Solve z/3-(1/4+1/5)

$$\frac { z } { 3 } - ( \frac { 1 } { 4 } + \frac { 1 } { 5 } )$$

Evaluate

$$\frac{z}{3}-\frac{9}{20}$$

Short Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{z}{3}-\left(\frac{5}{20}+\frac{4}{20}\right)$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{z}{3}-\frac{5+4}{20}$$

Add 5 and 4 to get 9.

$$\frac{z}{3}-\frac{9}{20}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 20 is 60. Multiply \frac{z}{3} times \frac{20}{20}. Multiply \frac{9}{20} times \frac{3}{3}.

$$\frac{20z}{60}-\frac{9\times 3}{60}$$

Since \frac{20z}{60} and \frac{9\times 3}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20z-9\times 3}{60}$$

Do the multiplications in 20z-9\times 3.

$$\frac{20z-27}{60}$$

Expand

$$\frac{z}{3}-\frac{9}{20}$$

Short Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{z}{3}-\left(\frac{5}{20}+\frac{4}{20}\right)$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{z}{3}-\frac{5+4}{20}$$

Add 5 and 4 to get 9.

$$\frac{z}{3}-\frac{9}{20}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 20 is 60. Multiply \frac{z}{3} times \frac{20}{20}. Multiply \frac{9}{20} times \frac{3}{3}.

$$\frac{20z}{60}-\frac{9\times 3}{60}$$

Since \frac{20z}{60} and \frac{9\times 3}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20z-9\times 3}{60}$$

Do the multiplications in 20z-9\times 3.

$$\frac{20z-27}{60}$$