Solve 34/5:19-3/n:2=

$$3 \frac { 4 } { 5 } : 19 - \frac { 3 } { n } : 2 =$$

Evaluate

$$\frac{1}{5}-\frac{3}{2n}$$

Short Solution Steps

Express \frac{\frac{3\times 5+4}{5}}{19} as a single fraction.

$$\frac{3\times 5+4}{5\times 19}-\frac{\frac{3}{n}}{2}$$

Multiply 3 and 5 to get 15.

$$\frac{15+4}{5\times 19}-\frac{\frac{3}{n}}{2}$$

Add 15 and 4 to get 19.

$$\frac{19}{5\times 19}-\frac{\frac{3}{n}}{2}$$

Multiply 5 and 19 to get 95.

$$\frac{19}{95}-\frac{\frac{3}{n}}{2}$$

Reduce the fraction \frac{19}{95} to lowest terms by extracting and canceling out 19.

$$\frac{1}{5}-\frac{\frac{3}{n}}{2}$$

Express \frac{\frac{3}{n}}{2} as a single fraction.

$$\frac{1}{5}-\frac{3}{n\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and n\times 2 is 10n. Multiply \frac{1}{5} times \frac{2n}{2n}. Multiply \frac{3}{n\times 2} times \frac{5}{5}.

$$\frac{2n}{10n}-\frac{3\times 5}{10n}$$

Since \frac{2n}{10n} and \frac{3\times 5}{10n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2n-3\times 5}{10n}$$

Do the multiplications in 2n-3\times 5.

$$\frac{2n-15}{10n}$$

Expand

$$\frac{1}{5}-\frac{3}{2n}$$

Short Solution Steps

Express \frac{\frac{3\times 5+4}{5}}{19} as a single fraction.

$$\frac{3\times 5+4}{5\times 19}-\frac{\frac{3}{n}}{2}$$

Multiply 3 and 5 to get 15.

$$\frac{15+4}{5\times 19}-\frac{\frac{3}{n}}{2}$$

Add 15 and 4 to get 19.

$$\frac{19}{5\times 19}-\frac{\frac{3}{n}}{2}$$

Multiply 5 and 19 to get 95.

$$\frac{19}{95}-\frac{\frac{3}{n}}{2}$$

Reduce the fraction \frac{19}{95} to lowest terms by extracting and canceling out 19.

$$\frac{1}{5}-\frac{\frac{3}{n}}{2}$$

Express \frac{\frac{3}{n}}{2} as a single fraction.

$$\frac{1}{5}-\frac{3}{n\times 2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and n\times 2 is 10n. Multiply \frac{1}{5} times \frac{2n}{2n}. Multiply \frac{3}{n\times 2} times \frac{5}{5}.

$$\frac{2n}{10n}-\frac{3\times 5}{10n}$$

Since \frac{2n}{10n} and \frac{3\times 5}{10n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2n-3\times 5}{10n}$$

Do the multiplications in 2n-3\times 5.

$$\frac{2n-15}{10n}$$