Basic Math Examples

$2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} - (3 - (1 + \frac{4}{5}) \cdot 2) \div 2 + \frac{1}{3}$

Step 1

Find the common denominator.

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Step 1.1

Write $2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}}$ as a fraction with denominator $1$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}}}{1} - (3 - (1 + \frac{4}{5}) \cdot 2) \div 2 + \frac{1}{3}$

Step 1.2

Multiply $\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}}}{1}$ by $\frac{6}{6}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}}}{1} \cdot \frac{6}{6} - (3 - (1 + \frac{4}{5}) \cdot 2) \div 2 + \frac{1}{3}$

Step 1.3

Multiply $\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}}}{1}$ by $\frac{6}{6}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - (3 - (1 + \frac{4}{5}) \cdot 2) \div 2 + \frac{1}{3}$

Step 1.4

Multiply $(3 - (1 + \frac{4}{5}) \cdot 2) \div 2$ by $\frac{3}{3}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - ((3 - (1 + \frac{4}{5}) \cdot 2) \div 2 \cdot \frac{3}{3}) + \frac{1}{3}$

Step 1.5

Multiply $(3 - (1 + \frac{4}{5}) \cdot 2) \div 2$ by $\frac{3}{3}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - \frac{(3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3}{2 \cdot 3} + \frac{1}{3}$

Step 1.6

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - \frac{(3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2}$

Step 1.7

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - \frac{(3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3}{2 \cdot 3} + \frac{2}{3 \cdot 2}$

Step 1.8

Multiply $2$ by $3$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - \frac{(3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3}{6} + \frac{2}{3 \cdot 2}$

Step 1.9

Reorder the factors of $3 \cdot 2$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - \frac{(3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3}{6} + \frac{2}{2 \cdot 3}$

Step 1.10

Multiply $2$ by $3$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6}{6} - \frac{(3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3}{6} + \frac{2}{6}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3

Simplify each term.

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Step 3.1

To write $\frac{4}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4}{3} \cdot \frac{3}{3}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.2

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

Multiply $\frac{4}{3}$ by $\frac{3}{3}$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4 \cdot 3}{3 \cdot 3}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.2.2

Multiply $3$ by $3$ .

$\frac{2 \cdot \sqrt{\frac{13}{9} + \frac{4 \cdot 3}{9}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{2 \cdot \sqrt{\frac{13 + 4 \cdot 3}{9}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $4$ by $3$ .

$\frac{2 \cdot \sqrt{\frac{13 + 12}{9}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.4.2

Add $13$ and $12$ .

$\frac{2 \cdot \sqrt{\frac{25}{9}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.5

Rewrite $\sqrt{\frac{25}{9}}$ as $\frac{\sqrt{25}}{\sqrt{9}}$ .

$\frac{2 \cdot \frac{\sqrt{25}}{\sqrt{9}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Rewrite $25$ as $5^{2}$ .

$\frac{2 \cdot \frac{\sqrt{5^{2}}}{\sqrt{9}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.6.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2 \cdot \frac{5}{\sqrt{9}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.7

Simplify the denominator.

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Step 3.7.1

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

$\frac{2 \cdot \frac{5}{\sqrt{3^{2}}} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.7.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{2 \cdot \frac{5}{3} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.8

Multiply $2 (\frac{5}{3})$ .

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Step 3.8.1

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

$\frac{\frac{2 \cdot 5}{3} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.8.2

Multiply $2$ by $5$ .

$\frac{\frac{10}{3} \cdot 6 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.9

Cancel the common factor of $3$ .

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Step 3.9.1

Factor $3$ out of $6$ .

$\frac{\frac{10}{3} \cdot (3 (2)) - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.9.2

Cancel the common factor.

$\frac{\frac{10}{3} \cdot (3 \cdot 2) - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.9.3

Rewrite the expression.

$\frac{10 \cdot 2 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.10

Multiply $10$ by $2$ .

$\frac{20 - (3 - (1 + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.11

Simplify each term.

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Step 3.11.1

Write $1$ as a fraction with a common denominator.

$\frac{20 - (3 - (\frac{5}{5} + \frac{4}{5}) \cdot 2) \cdot 3 + 2}{6}$

Step 3.11.2

Combine the numerators over the common denominator.

$\frac{20 - (3 - \frac{5 + 4}{5} \cdot 2) \cdot 3 + 2}{6}$

Step 3.11.3

Add $5$ and $4$ .

$\frac{20 - (3 - \frac{9}{5} \cdot 2) \cdot 3 + 2}{6}$

Step 3.11.4

Multiply $- \frac{9}{5} \cdot 2$ .

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Step 3.11.4.1

Multiply $2$ by $- 1$ .

$\frac{20 - (3 - 2 (\frac{9}{5})) \cdot 3 + 2}{6}$

Step 3.11.4.2

Combine $- 2$ and $\frac{9}{5}$ .

$\frac{20 - (3 + \frac{- 2 \cdot 9}{5}) \cdot 3 + 2}{6}$

Step 3.11.4.3

Multiply $- 2$ by $9$ .

$\frac{20 - (3 + \frac{- 18}{5}) \cdot 3 + 2}{6}$

Step 3.11.5

Move the negative in front of the fraction.

$\frac{20 - (3 - \frac{18}{5}) \cdot 3 + 2}{6}$

Step 3.12

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{20 - (3 \cdot \frac{5}{5} - \frac{18}{5}) \cdot 3 + 2}{6}$

Step 3.13

Combine $3$ and $\frac{5}{5}$ .

$\frac{20 - (\frac{3 \cdot 5}{5} - \frac{18}{5}) \cdot 3 + 2}{6}$

Step 3.14

Combine the numerators over the common denominator.

$\frac{20 - \frac{3 \cdot 5 - 18}{5} \cdot 3 + 2}{6}$

Step 3.15

Simplify the numerator.

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Step 3.15.1

Multiply $3$ by $5$ .

$\frac{20 - \frac{15 - 18}{5} \cdot 3 + 2}{6}$

Step 3.15.2

Subtract $18$ from $15$ .

$\frac{20 - \frac{- 3}{5} \cdot 3 + 2}{6}$

Step 3.16

Move the negative in front of the fraction.

$\frac{20 - - \frac{3}{5} \cdot 3 + 2}{6}$

Step 3.17

Multiply $- - \frac{3}{5}$ .

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Step 3.17.1

Multiply $- 1$ by $- 1$ .

$\frac{20 + 1 (\frac{3}{5}) \cdot 3 + 2}{6}$

Step 3.17.2

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

$\frac{20 + \frac{3}{5} \cdot 3 + 2}{6}$

Step 3.18

Multiply $\frac{3}{5} \cdot 3$ .

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Step 3.18.1

Combine $\frac{3}{5}$ and $3$ .

$\frac{20 + \frac{3 \cdot 3}{5} + 2}{6}$

Step 3.18.2

Multiply $3$ by $3$ .

$\frac{20 + \frac{9}{5} + 2}{6}$

Step 4

Find the common denominator.

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Step 4.1

Write $20$ as a fraction with denominator $1$ .

$\frac{\frac{20}{1} + \frac{9}{5} + 2}{6}$

Step 4.2

Multiply $\frac{20}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{20}{1} \cdot \frac{5}{5} + \frac{9}{5} + 2}{6}$

Step 4.3

Multiply $\frac{20}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{20 \cdot 5}{5} + \frac{9}{5} + 2}{6}$

Step 4.4

Write $2$ as a fraction with denominator $1$ .

$\frac{\frac{20 \cdot 5}{5} + \frac{9}{5} + \frac{2}{1}}{6}$

Step 4.5

Multiply $\frac{2}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{20 \cdot 5}{5} + \frac{9}{5} + \frac{2}{1} \cdot \frac{5}{5}}{6}$

Step 4.6

Multiply $\frac{2}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{20 \cdot 5}{5} + \frac{9}{5} + \frac{2 \cdot 5}{5}}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{20 \cdot 5 + 9 + 2 \cdot 5}{5}}{6}$

Step 6

Simplify each term.

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Step 6.1

Multiply $20$ by $5$ .

$\frac{\frac{100 + 9 + 2 \cdot 5}{5}}{6}$

Step 6.2

Multiply $2$ by $5$ .

$\frac{\frac{100 + 9 + 10}{5}}{6}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add $100$ and $9$ .

$\frac{\frac{109 + 10}{5}}{6}$

Step 7.2

Add $109$ and $10$ .

$\frac{\frac{119}{5}}{6}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{119}{5} \cdot \frac{1}{6}$

Step 9

Multiply $\frac{119}{5} \cdot \frac{1}{6}$ .

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Step 9.1

Multiply $\frac{119}{5}$ by $\frac{1}{6}$ .

$\frac{119}{5 \cdot 6}$

Step 9.2

Multiply $5$ by $6$ .

$\frac{119}{30}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{119}{30}$

Decimal Form:

$3.9\overline{6}$

Mixed Number Form:

$3 \frac{29}{30}$