Basic Math Examples

$\frac{2}{3} \cdot \frac{7}{9} - \frac{\sqrt{5}}{3} \cdot (- \frac{4 \sqrt{2}}{9})$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{2}{3} \cdot \frac{7}{9}$ .

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Step 1.1.1

Multiply $\frac{2}{3}$ by $\frac{7}{9}$ .

$\frac{2 \cdot 7}{3 \cdot 9} - \frac{\sqrt{5}}{3} \cdot (- \frac{4 \sqrt{2}}{9})$

Step 1.1.2

Multiply $2$ by $7$ .

$\frac{14}{3 \cdot 9} - \frac{\sqrt{5}}{3} \cdot (- \frac{4 \sqrt{2}}{9})$

Step 1.1.3

Multiply $3$ by $9$ .

$\frac{14}{27} - \frac{\sqrt{5}}{3} \cdot (- \frac{4 \sqrt{2}}{9})$

Step 1.2

Multiply $- \frac{\sqrt{5}}{3} (- \frac{4 \sqrt{2}}{9})$ .

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Step 1.2.1

Multiply $- 1$ by $- 1$ .

$\frac{14}{27} + 1 \frac{\sqrt{5}}{3} \frac{4 \sqrt{2}}{9}$

Step 1.2.2

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

$\frac{14}{27} + \frac{\sqrt{5}}{3} \cdot \frac{4 \sqrt{2}}{9}$

Step 1.2.3

Multiply $\frac{\sqrt{5}}{3}$ by $\frac{4 \sqrt{2}}{9}$ .

$\frac{14}{27} + \frac{\sqrt{5} (4 \sqrt{2})}{3 \cdot 9}$

Step 1.2.4

Combine using the product rule for radicals.

$\frac{14}{27} + \frac{4 \sqrt{5 \cdot 2}}{3 \cdot 9}$

Step 1.2.5

Multiply $5$ by $2$ .

$\frac{14}{27} + \frac{4 \sqrt{10}}{3 \cdot 9}$

Step 1.2.6

Multiply $3$ by $9$ .

$\frac{14}{27} + \frac{4 \sqrt{10}}{27}$

Step 2

Combine the numerators over the common denominator.

$\frac{14 + 4 \sqrt{10}}{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{14 + 4 \sqrt{10}}{27}$

Decimal Form:

$0.98700409 \dots$