Solve left(5a-12right)5/6-2/3

$$\left( 5a-12 \right) \frac{ 5 }{ 6 } - \frac{ 2 }{ 3 }$$

Evaluate

$$\frac{25a}{6}-\frac{32}{3}$$

Solution Steps

Use the distributive property to multiply 5a-12 by \frac{5}{6}.

$$5a\times \frac{5}{6}-12\times \frac{5}{6}-\frac{2}{3}$$

Express 5\times \frac{5}{6} as a single fraction.

$$\frac{5\times 5}{6}a-12\times \frac{5}{6}-\frac{2}{3}$$

Multiply 5 and 5 to get 25.

$$\frac{25}{6}a-12\times \frac{5}{6}-\frac{2}{3}$$

Express -12\times \frac{5}{6} as a single fraction.

$$\frac{25}{6}a+\frac{-12\times 5}{6}-\frac{2}{3}$$

Multiply -12 and 5 to get -60.

$$\frac{25}{6}a+\frac{-60}{6}-\frac{2}{3}$$

Divide -60 by 6 to get -10.

$$\frac{25}{6}a-10-\frac{2}{3}$$

Convert -10 to fraction -\frac{30}{3}.

$$\frac{25}{6}a-\frac{30}{3}-\frac{2}{3}$$

Since -\frac{30}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{6}a+\frac{-30-2}{3}$$

Subtract 2 from -30 to get -32.

$$\frac{25}{6}a-\frac{32}{3}$$

Expand

$$\frac{25a}{6}-\frac{32}{3}$$

Solution Steps

Use the distributive property to multiply 5a-12 by \frac{5}{6}.

$$5a\times \frac{5}{6}-12\times \frac{5}{6}-\frac{2}{3}$$

Express 5\times \frac{5}{6} as a single fraction.

$$\frac{5\times 5}{6}a-12\times \frac{5}{6}-\frac{2}{3}$$

Multiply 5 and 5 to get 25.

$$\frac{25}{6}a-12\times \frac{5}{6}-\frac{2}{3}$$

Express -12\times \frac{5}{6} as a single fraction.

$$\frac{25}{6}a+\frac{-12\times 5}{6}-\frac{2}{3}$$

Multiply -12 and 5 to get -60.

$$\frac{25}{6}a+\frac{-60}{6}-\frac{2}{3}$$

Divide -60 by 6 to get -10.

$$\frac{25}{6}a-10-\frac{2}{3}$$

Convert -10 to fraction -\frac{30}{3}.

$$\frac{25}{6}a-\frac{30}{3}-\frac{2}{3}$$

Since -\frac{30}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25}{6}a+\frac{-30-2}{3}$$

Subtract 2 from -30 to get -32.

$$\frac{25}{6}a-\frac{32}{3}$$