Basic Math Examples

$- \frac{- 5 - 4 y}{3} - \frac{- y - 1}{2}$

Step 1

To write $- \frac{- 5 - 4 y}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{- 5 - 4 y}{3} \cdot \frac{2}{2} - \frac{- y - 1}{2}$

Step 2

To write $- \frac{- y - 1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{- 5 - 4 y}{3} \cdot \frac{2}{2} - \frac{- y - 1}{2} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{- 5 - 4 y}{3}$ by $\frac{2}{2}$ .

$- \frac{(- 5 - 4 y) \cdot 2}{3 \cdot 2} - \frac{- y - 1}{2} \cdot \frac{3}{3}$

Step 3.2

Multiply $3$ by $2$ .

$- \frac{(- 5 - 4 y) \cdot 2}{6} - \frac{- y - 1}{2} \cdot \frac{3}{3}$

Step 3.3

Multiply $\frac{- y - 1}{2}$ by $\frac{3}{3}$ .

$- \frac{(- 5 - 4 y) \cdot 2}{6} - \frac{(- y - 1) \cdot 3}{2 \cdot 3}$

Step 3.4

Multiply $2$ by $3$ .

$- \frac{(- 5 - 4 y) \cdot 2}{6} - \frac{(- y - 1) \cdot 3}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{- (- 5 - 4 y) \cdot 2 - (- y - 1) \cdot 3}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $- 1$ out of $- (- 5 - 4 y) \cdot 2 - (- y - 1) \cdot 3$ .

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Step 5.1.1

Reorder the expression.

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Step 5.1.1.1

Reorder $- 5$ and $- 4 y$ .

$\frac{- (- 4 y - 5) \cdot 2 - (- y - 1) \cdot 3}{6}$

Step 5.1.1.2

Move $- 4 y - 5$ .

$\frac{- 1 \cdot 2 (- 4 y - 5) - (- y - 1) \cdot 3}{6}$

Step 5.1.1.3

Move $- y - 1$ .

$\frac{- 1 \cdot 2 (- 4 y - 5) - 1 \cdot 3 (- y - 1)}{6}$

Step 5.1.2

Factor $- 1$ out of $- 1 \cdot 2 (- 4 y - 5)$ .

$\frac{- (2 (- 4 y - 5)) - 1 \cdot 3 (- y - 1)}{6}$

Step 5.1.3

Factor $- 1$ out of $- 1 \cdot 3 (- y - 1)$ .

$\frac{- (2 (- 4 y - 5)) - (3 (- y - 1))}{6}$

Step 5.1.4

Factor $- 1$ out of $- (2 (- 4 y - 5)) - (3 (- y - 1))$ .

$\frac{- (2 (- 4 y - 5) + 3 (- y - 1))}{6}$

Step 5.2

Apply the distributive property.

$\frac{- (2 (- 4 y) + 2 \cdot - 5 + 3 (- y - 1))}{6}$

Step 5.3

Multiply $- 4$ by $2$ .

$\frac{- (- 8 y + 2 \cdot - 5 + 3 (- y - 1))}{6}$

Step 5.4

Multiply $2$ by $- 5$ .

$\frac{- (- 8 y - 10 + 3 (- y - 1))}{6}$

Step 5.5

Apply the distributive property.

$\frac{- (- 8 y - 10 + 3 (- y) + 3 \cdot - 1)}{6}$

Step 5.6

Multiply $- 1$ by $3$ .

$\frac{- (- 8 y - 10 - 3 y + 3 \cdot - 1)}{6}$

Step 5.7

Multiply $3$ by $- 1$ .

$\frac{- (- 8 y - 10 - 3 y - 3)}{6}$

Step 5.8

Subtract $3 y$ from $- 8 y$ .

$\frac{- (- 11 y - 10 - 3)}{6}$

Step 5.9

Subtract $3$ from $- 10$ .

$\frac{- (- 11 y - 13)}{6}$

Step 6

Simplify with factoring out.

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Step 6.1

Move the negative in front of the fraction.

$- \frac{- 11 y - 13}{6}$

Step 6.2

Factor $- 1$ out of $- 11 y$ .

$- \frac{- (11 y) - 13}{6}$

Step 6.3

Rewrite $- 13$ as $- 1 (13)$ .

$- \frac{- (11 y) - 1 (13)}{6}$

Step 6.4

Factor $- 1$ out of $- (11 y) - 1 (13)$ .

$- \frac{- (11 y + 13)}{6}$

Step 6.5

Simplify the expression.

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Step 6.5.1

Rewrite $- (11 y + 13)$ as $- 1 (11 y + 13)$ .

$- \frac{- 1 (11 y + 13)}{6}$

Step 6.5.2

Move the negative in front of the fraction.

$- - \frac{11 y + 13}{6}$

Step 6.5.3

Multiply $- 1$ by $- 1$ .

$1 \frac{11 y + 13}{6}$

Step 6.5.4

Multiply $\frac{11 y + 13}{6}$ by $1$ .

$\frac{11 y + 13}{6}$