{4}-\frac{4}{9}$$

Since \frac{4}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-7}{4}-\frac{4}{3}+\frac{5}{4}-\frac{4}{9}$$

Subtract 7 from 4 to get -3.

$$-\frac{3}{4}-\frac{4}{3}+\frac{5}{4}-\frac{4}{9}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{4}{3} to fractions with denominator 12.

$$-\frac{9}{12}-\frac{16}{12}+\frac{5}{4}-\frac{4}{9}$$

Since -\frac{9}{12} and \frac{16}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-9-16}{12}+\frac{5}{4}-\frac{4}{9}$$

Subtract 16 from -9 to get -25.

$$-\frac{25}{12}+\frac{5}{4}-\frac{4}{9}$$

Least common multiple of 12 and 4 is 12. Convert -\frac{25}{12} and \frac{5}{4} to fractions with denominator 12.

$$-\frac{25}{12}+\frac{15}{12}-\frac{4}{9}$$

Since -\frac{25}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{-25+15}{12}-\frac{4}{9}$$

Add -25 and 15 to get -10.

$$\frac{-10}{12}-\frac{4}{9}$$

Reduce the fraction \frac{-10}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{6}-\frac{4}{9}$$

Least common multiple of 6 and 9 is 18. Convert -\frac{5}{6} and \frac{4}{9} to fractions with denominator 18.

$$-\frac{15}{18}-\frac{8}{18}$$

Since -\frac{15}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-15-8}{18}$$

Subtract 8 from -15 to get -23.

$$-\frac{23}{18}$$

Factor

$$-\frac{23}{18} = -1\frac{5}{18} = -1.2777777777777777$$