Basic Math Examples

$(2 \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$(2 + \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 1.2

Add $2$ and $\frac{1}{3}$ .

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Step 1.2.1

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

$(2 \cdot \frac{3}{3} + \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 1.2.2

Combine $2$ and $\frac{3}{3}$ .

$(\frac{2 \cdot 3}{3} + \frac{1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{2 \cdot 3 + 1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $3$ .

$(\frac{6 + 1}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 1.2.4.2

Add $6$ and $1$ .

$(\frac{7}{3} + 2 \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 2

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

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Step 2.1

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

$(\frac{7}{3} + 2 + \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 2.2

Add $2$ and $\frac{2}{3}$ .

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Step 2.2.1

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

$(\frac{7}{3} + 2 \cdot \frac{3}{3} + \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 2.2.2

Combine $2$ and $\frac{3}{3}$ .

$(\frac{7}{3} + \frac{2 \cdot 3}{3} + \frac{2}{3}) \cdot (198 \sqrt{18})$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{7}{3} + \frac{2 \cdot 3 + 2}{3}) \cdot (198 \sqrt{18})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $3$ .

$(\frac{7}{3} + \frac{6 + 2}{3}) \cdot (198 \sqrt{18})$

Step 2.2.4.2

Add $6$ and $2$ .

$(\frac{7}{3} + \frac{8}{3}) \cdot (198 \sqrt{18})$

Step 3

Combine the numerators over the common denominator.

$\frac{7 + 8}{3} \cdot (198 \sqrt{18})$

Step 4

Add $7$ and $8$ .

$\frac{15}{3} \cdot (198 \sqrt{18})$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $198 \sqrt{18}$ .

$\frac{15}{3} \cdot (3 (66 \sqrt{18}))$

Step 5.2

Cancel the common factor.

$\frac{15}{3} \cdot (3 (66 \sqrt{18}))$

Step 5.3

Rewrite the expression.

$15 \cdot (66 \sqrt{18})$

Step 6

Multiply $66$ by $15$ .

$990 \cdot \sqrt{18}$

Step 7

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 7.1

Factor $9$ out of $18$ .

$990 \cdot \sqrt{9 (2)}$

Step 7.2

Rewrite $9$ as $3^{2}$ .

$990 \cdot \sqrt{3^{2} \cdot 2}$

Step 8

Pull terms out from under the radical.

$990 \cdot (3 \sqrt{2})$

Step 9

Multiply $3$ by $990$ .

$2970 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$2970 \sqrt{2}$

Decimal Form:

$4200.21428024 \dots$