Basic Math Examples

$\frac{33 r}{16} = \frac{39}{20}$

Step 1

Multiply both sides of the equation by $\frac{16}{33}$ .

$\frac{16}{33} \cdot \frac{33 r}{16} = \frac{16}{33} \cdot \frac{39}{20}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{16}{33} \cdot \frac{33 r}{16}$ .

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Step 2.1.1.1

Cancel the common factor of $16$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{16}{33} \cdot \frac{33 r}{16} = \frac{16}{33} \cdot \frac{39}{20}$

Step 2.1.1.1.2

Rewrite the expression.

$\frac{1}{33} (33 r) = \frac{16}{33} \cdot \frac{39}{20}$

Step 2.1.1.2

Cancel the common factor of $33$ .

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Step 2.1.1.2.1

Factor $33$ out of $33 r$ .

$\frac{1}{33} (33 (r)) = \frac{16}{33} \cdot \frac{39}{20}$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{1}{33} (33 r) = \frac{16}{33} \cdot \frac{39}{20}$

Step 2.1.1.2.3

Rewrite the expression.

$r = \frac{16}{33} \cdot \frac{39}{20}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{16}{33} \cdot \frac{39}{20}$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Factor $4$ out of $16$ .

$r = \frac{4 (4)}{33} \cdot \frac{39}{20}$

Step 2.2.1.1.2

Factor $4$ out of $20$ .

$r = \frac{4 \cdot 4}{33} \cdot \frac{39}{4 \cdot 5}$

Step 2.2.1.1.3

Cancel the common factor.

$r = \frac{4 \cdot 4}{33} \cdot \frac{39}{4 \cdot 5}$

Step 2.2.1.1.4

Rewrite the expression.

$r = \frac{4}{33} \cdot \frac{39}{5}$

Step 2.2.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.2.1

Factor $3$ out of $33$ .

$r = \frac{4}{3 (11)} \cdot \frac{39}{5}$

Step 2.2.1.2.2

Factor $3$ out of $39$ .

$r = \frac{4}{3 \cdot 11} \cdot \frac{3 \cdot 13}{5}$

Step 2.2.1.2.3

Cancel the common factor.

$r = \frac{4}{3 \cdot 11} \cdot \frac{3 \cdot 13}{5}$

Step 2.2.1.2.4

Rewrite the expression.

$r = \frac{4}{11} \cdot \frac{13}{5}$

Step 2.2.1.3

Multiply $\frac{4}{11}$ by $\frac{13}{5}$ .

$r = \frac{4 \cdot 13}{11 \cdot 5}$

Step 2.2.1.4

Multiply.

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Step 2.2.1.4.1

Multiply $4$ by $13$ .

$r = \frac{52}{11 \cdot 5}$

Step 2.2.1.4.2

Multiply $11$ by $5$ .

$r = \frac{52}{55}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$r = \frac{52}{55}$

Decimal Form:

$r = 0.9\overline{45}$