Basic Math Examples

$\frac{- 1}{5} = \frac{1}{2} y - \frac{5}{7}$

Step 1

Rewrite the equation as $\frac{1}{2} y - \frac{5}{7} = \frac{- 1}{5}$ .

$\frac{1}{2} y - \frac{5}{7} = \frac{- 1}{5}$

Step 2

Combine $\frac{1}{2}$ and $y$ .

$\frac{y}{2} - \frac{5}{7} = \frac{- 1}{5}$

Step 3

Move the negative in front of the fraction.

$\frac{y}{2} - \frac{5}{7} = - \frac{1}{5}$

Step 4

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

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Step 4.1

Add $\frac{5}{7}$ to both sides of the equation.

$\frac{y}{2} = - \frac{1}{5} + \frac{5}{7}$

Step 4.2

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{y}{2} = - \frac{1}{5} \cdot \frac{7}{7} + \frac{5}{7}$

Step 4.3

To write $\frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y}{2} = - \frac{1}{5} \cdot \frac{7}{7} + \frac{5}{7} \cdot \frac{5}{5}$

Step 4.4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{1}{5}$ by $\frac{7}{7}$ .

$\frac{y}{2} = - \frac{7}{5 \cdot 7} + \frac{5}{7} \cdot \frac{5}{5}$

Step 4.4.2

Multiply $5$ by $7$ .

$\frac{y}{2} = - \frac{7}{35} + \frac{5}{7} \cdot \frac{5}{5}$

Step 4.4.3

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

$\frac{y}{2} = - \frac{7}{35} + \frac{5 \cdot 5}{7 \cdot 5}$

Step 4.4.4

Multiply $7$ by $5$ .

$\frac{y}{2} = - \frac{7}{35} + \frac{5 \cdot 5}{35}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{y}{2} = \frac{- 7 + 5 \cdot 5}{35}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $5$ by $5$ .

$\frac{y}{2} = \frac{- 7 + 25}{35}$

Step 4.6.2

Add $- 7$ and $25$ .

$\frac{y}{2} = \frac{18}{35}$

Step 5

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 (\frac{18}{35})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (\frac{18}{35})$

Step 6.1.1.2

Rewrite the expression.

$y = 2 (\frac{18}{35})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $2 (\frac{18}{35})$ .

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Step 6.2.1.1

Combine $2$ and $\frac{18}{35}$ .

$y = \frac{2 \cdot 18}{35}$

Step 6.2.1.2

Multiply $2$ by $18$ .

$y = \frac{36}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{36}{35}$

Decimal Form:

$y = 1.02857142 \dots$

Mixed Number Form:

$y = 1 \frac{1}{35}$