Solve F4/9-7/5+5/6+1/1

$$F \frac{ 4 }{ 9 } - \frac{ 7 }{ 5 } + \frac{ 5 }{ 6 } + \frac{ 1 }{ 1 }$$

Evaluate

$$\frac{4F}{9}+\frac{13}{30}$$

Solution Steps

Divide 1 by 1 to get 1.

$$F\times \frac{4}{9}-\frac{7}{5}+\frac{5}{6}+1$$

Least common multiple of 5 and 6 is 30. Convert -\frac{7}{5} and \frac{5}{6} to fractions with denominator 30.

$$F\times \frac{4}{9}-\frac{42}{30}+\frac{25}{30}+1$$

Since -\frac{42}{30} and \frac{25}{30} have the same denominator, add them by adding their numerators.

$$F\times \frac{4}{9}+\frac{-42+25}{30}+1$$

Add -42 and 25 to get -17.

$$F\times \frac{4}{9}-\frac{17}{30}+1$$

Convert 1 to fraction \frac{30}{30}.

$$F\times \frac{4}{9}-\frac{17}{30}+\frac{30}{30}$$

Since -\frac{17}{30} and \frac{30}{30} have the same denominator, add them by adding their numerators.

$$F\times \frac{4}{9}+\frac{-17+30}{30}$$

Add -17 and 30 to get 13.

$$F\times \frac{4}{9}+\frac{13}{30}$$

Factor

$$\frac{40F+39}{90}$$

Solution Steps

Factor out \frac{1}{90}.

$$\frac{40F+39}{90}$$

Consider 40F-126+75+90. Multiply and combine like terms.

$$40F+39$$

Rewrite the complete factored expression.

$$\frac{40F+39}{90}$$