Basic Math Examples

$- \frac{5}{8} y + \frac{3}{4} = \frac{5}{8}$

Step 1

Simplify each term.

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Step 1.1

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

$- \frac{y \cdot 5}{8} + \frac{3}{4} = \frac{5}{8}$

Step 1.2

Move $5$ to the left of $y$ .

$- \frac{5 y}{8} + \frac{3}{4} = \frac{5}{8}$

Step 2

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

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Step 2.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$- \frac{5 y}{8} = \frac{5}{8} - \frac{3}{4}$

Step 2.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 y}{8} = \frac{5}{8} - \frac{3}{4} \cdot \frac{2}{2}$

Step 2.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$- \frac{5 y}{8} = \frac{5}{8} - \frac{3 \cdot 2}{4 \cdot 2}$

Step 2.3.2

Multiply $4$ by $2$ .

$- \frac{5 y}{8} = \frac{5}{8} - \frac{3 \cdot 2}{8}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{5 y}{8} = \frac{5 - 3 \cdot 2}{8}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 3$ by $2$ .

$- \frac{5 y}{8} = \frac{5 - 6}{8}$

Step 2.5.2

Subtract $6$ from $5$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 5 y = - 1$

Step 4

Divide each term in $- 5 y = - 1$ by $- 5$ and simplify.

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Step 4.1

Divide each term in $- 5 y = - 1$ by $- 5$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 5$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $y$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Dividing two negative values results in a positive value.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.2$