Basic Math Examples

$\frac{y}{\frac{5}{7}} = \frac{\frac{3}{10}}{\frac{9}{14}}$

Step 1

Multiply both sides of the equation by $\frac{5}{7}$ .

$\frac{5}{7} \cdot \frac{y}{\frac{5}{7}} = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

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 $\frac{5}{7} \cdot \frac{y}{\frac{5}{7}}$ .

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Step 2.1.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{7} (y \frac{7}{5}) = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

Step 2.1.1.2

Combine $y$ and $\frac{7}{5}$ .

$\frac{5}{7} \cdot \frac{y \cdot 7}{5} = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

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.

$\frac{5}{7} \cdot \frac{y \cdot 7}{5} = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

Step 2.1.1.3.2

Rewrite the expression.

$\frac{1}{7} (y \cdot 7) = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

Step 2.1.1.4

Cancel the common factor of $7$ .

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Step 2.1.1.4.1

Factor $7$ out of $y \cdot 7$ .

$\frac{1}{7} (7 \cdot y) = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{1}{7} (7 \cdot y) = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

Step 2.1.1.4.3

Rewrite the expression.

$y = \frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{5}{7} \cdot \frac{\frac{3}{10}}{\frac{9}{14}}$ .

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Step 2.2.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{5}{7} (\frac{3}{10} \cdot \frac{14}{9})$

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 $9$ .

$y = \frac{5}{7} (\frac{3}{10} \cdot \frac{14}{3 (3)})$

Step 2.2.1.2.2

Cancel the common factor.

$y = \frac{5}{7} (\frac{3}{10} \cdot \frac{14}{3 \cdot 3})$

Step 2.2.1.2.3

Rewrite the expression.

$y = \frac{5}{7} (\frac{1}{10} \cdot \frac{14}{3})$

Step 2.2.1.3

Cancel the common factor of $2$ .

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Step 2.2.1.3.1

Factor $2$ out of $10$ .

$y = \frac{5}{7} (\frac{1}{2 (5)} \cdot \frac{14}{3})$

Step 2.2.1.3.2

Factor $2$ out of $14$ .

$y = \frac{5}{7} (\frac{1}{2 \cdot 5} \cdot \frac{2 \cdot 7}{3})$

Step 2.2.1.3.3

Cancel the common factor.

$y = \frac{5}{7} (\frac{1}{2 \cdot 5} \cdot \frac{2 \cdot 7}{3})$

Step 2.2.1.3.4

Rewrite the expression.

$y = \frac{5}{7} (\frac{1}{5} \cdot \frac{7}{3})$

Step 2.2.1.4

Multiply $\frac{1}{5}$ by $\frac{7}{3}$ .

$y = \frac{5}{7} \cdot \frac{7}{5 \cdot 3}$

Step 2.2.1.5

Multiply $5$ by $3$ .

$y = \frac{5}{7} \cdot \frac{7}{15}$

Step 2.2.1.6

Cancel the common factor of $5$ .

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Step 2.2.1.6.1

Factor $5$ out of $15$ .

$y = \frac{5}{7} \cdot \frac{7}{5 (3)}$

Step 2.2.1.6.2

Cancel the common factor.

$y = \frac{5}{7} \cdot \frac{7}{5 \cdot 3}$

Step 2.2.1.6.3

Rewrite the expression.

$y = \frac{1}{7} \cdot \frac{7}{3}$

Step 2.2.1.7

Cancel the common factor of $7$ .

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Step 2.2.1.7.1

Cancel the common factor.

$y = \frac{1}{7} \cdot \frac{7}{3}$

Step 2.2.1.7.2

Rewrite the expression.

$y = \frac{1}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1}{3}$

Decimal Form:

$y = 0.\overline{3}$