Basic Math Examples

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

Step 1

Simplify the right side.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

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

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $4$ by $3$ .

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

Step 1.1.2.4.2

Add $12$ and $1$ .

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

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $\frac{1}{3}$ to both sides of the equation.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Add $13$ and $1$ .

$y = \frac{14}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{14}{3}$

Decimal Form:

$y = 4.\overline{6}$

Mixed Number Form:

$y = 4 \frac{2}{3}$