Pre-Algebra Examples

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

Step 1

Simplify $\frac{3}{5} y + \frac{8}{5} - \frac{5}{8} y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{3}{5}$ and $y$ .

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

Step 1.1.2

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

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

Step 1.1.3

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

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

Step 1.2

To write $\frac{3 y}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

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

Step 1.3

To write $- \frac{5 y}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{3 y}{5}$ by $\frac{8}{8}$ .

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

Step 1.4.2

Multiply $5$ by $8$ .

$\frac{3 y \cdot 8}{40} - \frac{5 y}{8} \cdot \frac{5}{5} + \frac{8}{5} = - \frac{5}{8}$

Step 1.4.3

Multiply $\frac{5 y}{8}$ by $\frac{5}{5}$ .

$\frac{3 y \cdot 8}{40} - \frac{5 y \cdot 5}{8 \cdot 5} + \frac{8}{5} = - \frac{5}{8}$

Step 1.4.4

Multiply $8$ by $5$ .

$\frac{3 y \cdot 8}{40} - \frac{5 y \cdot 5}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3 y \cdot 8 - 5 y \cdot 5}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $y$ out of $3 y \cdot 8 - 5 y \cdot 5$ .

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Step 1.6.1.1.1

Factor $y$ out of $3 y \cdot 8$ .

$\frac{y (3 \cdot 8) - 5 y \cdot 5}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6.1.1.2

Factor $y$ out of $- 5 y \cdot 5$ .

$\frac{y (3 \cdot 8) + y (- 5 \cdot 5)}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6.1.1.3

Factor $y$ out of $y (3 \cdot 8) + y (- 5 \cdot 5)$ .

$\frac{y (3 \cdot 8 - 5 \cdot 5)}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6.1.2

Multiply $3$ by $8$ .

$\frac{y (24 - 5 \cdot 5)}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6.1.3

Multiply $- 5$ by $5$ .

$\frac{y (24 - 25)}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6.1.4

Subtract $25$ from $24$ .

$\frac{y \cdot - 1}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6.2

Move $- 1$ to the left of $y$ .

$\frac{- 1 \cdot y}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 1.6.3

Move the negative in front of the fraction.

$- \frac{y}{40} + \frac{8}{5} = - \frac{5}{8}$

Step 2

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

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Step 2.1

Subtract $\frac{8}{5}$ from both sides of the equation.

$- \frac{y}{40} = - \frac{5}{8} - \frac{8}{5}$

Step 2.2

To write $- \frac{5}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{y}{40} = - \frac{5}{8} \cdot \frac{5}{5} - \frac{8}{5}$

Step 2.3

To write $- \frac{8}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{y}{40} = - \frac{5}{8} \cdot \frac{5}{5} - \frac{8}{5} \cdot \frac{8}{8}$

Step 2.4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{5}{8}$ by $\frac{5}{5}$ .

$- \frac{y}{40} = - \frac{5 \cdot 5}{8 \cdot 5} - \frac{8}{5} \cdot \frac{8}{8}$

Step 2.4.2

Multiply $8$ by $5$ .

$- \frac{y}{40} = - \frac{5 \cdot 5}{40} - \frac{8}{5} \cdot \frac{8}{8}$

Step 2.4.3

Multiply $\frac{8}{5}$ by $\frac{8}{8}$ .

$- \frac{y}{40} = - \frac{5 \cdot 5}{40} - \frac{8 \cdot 8}{5 \cdot 8}$

Step 2.4.4

Multiply $5$ by $8$ .

$- \frac{y}{40} = - \frac{5 \cdot 5}{40} - \frac{8 \cdot 8}{40}$

Step 2.5

Combine the numerators over the common denominator.

$- \frac{y}{40} = \frac{- 5 \cdot 5 - 8 \cdot 8}{40}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 5$ by $5$ .

$- \frac{y}{40} = \frac{- 25 - 8 \cdot 8}{40}$

Step 2.6.2

Multiply $- 8$ by $8$ .

$- \frac{y}{40} = \frac{- 25 - 64}{40}$

Step 2.6.3

Subtract $64$ from $- 25$ .

$- \frac{y}{40} = \frac{- 89}{40}$

Step 2.7

Move the negative in front of the fraction.

$- \frac{y}{40} = - \frac{89}{40}$

Step 3

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

$- y = - 89$

Step 4

Divide each term in $- y = - 89$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- y = - 89$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 89}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 89}{- 1}$

Step 4.2.2

Divide $y$ by $1$ .

$y = \frac{- 89}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 89$ by $- 1$ .

$y = 89$