Basic Math Examples

$\frac{1}{3 y} = 3 \frac{1}{4}$

Step 1

Simplify the right side.

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Step 1.1

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{1}{3 y} = 3 + \frac{1}{4}$

Step 1.1.2

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

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Step 1.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{3 y} = 3 \cdot \frac{4}{4} + \frac{1}{4}$

Step 1.1.2.2

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

$\frac{1}{3 y} = \frac{3 \cdot 4}{4} + \frac{1}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{1}{3 y} = \frac{3 \cdot 4 + 1}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $3$ by $4$ .

$\frac{1}{3 y} = \frac{12 + 1}{4}$

Step 1.1.2.4.2

Add $12$ and $1$ .

$\frac{1}{3 y} = \frac{13}{4}$

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.

$1 \cdot 4 = 3 y \cdot 13$

Step 3

Solve the equation for $y$ .

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Step 3.1

Rewrite the equation as $3 y \cdot 13 = 1 \cdot 4$ .

$3 y \cdot 13 = 1 \cdot 4$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $13$ by $3$ .

$39 y = 1 \cdot 4$

Step 3.2.2

Multiply $4$ by $1$ .

$39 y = 4$

Step 3.3

Divide each term in $39 y = 4$ by $39$ and simplify.

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Step 3.3.1

Divide each term in $39 y = 4$ by $39$ .

$\frac{39 y}{39} = \frac{4}{39}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $39$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{39 y}{39} = \frac{4}{39}$

Step 3.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{39}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{4}{39}$

Decimal Form:

$y = 0.\overline{102564}$