Solve =+6/5+9/4+11/5+1/5-frac{4}{1}-frac{3}{1}-frac{5}{2}-frac{5}{4}

$$= + \frac { 6 } { 5 } + \frac { 9 } { 4 } + \frac { 11 } { 5 } + \frac { 1 } { 5 } - \frac { 4 } { 1 } - \frac { 3 } { 1 } - \frac { 5 } { 2 } - \frac { 5 } { 4 }$$

Evaluate

$$-\frac{49}{10}=-4.9$$

Solution Steps

Least common multiple of 5 and 4 is 20. Convert \frac{6}{5} and \frac{9}{4} to fractions with denominator 20.

$$\frac{24}{20}+\frac{45}{20}+\frac{11}{5}+\frac{1}{5}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Since \frac{24}{20} and \frac{45}{20} have the same denominator, add them by adding their numerators.

$$\frac{24+45}{20}+\frac{11}{5}+\frac{1}{5}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Add 24 and 45 to get 69.

$$\frac{69}{20}+\frac{11}{5}+\frac{1}{5}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Least common multiple of 20 and 5 is 20. Convert \frac{69}{20} and \frac{11}{5} to fractions with denominator 20.

$$\frac{69}{20}+\frac{44}{20}+\frac{1}{5}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Since \frac{69}{20} and \frac{44}{20} have the same denominator, add them by adding their numerators.

$$\frac{69+44}{20}+\frac{1}{5}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Add 69 and 44 to get 113.

$$\frac{113}{20}+\frac{1}{5}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Least common multiple of 20 and 5 is 20. Convert \frac{113}{20} and \frac{1}{5} to fractions with denominator 20.

$$\frac{113}{20}+\frac{4}{20}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Since \frac{113}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{113+4}{20}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Add 113 and 4 to get 117.

$$\frac{117}{20}-\frac{4}{1}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Anything divided by one gives itself.

$$\frac{117}{20}-4-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Convert 4 to fraction \frac{80}{20}.

$$\frac{117}{20}-\frac{80}{20}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Since \frac{117}{20} and \frac{80}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{117-80}{20}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Subtract 80 from 117 to get 37.

$$\frac{37}{20}-\frac{3}{1}-\frac{5}{2}-\frac{5}{4}$$

Anything divided by one gives itself.

$$\frac{37}{20}-3-\frac{5}{2}-\frac{5}{4}$$

Convert 3 to fraction \frac{60}{20}.

$$\frac{37}{20}-\frac{60}{20}-\frac{5}{2}-\frac{5}{4}$$

Since \frac{37}{20} and \frac{60}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{37-60}{20}-\frac{5}{2}-\frac{5}{4}$$

Subtract 60 from 37 to get -23.

$$-\frac{23}{20}-\frac{5}{2}-\frac{5}{4}$$

Least common multiple of 20 and 2 is 20. Convert -\frac{23}{20} and \frac{5}{2} to fractions with denominator 20.

$$-\frac{23}{20}-\frac{50}{20}-\frac{5}{4}$$

Since -\frac{23}{20} and \frac{50}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-23-50}{20}-\frac{5}{4}$$

Subtract 50 from -23 to get -73.

$$-\frac{73}{20}-\frac{5}{4}$$

Least common multiple of 20 and 4 is 20. Convert -\frac{73}{20} and \frac{5}{4} to fractions with denominator 20.

$$-\frac{73}{20}-\frac{25}{20}$$

Since -\frac{73}{20} and \frac{25}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-73-25}{20}$$

Subtract 25 from -73 to get -98.

$$\frac{-98}{20}$$

Reduce the fraction \frac{-98}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{49}{10}$$

Factor

$$-\frac{49}{10} = -4\frac{9}{10} = -4.9$$