Basic Math Examples

$\frac{1}{5} + \frac{y}{2} = \frac{3}{10}$

Step 1

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

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Step 1.1

Subtract $\frac{1}{5}$ from both sides of the equation.

$\frac{y}{2} = \frac{3}{10} - \frac{1}{5}$

Step 1.2

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y}{2} = \frac{3}{10} - \frac{1}{5} \cdot \frac{2}{2}$

Step 1.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{5}$ by $\frac{2}{2}$ .

$\frac{y}{2} = \frac{3}{10} - \frac{2}{5 \cdot 2}$

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{y}{2} = \frac{3}{10} - \frac{2}{10}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y}{2} = \frac{3 - 2}{10}$

Step 1.5

Subtract $2$ from $3$ .

$\frac{y}{2} = \frac{1}{10}$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 (\frac{1}{10})$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (\frac{1}{10})$

Step 3.1.1.2

Rewrite the expression.

$y = 2 (\frac{1}{10})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Factor $2$ out of $10$ .

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

Step 3.2.1.2

Cancel the common factor.

$y = 2 \frac{1}{2 \cdot 5}$

Step 3.2.1.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.2$