Basic Math Examples

$\frac{5}{y} = \frac{6 (\frac{1}{4})}{100}$

Step 1

Simplify both sides.

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Step 1.1

Cancel the common factor of $6$ and $100$ .

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Step 1.1.1

Factor $2$ out of $6 (\frac{1}{4})$ .

$\frac{5}{y} = \frac{2 (3 (\frac{1}{4}))}{100}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $100$ .

$\frac{5}{y} = \frac{2 (3 (\frac{1}{4}))}{2 (50)}$

Step 1.1.2.2

Cancel the common factor.

$\frac{5}{y} = \frac{2 (3 (\frac{1}{4}))}{2 \cdot 50}$

Step 1.1.2.3

Rewrite the expression.

$\frac{5}{y} = \frac{3 (\frac{1}{4})}{50}$

Step 1.2

Combine $3$ and $\frac{1}{4}$ .

$\frac{5}{y} = \frac{\frac{3}{4}}{50}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{y} = \frac{3}{4} \cdot \frac{1}{50}$

Step 1.4

Multiply $\frac{3}{4} \cdot \frac{1}{50}$ .

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Step 1.4.1

Multiply $\frac{3}{4}$ by $\frac{1}{50}$ .

$\frac{5}{y} = \frac{3}{4 \cdot 50}$

Step 1.4.2

Multiply $4$ by $50$ .

$\frac{5}{y} = \frac{3}{200}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$5 \cdot 200 = y \cdot 3$

Step 3

Solve the equation for $y$ .

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Step 3.1

Rewrite the equation as $y \cdot 3 = 5 \cdot 200$ .

$y \cdot 3 = 5 \cdot 200$

Step 3.2

Multiply $5$ by $200$ .

$y \cdot 3 = 1000$

Step 3.3

Divide each term in $y \cdot 3 = 1000$ by $3$ and simplify.

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Step 3.3.1

Divide each term in $y \cdot 3 = 1000$ by $3$ .

$\frac{y \cdot 3}{3} = \frac{1000}{3}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{y \cdot 3}{3} = \frac{1000}{3}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{1000}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1000}{3}$

Decimal Form:

$y = 333.\overline{3}$

Mixed Number Form:

$y = 333 \frac{1}{3}$