Basic Math Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

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

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

Step 1.3.2

Multiply $3$ by $2$ .

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

Step 1.3.3

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

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

Step 1.3.4

Multiply $2$ by $3$ .

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

Step 1.4

Combine the numerators over the common denominator.

$\frac{\frac{5}{3} \cdot \frac{2 \cdot 2 + 3 \cdot 3}{6}}{\frac{4}{5} \cdot \frac{2}{3} \cdot \frac{2}{3}}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $2$ .

$\frac{\frac{5}{3} \cdot \frac{4 + 3 \cdot 3}{6}}{\frac{4}{5} \cdot \frac{2}{3} \cdot \frac{2}{3}}$

Step 1.5.2

Multiply $3$ by $3$ .

$\frac{\frac{5}{3} \cdot \frac{4 + 9}{6}}{\frac{4}{5} \cdot \frac{2}{3} \cdot \frac{2}{3}}$

Step 1.5.3

Add $4$ and $9$ .

$\frac{\frac{5}{3} \cdot \frac{13}{6}}{\frac{4}{5} \cdot \frac{2}{3} \cdot \frac{2}{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $\frac{4}{5}$ by $\frac{2}{3}$ .

$\frac{\frac{5}{3} \cdot \frac{13}{6}}{\frac{4 \cdot 2}{5 \cdot 3} \cdot \frac{2}{3}}$

Step 2.2

Multiply $\frac{4 \cdot 2}{5 \cdot 3}$ by $\frac{2}{3}$ .

$\frac{\frac{5}{3} \cdot \frac{13}{6}}{\frac{4 \cdot 2 \cdot 2}{5 \cdot 3 \cdot 3}}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $4$ by $2$ .

$\frac{\frac{5}{3} \cdot \frac{13}{6}}{\frac{8 \cdot 2}{5 \cdot 3 \cdot 3}}$

Step 3.2

Multiply $8$ by $2$ .

$\frac{\frac{5}{3} \cdot \frac{13}{6}}{\frac{16}{5 \cdot 3 \cdot 3}}$

Step 4

Simplify the denominator.

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Step 4.1

Multiply $5$ by $3$ .

$\frac{\frac{5}{3} \cdot \frac{13}{6}}{\frac{16}{15 \cdot 3}}$

Step 4.2

Multiply $15$ by $3$ .

$\frac{\frac{5}{3} \cdot \frac{13}{6}}{\frac{16}{45}}$

Step 5

Combine fractions.

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Step 5.1

Multiply $\frac{5}{3}$ by $\frac{13}{6}$ .

$\frac{\frac{5 \cdot 13}{3 \cdot 6}}{\frac{16}{45}}$

Step 5.2

Multiply.

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Step 5.2.1

Multiply $5$ by $13$ .

$\frac{\frac{65}{3 \cdot 6}}{\frac{16}{45}}$

Step 5.2.2

Multiply $3$ by $6$ .

$\frac{\frac{65}{18}}{\frac{16}{45}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{65}{18} \cdot \frac{45}{16}$

Step 7

Cancel the common factor of $9$ .

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Step 7.1

Factor $9$ out of $18$ .

$\frac{65}{9 (2)} \cdot \frac{45}{16}$

Step 7.2

Factor $9$ out of $45$ .

$\frac{65}{9 \cdot 2} \cdot \frac{9 \cdot 5}{16}$

Step 7.3

Cancel the common factor.

$\frac{65}{9 \cdot 2} \cdot \frac{9 \cdot 5}{16}$

Step 7.4

Rewrite the expression.

$\frac{65}{2} \cdot \frac{5}{16}$

Step 8

Multiply $\frac{65}{2}$ by $\frac{5}{16}$ .

$\frac{65 \cdot 5}{2 \cdot 16}$

Step 9

Multiply.

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Step 9.1

Multiply $65$ by $5$ .

$\frac{325}{2 \cdot 16}$

Step 9.2

Multiply $2$ by $16$ .

$\frac{325}{32}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{325}{32}$

Decimal Form:

$10.15625$

Mixed Number Form:

$10 \frac{5}{32}$