Basic Math Examples

\frac{3}{8} + \frac{4}{9} \div \frac{1}{4} + \frac{5}{9}

$\frac{3}{8} + \frac{4}{9} \div \frac{1}{4} + \frac{5}{9}$

Step 1

Find the common denominator.

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Step 1.1

Multiply

$\frac{3}{8}$ by

$\frac{\frac{9}{4}}{\frac{9}{4}}$ .

$\frac{3}{8} \cdot \frac{\frac{9}{4}}{\frac{9}{4}} + \frac{4}{9} \div \frac{1}{4} + \frac{5}{9}$

Step 1.2

Multiply

$\frac{3}{8}$ by

$\frac{\frac{9}{4}}{\frac{9}{4}}$ .

$\frac{3 (\frac{9}{4})}{8 (\frac{9}{4})} + \frac{4}{9} \div \frac{1}{4} + \frac{5}{9}$

Step 1.3

Multiply

$\frac{4}{9} \div \frac{1}{4}$ by

$\frac{72}{72}$ .

$\frac{3 (\frac{9}{4})}{8 (\frac{9}{4})} + \frac{4}{9} \div \frac{1}{4} \cdot \frac{72}{72} + \frac{5}{9}$

Step 1.4

Multiply

$\frac{4}{9} \div \frac{1}{4}$ by

$\frac{72}{72}$ .

$\frac{3 (\frac{9}{4})}{8 (\frac{9}{4})} + \frac{\frac{4}{9} \cdot 72}{\frac{1}{4} \cdot 72} + \frac{5}{9}$

Step 1.5

Multiply

$\frac{5}{9}$ by

$\frac{\frac{8}{4}}{\frac{8}{4}}$ .

$\frac{3 (\frac{9}{4})}{8 (\frac{9}{4})} + \frac{\frac{4}{9} \cdot 72}{\frac{1}{4} \cdot 72} + \frac{5}{9} \cdot \frac{\frac{8}{4}}{\frac{8}{4}}$

Step 1.6

Multiply

$\frac{5}{9}$ by

$\frac{\frac{8}{4}}{\frac{8}{4}}$ .

$\frac{3 (\frac{9}{4})}{8 (\frac{9}{4})} + \frac{\frac{4}{9} \cdot 72}{\frac{1}{4} \cdot 72} + \frac{5 (\frac{8}{4})}{9 (\frac{8}{4})}$

Step 1.7

Combine

$8$ and

$\frac{9}{4}$ .

$\frac{3 (\frac{9}{4})}{\frac{8 \cdot 9}{4}} + \frac{\frac{4}{9} \cdot 72}{\frac{1}{4} \cdot 72} + \frac{5 (\frac{8}{4})}{9 (\frac{8}{4})}$

Step 1.8

Multiply

$8$ by

$9$ .

$\frac{3 (\frac{9}{4})}{\frac{72}{4}} + \frac{\frac{4}{9} \cdot 72}{\frac{1}{4} \cdot 72} + \frac{5 (\frac{8}{4})}{9 (\frac{8}{4})}$

Step 1.9

Reorder the factors of

$\frac{1}{4} \cdot 72$ .

$\frac{3 (\frac{9}{4})}{\frac{72}{4}} + \frac{\frac{4}{9} \cdot 72}{72 (\frac{1}{4})} + \frac{5 (\frac{8}{4})}{9 (\frac{8}{4})}$

Step 1.10

Combine

$72$ and

$\frac{1}{4}$ .

$\frac{3 (\frac{9}{4})}{\frac{72}{4}} + \frac{\frac{4}{9} \cdot 72}{\frac{72}{4}} + \frac{5 (\frac{8}{4})}{9 (\frac{8}{4})}$

Step 1.11

Combine

$9$ and

$\frac{8}{4}$ .

$\frac{3 (\frac{9}{4})}{\frac{72}{4}} + \frac{\frac{4}{9} \cdot 72}{\frac{72}{4}} + \frac{5 (\frac{8}{4})}{\frac{9 \cdot 8}{4}}$

Step 1.12

Multiply

$9$ by

$8$ .

$\frac{3 (\frac{9}{4})}{\frac{72}{4}} + \frac{\frac{4}{9} \cdot 72}{\frac{72}{4}} + \frac{5 (\frac{8}{4})}{\frac{72}{4}}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 (\frac{9}{4}) + \frac{4}{9} \cdot 72 + 5 (\frac{8}{4})}{\frac{72}{4}}$

Step 3

Simplify each term.

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Step 3.1

Multiply

$3 (\frac{9}{4})$ .

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Step 3.1.1

Combine

$3$ and

$\frac{9}{4}$ .

$\frac{\frac{3 \cdot 9}{4} + \frac{4}{9} \cdot 72 + 5 (\frac{8}{4})}{\frac{72}{4}}$

Step 3.1.2

Multiply

$3$ by

$9$ .

$\frac{\frac{27}{4} + \frac{4}{9} \cdot 72 + 5 (\frac{8}{4})}{\frac{72}{4}}$

Step 3.2

Cancel the common factor of

$9$ .

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Step 3.2.1

Factor

$9$ out of

$72$ .

$\frac{\frac{27}{4} + \frac{4}{9} \cdot (9 (8)) + 5 (\frac{8}{4})}{\frac{72}{4}}$

Step 3.2.2

Cancel the common factor.

$\frac{\frac{27}{4} + \frac{4}{9} \cdot (9 \cdot 8) + 5 (\frac{8}{4})}{\frac{72}{4}}$

Step 3.2.3

Rewrite the expression.

$\frac{\frac{27}{4} + 4 \cdot 8 + 5 (\frac{8}{4})}{\frac{72}{4}}$

Step 3.3

Multiply

$4$ by

$8$ .

$\frac{\frac{27}{4} + 32 + 5 (\frac{8}{4})}{\frac{72}{4}}$

Step 3.4

Divide

$8$ by

$4$ .

$\frac{\frac{27}{4} + 32 + 5 \cdot 2}{\frac{72}{4}}$

Step 3.5

Multiply

$5$ by

$2$ .

$\frac{\frac{27}{4} + 32 + 10}{\frac{72}{4}}$

Step 4

Find the common denominator.

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Step 4.1

Write

$32$ as a fraction with denominator

$1$ .

$\frac{\frac{27}{4} + \frac{32}{1} + 10}{\frac{72}{4}}$

Step 4.2

Multiply

$\frac{32}{1}$ by

$\frac{4}{4}$ .

$\frac{\frac{27}{4} + \frac{32}{1} \cdot \frac{4}{4} + 10}{\frac{72}{4}}$

Step 4.3

Multiply

$\frac{32}{1}$ by

$\frac{4}{4}$ .

$\frac{\frac{27}{4} + \frac{32 \cdot 4}{4} + 10}{\frac{72}{4}}$

Step 4.4

Write

$10$ as a fraction with denominator

$1$ .

$\frac{\frac{27}{4} + \frac{32 \cdot 4}{4} + \frac{10}{1}}{\frac{72}{4}}$

Step 4.5

Multiply

$\frac{10}{1}$ by

$\frac{4}{4}$ .

$\frac{\frac{27}{4} + \frac{32 \cdot 4}{4} + \frac{10}{1} \cdot \frac{4}{4}}{\frac{72}{4}}$

Step 4.6

Multiply

$\frac{10}{1}$ by

$\frac{4}{4}$ .

$\frac{\frac{27}{4} + \frac{32 \cdot 4}{4} + \frac{10 \cdot 4}{4}}{\frac{72}{4}}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{27 + 32 \cdot 4 + 10 \cdot 4}{4}}{\frac{72}{4}}$

Step 6

Simplify each term.

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Step 6.1

Multiply

$32$ by

$4$ .

$\frac{\frac{27 + 128 + 10 \cdot 4}{4}}{\frac{72}{4}}$

Step 6.2

Multiply

$10$ by

$4$ .

$\frac{\frac{27 + 128 + 40}{4}}{\frac{72}{4}}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Add

$27$ and

$128$ .

$\frac{\frac{155 + 40}{4}}{\frac{72}{4}}$

Step 7.2

Add

$155$ and

$40$ .

$\frac{\frac{195}{4}}{\frac{72}{4}}$

Step 7.3

Cancel the common factor of

$72$ and

$4$ .

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Step 7.3.1

Factor

$4$ out of

$72$ .

$\frac{\frac{195}{4}}{\frac{4 \cdot 18}{4}}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor

$4$ out of

$4$ .

$\frac{\frac{195}{4}}{\frac{4 \cdot 18}{4 (1)}}$

Step 7.3.2.2

Cancel the common factor.

$\frac{\frac{195}{4}}{\frac{4 \cdot 18}{4 \cdot 1}}$

Step 7.3.2.3

Rewrite the expression.

$\frac{\frac{195}{4}}{\frac{18}{1}}$

Step 7.3.2.4

Divide

$18$ by

$1$ .

$\frac{\frac{195}{4}}{18}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\frac{195}{4} \cdot \frac{1}{18}$

Step 9

Cancel the common factor of

$3$ .

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Step 9.1

Factor

$3$ out of

$195$ .

$\frac{3 (65)}{4} \cdot \frac{1}{18}$

Step 9.2

Factor

$3$ out of

$18$ .

$\frac{3 \cdot 65}{4} \cdot \frac{1}{3 \cdot 6}$

Step 9.3

Cancel the common factor.

$\frac{3 \cdot 65}{4} \cdot \frac{1}{3 \cdot 6}$

Step 9.4

Rewrite the expression.

$\frac{65}{4} \cdot \frac{1}{6}$

Step 10

Multiply

$\frac{65}{4}$ by

$\frac{1}{6}$ .

$\frac{65}{4 \cdot 6}$

Step 11

Multiply

$4$ by

$6$ .

$\frac{65}{24}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{65}{24}$

Decimal Form:

$2.708\overline{3}$

Mixed Number Form:

$2 \frac{17}{24}$