Pre-Algebra Examples

$(4 \frac{7}{8} x^{2} - 6 \frac{3}{5} x) + (4 \frac{4}{5} x - 2 \frac{3}{8} x^{2})$

Step 1

Remove parentheses.

$4 \frac{7}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2

Convert

$4 \frac{7}{8}$ to an improper fraction.

Tap for more steps...

Step 2.1

A mixed number is an addition of its whole and fractional parts.

$(4 + \frac{7}{8}) x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2

Add

$4$ and

$\frac{7}{8}$ .

Tap for more steps...

Step 2.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$(4 \cdot \frac{8}{8} + \frac{7}{8}) x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.2

Combine

$4$ and

$\frac{8}{8}$ .

$(\frac{4 \cdot 8}{8} + \frac{7}{8}) x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 + 7}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply

$4$ by

$8$ .

$\frac{32 + 7}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 2.2.4.2

Add

$32$ and

$7$ .

$\frac{39}{8} x^{2} - 6 \frac{3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3

Convert

$6 \frac{3}{5}$ to an improper fraction.

Tap for more steps...

Step 3.1

A mixed number is an addition of its whole and fractional parts.

$\frac{39}{8} x^{2} - (6 + \frac{3}{5}) x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2

Add

$6$ and

$\frac{3}{5}$ .

Tap for more steps...

Step 3.2.1

To write

$6$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{39}{8} x^{2} - (6 \cdot \frac{5}{5} + \frac{3}{5}) x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.2

Combine

$6$ and

$\frac{5}{5}$ .

$\frac{39}{8} x^{2} - (\frac{6 \cdot 5}{5} + \frac{3}{5}) x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} x^{2} - \frac{6 \cdot 5 + 3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply

$6$ by

$5$ .

$\frac{39}{8} x^{2} - \frac{30 + 3}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 3.2.4.2

Add

$30$ and

$3$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + 4 \frac{4}{5} x - 2 \frac{3}{8} x^{2}$

Step 4

Convert

$4 \frac{4}{5}$ to an improper fraction.

Tap for more steps...

Step 4.1

A mixed number is an addition of its whole and fractional parts.

$\frac{39}{8} x^{2} - \frac{33}{5} x + (4 + \frac{4}{5}) x - 2 \frac{3}{8} x^{2}$

Step 4.2

Add

$4$ and

$\frac{4}{5}$ .

Tap for more steps...

Step 4.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + (4 \cdot \frac{5}{5} + \frac{4}{5}) x - 2 \frac{3}{8} x^{2}$

Step 4.2.2

Combine

$4$ and

$\frac{5}{5}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + (\frac{4 \cdot 5}{5} + \frac{4}{5}) x - 2 \frac{3}{8} x^{2}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{4 \cdot 5 + 4}{5} x - 2 \frac{3}{8} x^{2}$

Step 4.2.4

Simplify the numerator.

Tap for more steps...

Step 4.2.4.1

Multiply

$4$ by

$5$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{20 + 4}{5} x - 2 \frac{3}{8} x^{2}$

Step 4.2.4.2

Add

$20$ and

$4$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - 2 \frac{3}{8} x^{2}$

Step 5

Convert

$2 \frac{3}{8}$ to an improper fraction.

Tap for more steps...

Step 5.1

A mixed number is an addition of its whole and fractional parts.

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - (2 + \frac{3}{8}) x^{2}$

Step 5.2

Add

$2$ and

$\frac{3}{8}$ .

Tap for more steps...

Step 5.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - (2 \cdot \frac{8}{8} + \frac{3}{8}) x^{2}$

Step 5.2.2

Combine

$2$ and

$\frac{8}{8}$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - (\frac{2 \cdot 8}{8} + \frac{3}{8}) x^{2}$

Step 5.2.3

Combine the numerators over the common denominator.

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - \frac{2 \cdot 8 + 3}{8} x^{2}$

Step 5.2.4

Simplify the numerator.

Tap for more steps...

Step 5.2.4.1

Multiply

$2$ by

$8$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - \frac{16 + 3}{8} x^{2}$

Step 5.2.4.2

Add

$16$ and

$3$ .

$\frac{39}{8} x^{2} - \frac{33}{5} x + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6

Simplify each term.

Tap for more steps...

Step 6.1

Combine

$\frac{39}{8}$ and

$x^{2}$ .

$\frac{39 x^{2}}{8} - \frac{33}{5} x + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6.2

Combine

$x$ and

$\frac{33}{5}$ .

$\frac{39 x^{2}}{8} - \frac{x \cdot 33}{5} + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6.3

Move

$33$ to the left of

$x$ .

$\frac{39 x^{2}}{8} - \frac{33 \cdot x}{5} + \frac{24}{5} x - \frac{19}{8} x^{2}$

Step 6.4

Combine

$\frac{24}{5}$ and

$x$ .

$\frac{39 x^{2}}{8} - \frac{33 x}{5} + \frac{24 x}{5} - \frac{19}{8} x^{2}$

Step 6.5

Combine

$x^{2}$ and

$\frac{19}{8}$ .

$\frac{39 x^{2}}{8} - \frac{33 x}{5} + \frac{24 x}{5} - \frac{x^{2} \cdot 19}{8}$

Step 6.6

Move

$19$ to the left of

$x^{2}$ .

$\frac{39 x^{2}}{8} - \frac{33 x}{5} + \frac{24 x}{5} - \frac{19 x^{2}}{8}$

Step 7

Simplify terms.

Tap for more steps...

Step 7.1

Combine the numerators over the common denominator.

$\frac{39 x^{2} - 19 x^{2}}{8} + \frac{- 33 x + 24 x}{5}$

Step 7.2

Subtract

$19 x^{2}$ from

$39 x^{2}$ .

$\frac{20 x^{2}}{8} + \frac{- 33 x + 24 x}{5}$

Step 7.3

Add

$- 33 x$ and

$24 x$ .

$\frac{20 x^{2}}{8} + \frac{- 9 x}{5}$

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

Cancel the common factor of

$20$ and

$8$ .

Tap for more steps...

Step 8.1.1

Factor

$4$ out of

$20 x^{2}$ .

$\frac{4 (5 x^{2})}{8} + \frac{- 9 x}{5}$

Step 8.1.2

Cancel the common factors.

Tap for more steps...

Step 8.1.2.1

Factor

$4$ out of

$8$ .

$\frac{4 (5 x^{2})}{4 (2)} + \frac{- 9 x}{5}$

Step 8.1.2.2

Cancel the common factor.

$\frac{4 (5 x^{2})}{4 \cdot 2} + \frac{- 9 x}{5}$

Step 8.1.2.3

Rewrite the expression.

$\frac{5 x^{2}}{2} + \frac{- 9 x}{5}$

Step 8.2

Move the negative in front of the fraction.

$\frac{5 x^{2}}{2} - \frac{9 x}{5}$