Solve 4mn/9+7-2mn/5-12

$$\frac { 4 m n } { 9 } + 7 - \frac { 2 m n } { 5 } - 12$$

Evaluate

$$\frac{2mn}{45}-5$$

Short Solution Steps

Subtract 12 from 7 to get -5.

$$\frac{4mn}{9}-5-\frac{2mn}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{9}{9}.

$$\frac{4mn}{9}-\frac{5\times 9}{9}-\frac{2mn}{5}$$

Since \frac{4mn}{9} and \frac{5\times 9}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4mn-5\times 9}{9}-\frac{2mn}{5}$$

Do the multiplications in 4mn-5\times 9.

$$\frac{4mn-45}{9}-\frac{2mn}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 5 is 45. Multiply \frac{4mn-45}{9} times \frac{5}{5}. Multiply \frac{2mn}{5} times \frac{9}{9}.

$$\frac{5\left(4mn-45\right)}{45}-\frac{9\times 2mn}{45}$$

Since \frac{5\left(4mn-45\right)}{45} and \frac{9\times 2mn}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(4mn-45\right)-9\times 2mn}{45}$$

Do the multiplications in 5\left(4mn-45\right)-9\times 2mn.

$$\frac{20mn-225-18mn}{45}$$

Combine like terms in 20mn-225-18mn.

$$\frac{2mn-225}{45}$$

Factor

$$\frac{2mn-225}{45}$$

Solution Steps

Factor out \frac{1}{45}.

$$\frac{2mn-225}{45}$$