Basic Math Examples

$5 + y = \frac{1}{2} - \frac{1}{3}$

Step 1

Simplify $\frac{1}{2} - \frac{1}{3}$ .

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Step 1.1

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 + y = \frac{1}{2} \cdot \frac{3}{3} - \frac{1}{3}$

Step 1.2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 + y = \frac{1}{2} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{2}{2}$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$5 + y = \frac{3}{2 \cdot 3} - \frac{1}{3} \cdot \frac{2}{2}$

Step 1.3.2

Multiply $2$ by $3$ .

$5 + y = \frac{3}{6} - \frac{1}{3} \cdot \frac{2}{2}$

Step 1.3.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$5 + y = \frac{3}{6} - \frac{2}{3 \cdot 2}$

Step 1.3.4

Multiply $3$ by $2$ .

$5 + y = \frac{3}{6} - \frac{2}{6}$

Step 1.4

Combine the numerators over the common denominator.

$5 + y = \frac{3 - 2}{6}$

Step 1.5

Subtract $2$ from $3$ .

$5 + y = \frac{1}{6}$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$y = \frac{1}{6} - 5$

Step 2.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = \frac{1}{6} - 5 \cdot \frac{6}{6}$

Step 2.3

Combine $- 5$ and $\frac{6}{6}$ .

$y = \frac{1}{6} + \frac{- 5 \cdot 6}{6}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{1 - 5 \cdot 6}{6}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 5$ by $6$ .

$y = \frac{1 - 30}{6}$

Step 2.5.2

Subtract $30$ from $1$ .

$y = \frac{- 29}{6}$

Step 2.6

Move the negative in front of the fraction.

$y = - \frac{29}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{29}{6}$

Decimal Form:

$y = - 4.8\overline{3}$

Mixed Number Form:

$y = - 4 \frac{5}{6}$