Basic Math Examples

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

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:

$2 \frac{17}{24}$