Basic Math Examples

$\frac{5}{4} w^{2} + \frac{8}{7} w^{5} + \frac{3}{2} w^{5} - \frac{9}{8} w^{2}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{5}{4}$ and $w^{2}$ .

$\frac{5 w^{2}}{4} + \frac{8}{7} w^{5} + \frac{3}{2} w^{5} - \frac{9}{8} w^{2}$

Step 1.2

Combine $\frac{8}{7}$ and $w^{5}$ .

$\frac{5 w^{2}}{4} + \frac{8 w^{5}}{7} + \frac{3}{2} w^{5} - \frac{9}{8} w^{2}$

Step 1.3

Combine $\frac{3}{2}$ and $w^{5}$ .

$\frac{5 w^{2}}{4} + \frac{8 w^{5}}{7} + \frac{3 w^{5}}{2} - \frac{9}{8} w^{2}$

Step 1.4

Combine $w^{2}$ and $\frac{9}{8}$ .

$\frac{5 w^{2}}{4} + \frac{8 w^{5}}{7} + \frac{3 w^{5}}{2} - \frac{w^{2} \cdot 9}{8}$

Step 1.5

Move $9$ to the left of $w^{2}$ .

$\frac{5 w^{2}}{4} + \frac{8 w^{5}}{7} + \frac{3 w^{5}}{2} - \frac{9 w^{2}}{8}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{5 w^{2}}{4}$ by $\frac{14}{14}$ .

$\frac{5 w^{2}}{4} \cdot \frac{14}{14} + \frac{8 w^{5}}{7} + \frac{3 w^{5}}{2} - \frac{9 w^{2}}{8}$

Step 2.2

Multiply $\frac{5 w^{2}}{4}$ by $\frac{14}{14}$ .

$\frac{5 w^{2} \cdot 14}{4 \cdot 14} + \frac{8 w^{5}}{7} + \frac{3 w^{5}}{2} - \frac{9 w^{2}}{8}$

Step 2.3

Multiply $\frac{8 w^{5}}{7}$ by $\frac{8}{8}$ .

$\frac{5 w^{2} \cdot 14}{4 \cdot 14} + \frac{8 w^{5}}{7} \cdot \frac{8}{8} + \frac{3 w^{5}}{2} - \frac{9 w^{2}}{8}$

Step 2.4

Multiply $\frac{8 w^{5}}{7}$ by $\frac{8}{8}$ .

$\frac{5 w^{2} \cdot 14}{4 \cdot 14} + \frac{8 w^{5} \cdot 8}{7 \cdot 8} + \frac{3 w^{5}}{2} - \frac{9 w^{2}}{8}$

Step 2.5

Multiply $\frac{3 w^{5}}{2}$ by $\frac{28}{28}$ .

$\frac{5 w^{2} \cdot 14}{4 \cdot 14} + \frac{8 w^{5} \cdot 8}{7 \cdot 8} + \frac{3 w^{5}}{2} \cdot \frac{28}{28} - \frac{9 w^{2}}{8}$

Step 2.6

Multiply $\frac{3 w^{5}}{2}$ by $\frac{28}{28}$ .

$\frac{5 w^{2} \cdot 14}{4 \cdot 14} + \frac{8 w^{5} \cdot 8}{7 \cdot 8} + \frac{3 w^{5} \cdot 28}{2 \cdot 28} - \frac{9 w^{2}}{8}$

Step 2.7

Multiply $\frac{9 w^{2}}{8}$ by $\frac{7}{7}$ .

$\frac{5 w^{2} \cdot 14}{4 \cdot 14} + \frac{8 w^{5} \cdot 8}{7 \cdot 8} + \frac{3 w^{5} \cdot 28}{2 \cdot 28} - (\frac{9 w^{2}}{8} \cdot \frac{7}{7})$

Step 2.8

Multiply $\frac{9 w^{2}}{8}$ by $\frac{7}{7}$ .

$\frac{5 w^{2} \cdot 14}{4 \cdot 14} + \frac{8 w^{5} \cdot 8}{7 \cdot 8} + \frac{3 w^{5} \cdot 28}{2 \cdot 28} - \frac{9 w^{2} \cdot 7}{8 \cdot 7}$

Step 2.9

Multiply $4$ by $14$ .

$\frac{5 w^{2} \cdot 14}{56} + \frac{8 w^{5} \cdot 8}{7 \cdot 8} + \frac{3 w^{5} \cdot 28}{2 \cdot 28} - \frac{9 w^{2} \cdot 7}{8 \cdot 7}$

Step 2.10

Multiply $7$ by $8$ .

$\frac{5 w^{2} \cdot 14}{56} + \frac{8 w^{5} \cdot 8}{56} + \frac{3 w^{5} \cdot 28}{2 \cdot 28} - \frac{9 w^{2} \cdot 7}{8 \cdot 7}$

Step 2.11

Multiply $2$ by $28$ .

$\frac{5 w^{2} \cdot 14}{56} + \frac{8 w^{5} \cdot 8}{56} + \frac{3 w^{5} \cdot 28}{56} - \frac{9 w^{2} \cdot 7}{8 \cdot 7}$

Step 2.12

Reorder the factors of $8 \cdot 7$ .

$\frac{5 w^{2} \cdot 14}{56} + \frac{8 w^{5} \cdot 8}{56} + \frac{3 w^{5} \cdot 28}{56} - \frac{9 w^{2} \cdot 7}{7 \cdot 8}$

Step 2.13

Multiply $7$ by $8$ .

$\frac{5 w^{2} \cdot 14}{56} + \frac{8 w^{5} \cdot 8}{56} + \frac{3 w^{5} \cdot 28}{56} - \frac{9 w^{2} \cdot 7}{56}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 w^{2} \cdot 14 + 8 w^{5} \cdot 8 + 3 w^{5} \cdot 28 - 9 w^{2} \cdot 7}{56}$

Step 4

Simplify each term.

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Step 4.1

Multiply $14$ by $5$ .

$\frac{70 w^{2} + 8 w^{5} \cdot 8 + 3 w^{5} \cdot 28 - 9 w^{2} \cdot 7}{56}$

Step 4.2

Multiply $8$ by $8$ .

$\frac{70 w^{2} + 64 w^{5} + 3 w^{5} \cdot 28 - 9 w^{2} \cdot 7}{56}$

Step 4.3

Multiply $28$ by $3$ .

$\frac{70 w^{2} + 64 w^{5} + 84 w^{5} - 9 w^{2} \cdot 7}{56}$

Step 4.4

Multiply $7$ by $- 9$ .

$\frac{70 w^{2} + 64 w^{5} + 84 w^{5} - 63 w^{2}}{56}$

Step 5

Simplify terms.

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Step 5.1

Subtract $63 w^{2}$ from $70 w^{2}$ .

$\frac{64 w^{5} + 84 w^{5} + 7 w^{2}}{56}$

Step 5.2

Add $64 w^{5}$ and $84 w^{5}$ .

$\frac{148 w^{5} + 7 w^{2}}{56}$

Step 5.3

Factor $w^{2}$ out of $148 w^{5} + 7 w^{2}$ .

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Step 5.3.1

Factor $w^{2}$ out of $148 w^{5}$ .

$\frac{w^{2} (148 w^{3}) + 7 w^{2}}{56}$

Step 5.3.2

Factor $w^{2}$ out of $7 w^{2}$ .

$\frac{w^{2} (148 w^{3}) + w^{2} \cdot 7}{56}$

Step 5.3.3

Factor $w^{2}$ out of $w^{2} (148 w^{3}) + w^{2} \cdot 7$ .

$\frac{w^{2} (148 w^{3} + 7)}{56}$