Basic Math Examples

$\frac{5}{6} + \frac{5}{9} \div \frac{2}{3} + \frac{1}{9}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{5}{6}$ by $\frac{\frac{3 \cdot 2}{3}}{\frac{3 \cdot 2}{3}}$ .

$\frac{5}{6} \cdot \frac{\frac{3 \cdot 2}{3}}{\frac{3 \cdot 2}{3}} + \frac{5}{9} \div \frac{2}{3} + \frac{1}{9}$

Step 1.2

Multiply $\frac{5}{6}$ by $\frac{\frac{3 \cdot 2}{3}}{\frac{3 \cdot 2}{3}}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{6 \frac{3 \cdot 2}{3}} + \frac{5}{9} \div \frac{2}{3} + \frac{1}{9}$

Step 1.3

Multiply $\frac{5}{9} \div \frac{2}{3}$ by $\frac{18}{18}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{6 \frac{3 \cdot 2}{3}} + \frac{5}{9} \div \frac{2}{3} \cdot \frac{18}{18} + \frac{1}{9}$

Step 1.4

Multiply $\frac{5}{9} \div \frac{2}{3}$ by $\frac{18}{18}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{6 \frac{3 \cdot 2}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{2}{3} \cdot 18} + \frac{1}{9}$

Step 1.5

Multiply $\frac{1}{9}$ by $\frac{\frac{2 \cdot 2}{3}}{\frac{2 \cdot 2}{3}}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{6 \frac{3 \cdot 2}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{2}{3} \cdot 18} + \frac{1}{9} \cdot \frac{\frac{2 \cdot 2}{3}}{\frac{2 \cdot 2}{3}}$

Step 1.6

Multiply $\frac{1}{9}$ by $\frac{\frac{2 \cdot 2}{3}}{\frac{2 \cdot 2}{3}}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{6 \frac{3 \cdot 2}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{2}{3} \cdot 18} + \frac{\frac{2 \cdot 2}{3}}{9 \frac{2 \cdot 2}{3}}$

Step 1.7

Multiply $3$ by $2$ .

$\frac{5 \frac{3 \cdot 2}{3}}{6 (\frac{6}{3})} + \frac{\frac{5}{9} \cdot 18}{\frac{2}{3} \cdot 18} + \frac{\frac{2 \cdot 2}{3}}{9 \frac{2 \cdot 2}{3}}$

Step 1.8

Combine $6$ and $\frac{6}{3}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{6 \cdot 6}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{2}{3} \cdot 18} + \frac{\frac{2 \cdot 2}{3}}{9 \frac{2 \cdot 2}{3}}$

Step 1.9

Multiply $6$ by $6$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{36}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{2}{3} \cdot 18} + \frac{\frac{2 \cdot 2}{3}}{9 \frac{2 \cdot 2}{3}}$

Step 1.10

Reorder the factors of $\frac{2}{3} \cdot 18$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{36}{3}} + \frac{\frac{5}{9} \cdot 18}{18 (\frac{2}{3})} + \frac{\frac{2 \cdot 2}{3}}{9 \frac{2 \cdot 2}{3}}$

Step 1.11

Combine $18$ and $\frac{2}{3}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{36}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{18 \cdot 2}{3}} + \frac{\frac{2 \cdot 2}{3}}{9 \frac{2 \cdot 2}{3}}$

Step 1.12

Multiply $18$ by $2$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{36}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{36}{3}} + \frac{\frac{2 \cdot 2}{3}}{9 \frac{2 \cdot 2}{3}}$

Step 1.13

Multiply $2$ by $2$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{36}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{36}{3}} + \frac{\frac{2 \cdot 2}{3}}{9 (\frac{4}{3})}$

Step 1.14

Combine $9$ and $\frac{4}{3}$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{36}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{36}{3}} + \frac{\frac{2 \cdot 2}{3}}{\frac{9 \cdot 4}{3}}$

Step 1.15

Multiply $9$ by $4$ .

$\frac{5 \frac{3 \cdot 2}{3}}{\frac{36}{3}} + \frac{\frac{5}{9} \cdot 18}{\frac{36}{3}} + \frac{\frac{2 \cdot 2}{3}}{\frac{36}{3}}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 \frac{3 \cdot 2}{3} + \frac{5}{9} \cdot 18 + \frac{2 \cdot 2}{3}}{\frac{36}{3}}$

Step 2.2

Multiply $2$ by $2$ .

$\frac{5 \frac{3 \cdot 2}{3} + \frac{5}{9} \cdot 18 + \frac{4}{3}}{\frac{36}{3}}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{5 \frac{3 \cdot 2}{3} + \frac{5}{9} \cdot 18 + \frac{4}{3}}{\frac{36}{3}}$

Step 3.1.2

Divide $2$ by $1$ .

$\frac{5 \cdot 2 + \frac{5}{9} \cdot 18 + \frac{4}{3}}{\frac{36}{3}}$

Step 3.2

Multiply $5$ by $2$ .

$\frac{10 + \frac{5}{9} \cdot 18 + \frac{4}{3}}{\frac{36}{3}}$

Step 3.3

Cancel the common factor of $9$ .

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Step 3.3.1

Factor $9$ out of $18$ .

$\frac{10 + \frac{5}{9} \cdot (9 (2)) + \frac{4}{3}}{\frac{36}{3}}$

Step 3.3.2

Cancel the common factor.

$\frac{10 + \frac{5}{9} \cdot (9 \cdot 2) + \frac{4}{3}}{\frac{36}{3}}$

Step 3.3.3

Rewrite the expression.

$\frac{10 + 5 \cdot 2 + \frac{4}{3}}{\frac{36}{3}}$

Step 3.4

Multiply $5$ by $2$ .

$\frac{10 + 10 + \frac{4}{3}}{\frac{36}{3}}$

Step 4

Find the common denominator.

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Step 4.1

Write $10$ as a fraction with denominator $1$ .

$\frac{\frac{10}{1} + 10 + \frac{4}{3}}{\frac{36}{3}}$

Step 4.2

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10}{1} \cdot \frac{3}{3} + 10 + \frac{4}{3}}{\frac{36}{3}}$

Step 4.3

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10 \cdot 3}{3} + 10 + \frac{4}{3}}{\frac{36}{3}}$

Step 4.4

Write $10$ as a fraction with denominator $1$ .

$\frac{\frac{10 \cdot 3}{3} + \frac{10}{1} + \frac{4}{3}}{\frac{36}{3}}$

Step 4.5

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10 \cdot 3}{3} + \frac{10}{1} \cdot \frac{3}{3} + \frac{4}{3}}{\frac{36}{3}}$

Step 4.6

Multiply $\frac{10}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{10 \cdot 3}{3} + \frac{10 \cdot 3}{3} + \frac{4}{3}}{\frac{36}{3}}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{10 \cdot 3 + 10 \cdot 3 + 4}{3}}{\frac{36}{3}}$

Step 6

Simplify each term.

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Step 6.1

Multiply $10$ by $3$ .

$\frac{\frac{30 + 10 \cdot 3 + 4}{3}}{\frac{36}{3}}$

Step 6.2

Multiply $10$ by $3$ .

$\frac{\frac{30 + 30 + 4}{3}}{\frac{36}{3}}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Add $30$ and $30$ .

$\frac{\frac{60 + 4}{3}}{\frac{36}{3}}$

Step 7.2

Add $60$ and $4$ .

$\frac{\frac{64}{3}}{\frac{36}{3}}$

Step 7.3

Cancel the common factor of $36$ and $3$ .

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Step 7.3.1

Factor $3$ out of $36$ .

$\frac{\frac{64}{3}}{\frac{3 \cdot 12}{3}}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $3$ out of $3$ .

$\frac{\frac{64}{3}}{\frac{3 \cdot 12}{3 (1)}}$

Step 7.3.2.2

Cancel the common factor.

$\frac{\frac{64}{3}}{\frac{3 \cdot 12}{3 \cdot 1}}$

Step 7.3.2.3

Rewrite the expression.

$\frac{\frac{64}{3}}{\frac{12}{1}}$

Step 7.3.2.4

Divide $12$ by $1$ .

$\frac{\frac{64}{3}}{12}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{64}{3} \cdot \frac{1}{12}$

Step 9

Cancel the common factor of $4$ .

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Step 9.1

Factor $4$ out of $64$ .

$\frac{4 (16)}{3} \cdot \frac{1}{12}$

Step 9.2

Factor $4$ out of $12$ .

$\frac{4 \cdot 16}{3} \cdot \frac{1}{4 \cdot 3}$

Step 9.3

Cancel the common factor.

$\frac{4 \cdot 16}{3} \cdot \frac{1}{4 \cdot 3}$

Step 9.4

Rewrite the expression.

$\frac{16}{3} \cdot \frac{1}{3}$

Step 10

Multiply $\frac{16}{3}$ by $\frac{1}{3}$ .

$\frac{16}{3 \cdot 3}$

Step 11

Multiply $3$ by $3$ .

$\frac{16}{9}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{9}$

Decimal Form:

$1.\overline{7}$

Mixed Number Form:

$1 \frac{7}{9}$