Basic Math Examples

$\frac{y}{\frac{5}{2}} = \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 1

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{y}{\frac{5}{2}} = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

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 $\frac{5}{2} \cdot \frac{y}{\frac{5}{2}}$ .

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Step 2.1.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{2} (y \frac{2}{5}) = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 2.1.1.2

Combine $y$ and $\frac{2}{5}$ .

$\frac{5}{2} \cdot \frac{y \cdot 2}{5} = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{y \cdot 2}{5} = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 2.1.1.3.2

Rewrite the expression.

$\frac{1}{2} (y \cdot 2) = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 2.1.1.4

Cancel the common factor of $2$ .

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Step 2.1.1.4.1

Factor $2$ out of $y \cdot 2$ .

$\frac{1}{2} (2 \cdot y) = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{1}{2} (2 \cdot y) = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 2.1.1.4.3

Rewrite the expression.

$y = \frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{2} \cdot \frac{3}{\frac{10}{\frac{9}{8}}}$ .

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Step 2.2.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{5}{2} (3 \frac{\frac{9}{8}}{10})$

Step 2.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{5}{2} (3 (\frac{9}{8} \cdot \frac{1}{10}))$

Step 2.2.1.3

Multiply $\frac{9}{8} \cdot \frac{1}{10}$ .

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Step 2.2.1.3.1

Multiply $\frac{9}{8}$ by $\frac{1}{10}$ .

$y = \frac{5}{2} (3 \frac{9}{8 \cdot 10})$

Step 2.2.1.3.2

Multiply $8$ by $10$ .

$y = \frac{5}{2} (3 (\frac{9}{80}))$

Step 2.2.1.4

Multiply $3 (\frac{9}{80})$ .

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Step 2.2.1.4.1

Combine $3$ and $\frac{9}{80}$ .

$y = \frac{5}{2} \cdot \frac{3 \cdot 9}{80}$

Step 2.2.1.4.2

Multiply $3$ by $9$ .

$y = \frac{5}{2} \cdot \frac{27}{80}$

Step 2.2.1.5

Cancel the common factor of $5$ .

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Step 2.2.1.5.1

Factor $5$ out of $80$ .

$y = \frac{5}{2} \cdot \frac{27}{5 (16)}$

Step 2.2.1.5.2

Cancel the common factor.

$y = \frac{5}{2} \cdot \frac{27}{5 \cdot 16}$

Step 2.2.1.5.3

Rewrite the expression.

$y = \frac{1}{2} \cdot \frac{27}{16}$

Step 2.2.1.6

Multiply $\frac{1}{2}$ by $\frac{27}{16}$ .

$y = \frac{27}{2 \cdot 16}$

Step 2.2.1.7

Multiply $2$ by $16$ .

$y = \frac{27}{32}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{27}{32}$

Decimal Form:

$y = 0.84375$