Algebra Examples

$- \frac{5}{3} (- \frac{7}{4} a - \frac{1}{4}) - 8 a$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Combine $a$ and $\frac{7}{4}$ .

$- \frac{5}{3} \cdot (- \frac{a \cdot 7}{4} - \frac{1}{4}) - 8 a$

Step 1.1.2

Move $7$ to the left of $a$ .

$- \frac{5}{3} \cdot (- \frac{7 a}{4} - \frac{1}{4}) - 8 a$

Step 1.2

Apply the distributive property.

$- \frac{5}{3} (- \frac{7 a}{4}) - \frac{5}{3} (- \frac{1}{4}) - 8 a$

Step 1.3

Multiply $- \frac{5}{3} (- \frac{7 a}{4})$ .

Tap for more steps...

Step 1.3.1

Multiply $- 1$ by $- 1$ .

$1 (\frac{5}{3}) \frac{7 a}{4} - \frac{5}{3} (- \frac{1}{4}) - 8 a$

Step 1.3.2

Multiply $\frac{5}{3}$ by $1$ .

$\frac{5}{3} \cdot \frac{7 a}{4} - \frac{5}{3} (- \frac{1}{4}) - 8 a$

Step 1.3.3

Multiply $\frac{5}{3}$ by $\frac{7 a}{4}$ .

$\frac{5 (7 a)}{3 \cdot 4} - \frac{5}{3} (- \frac{1}{4}) - 8 a$

Step 1.3.4

Multiply $7$ by $5$ .

$\frac{35 a}{3 \cdot 4} - \frac{5}{3} (- \frac{1}{4}) - 8 a$

Step 1.3.5

Multiply $3$ by $4$ .

$\frac{35 a}{12} - \frac{5}{3} (- \frac{1}{4}) - 8 a$

Step 1.4

Multiply $- \frac{5}{3} (- \frac{1}{4})$ .

Tap for more steps...

Step 1.4.1

Multiply $- 1$ by $- 1$ .

$\frac{35 a}{12} + 1 (\frac{5}{3}) \frac{1}{4} - 8 a$

Step 1.4.2

Multiply $\frac{5}{3}$ by $1$ .

$\frac{35 a}{12} + \frac{5}{3} \cdot \frac{1}{4} - 8 a$

Step 1.4.3

Multiply $\frac{5}{3}$ by $\frac{1}{4}$ .

$\frac{35 a}{12} + \frac{5}{3 \cdot 4} - 8 a$

Step 1.4.4

Multiply $3$ by $4$ .

$\frac{35 a}{12} + \frac{5}{12} - 8 a$

Step 2

To write $- 8 a$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$\frac{35 a}{12} - 8 a \cdot \frac{12}{12} + \frac{5}{12}$

Step 3

Combine $- 8 a$ and $\frac{12}{12}$ .

$\frac{35 a}{12} + \frac{- 8 a \cdot 12}{12} + \frac{5}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{35 a - 8 a \cdot 12}{12} + \frac{5}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{35 a - 8 a \cdot 12 + 5}{12}$

Step 6

Multiply $12$ by $- 8$ .

$\frac{35 a - 96 a + 5}{12}$

Step 7

Subtract $96 a$ from $35 a$ .

$\frac{- 61 a + 5}{12}$

Step 8

Factor $- 1$ out of $- 61 a$ .

$\frac{- (61 a) + 5}{12}$

Step 9

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{- (61 a) - 1 (- 5)}{12}$

Step 10

Factor $- 1$ out of $- (61 a) - 1 (- 5)$ .

$\frac{- (61 a - 5)}{12}$

Step 11

Simplify the expression.

Tap for more steps...

Step 11.1

Rewrite $- (61 a - 5)$ as $- 1 (61 a - 5)$ .

$\frac{- 1 (61 a - 5)}{12}$

Step 11.2

Move the negative in front of the fraction.

$- \frac{61 a - 5}{12}$