Algebra Examples

$\frac{2}{5} y - 4 + 7 - \frac{9}{10} y$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{2}{5}$ and $y$ .

$\frac{2 y}{5} - 4 + 7 - \frac{9}{10} y$

Step 1.2

Combine $y$ and $\frac{9}{10}$ .

$\frac{2 y}{5} - 4 + 7 - \frac{y \cdot 9}{10}$

Step 1.3

Move $9$ to the left of $y$ .

$\frac{2 y}{5} - 4 + 7 - \frac{9 y}{10}$

Step 2

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

$\frac{2 y}{5} \cdot \frac{2}{2} - \frac{9 y}{10} - 4 + 7$

Step 3

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

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Step 3.1

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

$\frac{2 y \cdot 2}{5 \cdot 2} - \frac{9 y}{10} - 4 + 7$

Step 3.2

Multiply $5$ by $2$ .

$\frac{2 y \cdot 2}{10} - \frac{9 y}{10} - 4 + 7$

Step 4

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 - 9 y}{10} - 4 + 7$

Step 5

Find the common denominator.

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Step 5.1

Write $- 4$ as a fraction with denominator $1$ .

$\frac{2 y \cdot 2 - 9 y}{10} + \frac{- 4}{1} + 7$

Step 5.2

Multiply $\frac{- 4}{1}$ by $\frac{10}{10}$ .

$\frac{2 y \cdot 2 - 9 y}{10} + \frac{- 4}{1} \cdot \frac{10}{10} + 7$

Step 5.3

Multiply $\frac{- 4}{1}$ by $\frac{10}{10}$ .

$\frac{2 y \cdot 2 - 9 y}{10} + \frac{- 4 \cdot 10}{10} + 7$

Step 5.4

Write $7$ as a fraction with denominator $1$ .

$\frac{2 y \cdot 2 - 9 y}{10} + \frac{- 4 \cdot 10}{10} + \frac{7}{1}$

Step 5.5

Multiply $\frac{7}{1}$ by $\frac{10}{10}$ .

$\frac{2 y \cdot 2 - 9 y}{10} + \frac{- 4 \cdot 10}{10} + \frac{7}{1} \cdot \frac{10}{10}$

Step 5.6

Multiply $\frac{7}{1}$ by $\frac{10}{10}$ .

$\frac{2 y \cdot 2 - 9 y}{10} + \frac{- 4 \cdot 10}{10} + \frac{7 \cdot 10}{10}$

Step 6

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 - 9 y - 4 \cdot 10 + 7 \cdot 10}{10}$

Step 7

Simplify each term.

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Step 7.1

Multiply $2$ by $2$ .

$\frac{4 y - 9 y - 4 \cdot 10 + 7 \cdot 10}{10}$

Step 7.2

Multiply $- 4$ by $10$ .

$\frac{4 y - 9 y - 40 + 7 \cdot 10}{10}$

Step 7.3

Multiply $7$ by $10$ .

$\frac{4 y - 9 y - 40 + 70}{10}$

Step 8

Simplify terms.

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Step 8.1

Subtract $9 y$ from $4 y$ .

$\frac{- 5 y - 40 + 70}{10}$

Step 8.2

Add $- 40$ and $70$ .

$\frac{- 5 y + 30}{10}$

Step 8.3

Cancel the common factor of $- 5 y + 30$ and $10$ .

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Step 8.3.1

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

$\frac{5 (- y) + 30}{10}$

Step 8.3.2

Factor $5$ out of $30$ .

$\frac{5 (- y) + 5 (6)}{10}$

Step 8.3.3

Factor $5$ out of $5 (- y) + 5 (6)$ .

$\frac{5 (- y + 6)}{10}$

Step 8.3.4

Cancel the common factors.

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Step 8.3.4.1

Factor $5$ out of $10$ .

$\frac{5 (- y + 6)}{5 (2)}$

Step 8.3.4.2

Cancel the common factor.

$\frac{5 (- y + 6)}{5 \cdot 2}$

Step 8.3.4.3

Rewrite the expression.

$\frac{- y + 6}{2}$

Step 8.4

Factor $- 1$ out of $- y$ .

$\frac{- (y) + 6}{2}$

Step 8.5

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{- (y) - 1 (- 6)}{2}$

Step 8.6

Factor $- 1$ out of $- (y) - 1 (- 6)$ .

$\frac{- (y - 6)}{2}$

Step 8.7

Simplify the expression.

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Step 8.7.1

Rewrite $- (y - 6)$ as $- 1 (y - 6)$ .

$\frac{- 1 (y - 6)}{2}$

Step 8.7.2

Move the negative in front of the fraction.

$- \frac{y - 6}{2}$