Solve 3t/5-2/3-1/2

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

Evaluate

$$\frac{3t}{5}-\frac{7}{6}$$

Short Solution Steps

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{3t}{5}-\frac{4}{6}-\frac{3}{6}$$

Since -\frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3t}{5}+\frac{-4-3}{6}$$

Subtract 3 from -4 to get -7.

$$\frac{3t}{5}-\frac{7}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 6 is 30. Multiply \frac{3t}{5} times \frac{6}{6}. Multiply \frac{7}{6} times \frac{5}{5}.

$$\frac{6\times 3t}{30}-\frac{7\times 5}{30}$$

Since \frac{6\times 3t}{30} and \frac{7\times 5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\times 3t-7\times 5}{30}$$

Do the multiplications in 6\times 3t-7\times 5.

$$\frac{18t-35}{30}$$

Factor

$$\frac{18t-35}{30}$$

Solution Steps

Factor out \frac{1}{30}.

$$\frac{18t-35}{30}$$

Consider 18t-20-15. Multiply and combine like terms.

$$18t-35$$

Rewrite the complete factored expression.

$$\frac{18t-35}{30}$$