Basic Math Examples

\frac{y}{\frac{8}{3}} = \frac{2}{15}

$\frac{y}{\frac{8}{3}} = \frac{2}{15}$

Step 1

Multiply both sides of the equation by

\frac{8}{3}

$\frac{8}{3}$ .

\frac{8}{3} \cdot \frac{y}{\frac{8}{3}} = \frac{8}{3} \cdot \frac{2}{15}

$\frac{8}{3} \cdot \frac{y}{\frac{8}{3}} = \frac{8}{3} \cdot \frac{2}{15}$

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{8}{3} \cdot \frac{y}{\frac{8}{3}}

$\frac{8}{3} \cdot \frac{y}{\frac{8}{3}}$ .

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Step 2.1.1.1

Multiply the numerator by the reciprocal of the denominator.

\frac{8}{3} (y \frac{3}{8}) = \frac{8}{3} \cdot \frac{2}{15}

$\frac{8}{3} (y \frac{3}{8}) = \frac{8}{3} \cdot \frac{2}{15}$

Step 2.1.1.2

Combine

y

$y$ and

\frac{3}{8}

$\frac{3}{8}$ .

\frac{8}{3} \cdot \frac{y \cdot 3}{8} = \frac{8}{3} \cdot \frac{2}{15}

$\frac{8}{3} \cdot \frac{y \cdot 3}{8} = \frac{8}{3} \cdot \frac{2}{15}$

Step 2.1.1.3

Cancel the common factor of

8

$8$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{8}{3} \cdot \frac{y \cdot 3}{8} = \frac{8}{3} \cdot \frac{2}{15}$

Step 2.1.1.3.2

Rewrite the expression.

$\frac{1}{3} (y \cdot 3) = \frac{8}{3} \cdot \frac{2}{15}$

Step 2.1.1.4

Cancel the common factor of

$3$ .

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Step 2.1.1.4.1

Factor

$3$ out of

$y \cdot 3$ .

$\frac{1}{3} (3 \cdot y) = \frac{8}{3} \cdot \frac{2}{15}$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{1}{3} (3 \cdot y) = \frac{8}{3} \cdot \frac{2}{15}$

Step 2.1.1.4.3

Rewrite the expression.

$y = \frac{8}{3} \cdot \frac{2}{15}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply

$\frac{8}{3} \cdot \frac{2}{15}$ .

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Step 2.2.1.1

Multiply

$\frac{8}{3}$ by

$\frac{2}{15}$ .

$y = \frac{8 \cdot 2}{3 \cdot 15}$

Step 2.2.1.2

Multiply

$8$ by

$2$ .

$y = \frac{16}{3 \cdot 15}$

Step 2.2.1.3

Multiply

$3$ by

$15$ .

$y = \frac{16}{45}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{16}{45}$

Decimal Form:

$y = 0.3\overline{5}$