Basic Math Examples

$\frac{7}{3} \cdot \sqrt[3]{2} - 2 \sqrt[3]{2} - \frac{5}{4} \cdot \sqrt[3]{2}$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{7}{3}$ and $\sqrt[3]{2}$ .

$\frac{7 \sqrt[3]{2}}{3} - 2 \sqrt[3]{2} - \frac{5}{4} \cdot \sqrt[3]{2}$

Step 1.2

Combine $\sqrt[3]{2}$ and $\frac{5}{4}$ .

$\frac{7 \sqrt[3]{2}}{3} - 2 \sqrt[3]{2} - \frac{\sqrt[3]{2} \cdot 5}{4}$

Step 1.3

Move $5$ to the left of $\sqrt[3]{2}$ .

$\frac{7 \sqrt[3]{2}}{3} - 2 \sqrt[3]{2} - \frac{5 \sqrt[3]{2}}{4}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{7 \sqrt[3]{2}}{3}$ by $\frac{4}{4}$ .

$\frac{7 \sqrt[3]{2}}{3} \cdot \frac{4}{4} - 2 \sqrt[3]{2} - \frac{5 \sqrt[3]{2}}{4}$

Step 2.2

Multiply $\frac{7 \sqrt[3]{2}}{3}$ by $\frac{4}{4}$ .

$\frac{7 \sqrt[3]{2} \cdot 4}{3 \cdot 4} - 2 \sqrt[3]{2} - \frac{5 \sqrt[3]{2}}{4}$

Step 2.3

Write $- 2 \sqrt[3]{2}$ as a fraction with denominator $1$ .

$\frac{7 \sqrt[3]{2} \cdot 4}{3 \cdot 4} + \frac{- 2 \sqrt[3]{2}}{1} - \frac{5 \sqrt[3]{2}}{4}$

Step 2.4

Multiply $\frac{- 2 \sqrt[3]{2}}{1}$ by $\frac{12}{12}$ .

$\frac{7 \sqrt[3]{2} \cdot 4}{3 \cdot 4} + \frac{- 2 \sqrt[3]{2}}{1} \cdot \frac{12}{12} - \frac{5 \sqrt[3]{2}}{4}$

Step 2.5

Multiply $\frac{- 2 \sqrt[3]{2}}{1}$ by $\frac{12}{12}$ .

$\frac{7 \sqrt[3]{2} \cdot 4}{3 \cdot 4} + \frac{- 2 \sqrt[3]{2} \cdot 12}{12} - \frac{5 \sqrt[3]{2}}{4}$

Step 2.6

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

$\frac{7 \sqrt[3]{2} \cdot 4}{3 \cdot 4} + \frac{- 2 \sqrt[3]{2} \cdot 12}{12} - (\frac{5 \sqrt[3]{2}}{4} \cdot \frac{3}{3})$

Step 2.7

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

$\frac{7 \sqrt[3]{2} \cdot 4}{3 \cdot 4} + \frac{- 2 \sqrt[3]{2} \cdot 12}{12} - \frac{5 \sqrt[3]{2} \cdot 3}{4 \cdot 3}$

Step 2.8

Multiply $3$ by $4$ .

$\frac{7 \sqrt[3]{2} \cdot 4}{12} + \frac{- 2 \sqrt[3]{2} \cdot 12}{12} - \frac{5 \sqrt[3]{2} \cdot 3}{4 \cdot 3}$

Step 2.9

Reorder the factors of $4 \cdot 3$ .

$\frac{7 \sqrt[3]{2} \cdot 4}{12} + \frac{- 2 \sqrt[3]{2} \cdot 12}{12} - \frac{5 \sqrt[3]{2} \cdot 3}{3 \cdot 4}$

Step 2.10

Multiply $3$ by $4$ .

$\frac{7 \sqrt[3]{2} \cdot 4}{12} + \frac{- 2 \sqrt[3]{2} \cdot 12}{12} - \frac{5 \sqrt[3]{2} \cdot 3}{12}$

Step 3

Combine the numerators over the common denominator.

$\frac{7 \sqrt[3]{2} \cdot 4 - 2 \sqrt[3]{2} \cdot 12 - 5 \sqrt[3]{2} \cdot 3}{12}$

Step 4

Simplify each term.

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Step 4.1

Multiply $4$ by $7$ .

$\frac{28 \sqrt[3]{2} - 2 \sqrt[3]{2} \cdot 12 - 5 \sqrt[3]{2} \cdot 3}{12}$

Step 4.2

Multiply $12$ by $- 2$ .

$\frac{28 \sqrt[3]{2} - 24 \sqrt[3]{2} - 5 \sqrt[3]{2} \cdot 3}{12}$

Step 4.3

Multiply $3$ by $- 5$ .

$\frac{28 \sqrt[3]{2} - 24 \sqrt[3]{2} - 15 \sqrt[3]{2}}{12}$

Step 5

Simplify by adding terms.

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Step 5.1

Subtract $24 \sqrt[3]{2}$ from $28 \sqrt[3]{2}$ .

$\frac{4 \sqrt[3]{2} - 15 \sqrt[3]{2}}{12}$

Step 5.2

Subtract $15 \sqrt[3]{2}$ from $4 \sqrt[3]{2}$ .

$\frac{- 11 \sqrt[3]{2}}{12}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{11 \sqrt[3]{2}}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{11 \sqrt[3]{2}}{12}$

Decimal Form:

$- 1.15492762 \dots$