Pre-Algebra Examples

$\frac{4}{3} a^{2} + \frac{2}{5} a - \frac{1}{2} a^{2} - \frac{4}{3} a$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{4}{3}$ and $a^{2}$ .

$\frac{4 a^{2}}{3} + \frac{2}{5} a - \frac{1}{2} a^{2} - \frac{4}{3} a$

Step 1.2

Combine $\frac{2}{5}$ and $a$ .

$\frac{4 a^{2}}{3} + \frac{2 a}{5} - \frac{1}{2} a^{2} - \frac{4}{3} a$

Step 1.3

Combine $a^{2}$ and $\frac{1}{2}$ .

$\frac{4 a^{2}}{3} + \frac{2 a}{5} - \frac{a^{2}}{2} - \frac{4}{3} a$

Step 1.4

Combine $a$ and $\frac{4}{3}$ .

$\frac{4 a^{2}}{3} + \frac{2 a}{5} - \frac{a^{2}}{2} - \frac{a \cdot 4}{3}$

Step 1.5

Move $4$ to the left of $a$ .

$\frac{4 a^{2}}{3} + \frac{2 a}{5} - \frac{a^{2}}{2} - \frac{4 a}{3}$

Step 2

To write $\frac{4 a^{2}}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 a}{5} + \frac{4 a^{2}}{3} \cdot \frac{2}{2} - \frac{a^{2}}{2} - \frac{4 a}{3}$

Step 3

To write $- \frac{a^{2}}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 a}{5} + \frac{4 a^{2}}{3} \cdot \frac{2}{2} - \frac{a^{2}}{2} \cdot \frac{3}{3} - \frac{4 a}{3}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 4.1

Multiply $\frac{4 a^{2}}{3}$ by $\frac{2}{2}$ .

$\frac{2 a}{5} + \frac{4 a^{2} \cdot 2}{3 \cdot 2} - \frac{a^{2}}{2} \cdot \frac{3}{3} - \frac{4 a}{3}$

Step 4.2

Multiply $3$ by $2$ .

$\frac{2 a}{5} + \frac{4 a^{2} \cdot 2}{6} - \frac{a^{2}}{2} \cdot \frac{3}{3} - \frac{4 a}{3}$

Step 4.3

Multiply $\frac{a^{2}}{2}$ by $\frac{3}{3}$ .

$\frac{2 a}{5} + \frac{4 a^{2} \cdot 2}{6} - \frac{a^{2} \cdot 3}{2 \cdot 3} - \frac{4 a}{3}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{2 a}{5} + \frac{4 a^{2} \cdot 2}{6} - \frac{a^{2} \cdot 3}{6} - \frac{4 a}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 a}{5} + \frac{4 a^{2} \cdot 2 - a^{2} \cdot 3}{6} - \frac{4 a}{3}$

Step 6

Find the common denominator.

Tap for more steps...

Step 6.1

Multiply $\frac{2 a}{5}$ by $\frac{6}{6}$ .

$\frac{2 a}{5} \cdot \frac{6}{6} + \frac{4 a^{2} \cdot 2 - a^{2} \cdot 3}{6} - \frac{4 a}{3}$

Step 6.2

Multiply $\frac{2 a}{5}$ by $\frac{6}{6}$ .

$\frac{2 a \cdot 6}{5 \cdot 6} + \frac{4 a^{2} \cdot 2 - a^{2} \cdot 3}{6} - \frac{4 a}{3}$

Step 6.3

Multiply $\frac{4 a^{2} \cdot 2 - a^{2} \cdot 3}{6}$ by $\frac{5}{5}$ .

$\frac{2 a \cdot 6}{5 \cdot 6} + \frac{4 a^{2} \cdot 2 - a^{2} \cdot 3}{6} \cdot \frac{5}{5} - \frac{4 a}{3}$

Step 6.4

Multiply $\frac{4 a^{2} \cdot 2 - a^{2} \cdot 3}{6}$ by $\frac{5}{5}$ .

$\frac{2 a \cdot 6}{5 \cdot 6} + \frac{(4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5}{6 \cdot 5} - \frac{4 a}{3}$

Step 6.5

Multiply $\frac{4 a}{3}$ by $\frac{10}{10}$ .

$\frac{2 a \cdot 6}{5 \cdot 6} + \frac{(4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5}{6 \cdot 5} - (\frac{4 a}{3} \cdot \frac{10}{10})$

Step 6.6

Multiply $\frac{4 a}{3}$ by $\frac{10}{10}$ .

$\frac{2 a \cdot 6}{5 \cdot 6} + \frac{(4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5}{6 \cdot 5} - \frac{4 a \cdot 10}{3 \cdot 10}$

Step 6.7

Multiply $5$ by $6$ .

$\frac{2 a \cdot 6}{30} + \frac{(4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5}{6 \cdot 5} - \frac{4 a \cdot 10}{3 \cdot 10}$

Step 6.8

Reorder the factors of $6 \cdot 5$ .

$\frac{2 a \cdot 6}{30} + \frac{(4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5}{5 \cdot 6} - \frac{4 a \cdot 10}{3 \cdot 10}$

Step 6.9

Multiply $5$ by $6$ .

$\frac{2 a \cdot 6}{30} + \frac{(4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5}{30} - \frac{4 a \cdot 10}{3 \cdot 10}$

Step 6.10

Multiply $3$ by $10$ .

$\frac{2 a \cdot 6}{30} + \frac{(4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5}{30} - \frac{4 a \cdot 10}{30}$

Step 7

Combine the numerators over the common denominator.

$\frac{2 a \cdot 6 + (4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5 - 4 a \cdot 10}{30}$

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

Multiply $6$ by $2$ .

$\frac{12 a + (4 a^{2} \cdot 2 - a^{2} \cdot 3) \cdot 5 - 4 a \cdot 10}{30}$

Step 8.2

Simplify each term.

Tap for more steps...

Step 8.2.1

Multiply $2$ by $4$ .

$\frac{12 a + (8 a^{2} - a^{2} \cdot 3) \cdot 5 - 4 a \cdot 10}{30}$

Step 8.2.2

Multiply $3$ by $- 1$ .

$\frac{12 a + (8 a^{2} - 3 a^{2}) \cdot 5 - 4 a \cdot 10}{30}$

Step 8.3

Subtract $3 a^{2}$ from $8 a^{2}$ .

$\frac{12 a + 5 a^{2} \cdot 5 - 4 a \cdot 10}{30}$

Step 8.4

Multiply $5$ by $5$ .

$\frac{12 a + 25 a^{2} - 4 a \cdot 10}{30}$

Step 8.5

Multiply $10$ by $- 4$ .

$\frac{12 a + 25 a^{2} - 40 a}{30}$

Step 9

Simplify terms.

Tap for more steps...

Step 9.1

Subtract $40 a$ from $12 a$ .

$\frac{25 a^{2} - 28 a}{30}$

Step 9.2

Factor $a$ out of $25 a^{2} - 28 a$ .

Tap for more steps...

Step 9.2.1

Factor $a$ out of $25 a^{2}$ .

$\frac{a (25 a) - 28 a}{30}$

Step 9.2.2

Factor $a$ out of $- 28 a$ .

$\frac{a (25 a) + a \cdot - 28}{30}$

Step 9.2.3

Factor $a$ out of $a (25 a) + a \cdot - 28$ .

$\frac{a (25 a - 28)}{30}$