Basic Math Examples

$\frac{5}{8} y - \frac{1}{5} = \frac{1}{2}$

Step 1

Combine $\frac{5}{8}$ and $y$ .

$\frac{5 y}{8} - \frac{1}{5} = \frac{1}{2}$

Step 2

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

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Step 2.1

Add $\frac{1}{5}$ to both sides of the equation.

$\frac{5 y}{8} = \frac{1}{2} + \frac{1}{5}$

Step 2.2

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

$\frac{5 y}{8} = \frac{1}{2} \cdot \frac{5}{5} + \frac{1}{5}$

Step 2.3

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

$\frac{5 y}{8} = \frac{1}{2} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{2}{2}$

Step 2.4

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

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Step 2.4.1

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

$\frac{5 y}{8} = \frac{5}{2 \cdot 5} + \frac{1}{5} \cdot \frac{2}{2}$

Step 2.4.2

Multiply $2$ by $5$ .

$\frac{5 y}{8} = \frac{5}{10} + \frac{1}{5} \cdot \frac{2}{2}$

Step 2.4.3

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

$\frac{5 y}{8} = \frac{5}{10} + \frac{2}{5 \cdot 2}$

Step 2.4.4

Multiply $5$ by $2$ .

$\frac{5 y}{8} = \frac{5}{10} + \frac{2}{10}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 y}{8} = \frac{5 + 2}{10}$

Step 2.6

Add $5$ and $2$ .

$\frac{5 y}{8} = \frac{7}{10}$

Step 3

Multiply both sides of the equation by $\frac{8}{5}$ .

$\frac{8}{5} \cdot \frac{5 y}{8} = \frac{8}{5} \cdot \frac{7}{10}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{8}{5} \cdot \frac{5 y}{8}$ .

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Step 4.1.1.1

Cancel the common factor of $8$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 y}{8} = \frac{8}{5} \cdot \frac{7}{10}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 y) = \frac{8}{5} \cdot \frac{7}{10}$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 y$ .

$\frac{1}{5} (5 (y)) = \frac{8}{5} \cdot \frac{7}{10}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 y) = \frac{8}{5} \cdot \frac{7}{10}$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{8}{5} \cdot \frac{7}{10}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{8}{5} \cdot \frac{7}{10}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $8$ .

$y = \frac{2 (4)}{5} \cdot \frac{7}{10}$

Step 4.2.1.1.2

Factor $2$ out of $10$ .

$y = \frac{2 \cdot 4}{5} \cdot \frac{7}{2 \cdot 5}$

Step 4.2.1.1.3

Cancel the common factor.

$y = \frac{2 \cdot 4}{5} \cdot \frac{7}{2 \cdot 5}$

Step 4.2.1.1.4

Rewrite the expression.

$y = \frac{4}{5} \cdot \frac{7}{5}$

Step 4.2.1.2

Multiply $\frac{4}{5}$ by $\frac{7}{5}$ .

$y = \frac{4 \cdot 7}{5 \cdot 5}$

Step 4.2.1.3

Multiply.

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Step 4.2.1.3.1

Multiply $4$ by $7$ .

$y = \frac{28}{5 \cdot 5}$

Step 4.2.1.3.2

Multiply $5$ by $5$ .

$y = \frac{28}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{28}{25}$

Decimal Form:

$y = 1.12$

Mixed Number Form:

$y = 1 \frac{3}{25}$