Solve 5/8(t-2)-4/5(2t-5)=

$$\frac { 5 } { 8 } ( t - 2 ) - \frac { 4 } { 5 } ( 2 t - 5 ) =$$

Evaluate

$$-\frac{39t}{40}+\frac{11}{4}$$

Solution Steps

Use the distributive property to multiply \frac{5}{8} by t-2.

$$\frac{5}{8}t+\frac{5}{8}\left(-2\right)-\frac{4}{5}\left(2t-5\right)$$

Express \frac{5}{8}\left(-2\right) as a single fraction.

$$\frac{5}{8}t+\frac{5\left(-2\right)}{8}-\frac{4}{5}\left(2t-5\right)$$

Multiply 5 and -2 to get -10.

$$\frac{5}{8}t+\frac{-10}{8}-\frac{4}{5}\left(2t-5\right)$$

Reduce the fraction \frac{-10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{5}{8}t-\frac{5}{4}-\frac{4}{5}\left(2t-5\right)$$

Use the distributive property to multiply -\frac{4}{5} by 2t-5.

$$\frac{5}{8}t-\frac{5}{4}-\frac{4}{5}\times 2t-\frac{4}{5}\left(-5\right)$$

Express -\frac{4}{5}\times 2 as a single fraction.

$$\frac{5}{8}t-\frac{5}{4}+\frac{-4\times 2}{5}t-\frac{4}{5}\left(-5\right)$$

Multiply -4 and 2 to get -8.

$$\frac{5}{8}t-\frac{5}{4}+\frac{-8}{5}t-\frac{4}{5}\left(-5\right)$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t-\frac{4}{5}\left(-5\right)$$

Express -\frac{4}{5}\left(-5\right) as a single fraction.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t+\frac{-4\left(-5\right)}{5}$$

Multiply -4 and -5 to get 20.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t+\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t+4$$

Combine \frac{5}{8}t and -\frac{8}{5}t to get -\frac{39}{40}t.

$$-\frac{39}{40}t-\frac{5}{4}+4$$

Convert 4 to fraction \frac{16}{4}.

$$-\frac{39}{40}t-\frac{5}{4}+\frac{16}{4}$$

Since -\frac{5}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$-\frac{39}{40}t+\frac{-5+16}{4}$$

Add -5 and 16 to get 11.

$$-\frac{39}{40}t+\frac{11}{4}$$

Expand

$$-\frac{39t}{40}+\frac{11}{4}$$

Solution Steps

Use the distributive property to multiply \frac{5}{8} by t-2.

$$\frac{5}{8}t+\frac{5}{8}\left(-2\right)-\frac{4}{5}\left(2t-5\right)$$

Express \frac{5}{8}\left(-2\right) as a single fraction.

$$\frac{5}{8}t+\frac{5\left(-2\right)}{8}-\frac{4}{5}\left(2t-5\right)$$

Multiply 5 and -2 to get -10.

$$\frac{5}{8}t+\frac{-10}{8}-\frac{4}{5}\left(2t-5\right)$$

Reduce the fraction \frac{-10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{5}{8}t-\frac{5}{4}-\frac{4}{5}\left(2t-5\right)$$

Use the distributive property to multiply -\frac{4}{5} by 2t-5.

$$\frac{5}{8}t-\frac{5}{4}-\frac{4}{5}\times 2t-\frac{4}{5}\left(-5\right)$$

Express -\frac{4}{5}\times 2 as a single fraction.

$$\frac{5}{8}t-\frac{5}{4}+\frac{-4\times 2}{5}t-\frac{4}{5}\left(-5\right)$$

Multiply -4 and 2 to get -8.

$$\frac{5}{8}t-\frac{5}{4}+\frac{-8}{5}t-\frac{4}{5}\left(-5\right)$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t-\frac{4}{5}\left(-5\right)$$

Express -\frac{4}{5}\left(-5\right) as a single fraction.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t+\frac{-4\left(-5\right)}{5}$$

Multiply -4 and -5 to get 20.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t+\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$\frac{5}{8}t-\frac{5}{4}-\frac{8}{5}t+4$$

Combine \frac{5}{8}t and -\frac{8}{5}t to get -\frac{39}{40}t.

$$-\frac{39}{40}t-\frac{5}{4}+4$$

Convert 4 to fraction \frac{16}{4}.

$$-\frac{39}{40}t-\frac{5}{4}+\frac{16}{4}$$

Since -\frac{5}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$-\frac{39}{40}t+\frac{-5+16}{4}$$

Add -5 and 16 to get 11.

$$-\frac{39}{40}t+\frac{11}{4}$$