Basic Math Examples

$\frac{(a + 12) \cdot 5}{6} - 5 a + 11$

Step 1

Move $5$ to the left of $a + 12$ .

$\frac{5 (a + 12)}{6} - 5 a + 11$

Step 2

To write $- 5 a$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 (a + 12)}{6} - 5 a \cdot \frac{6}{6} + 11$

Step 3

Simplify terms.

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Step 3.1

Combine $- 5 a$ and $\frac{6}{6}$ .

$\frac{5 (a + 12)}{6} + \frac{- 5 a \cdot 6}{6} + 11$

Step 3.2

Combine the numerators over the common denominator.

$\frac{5 (a + 12) - 5 a \cdot 6}{6} + 11$

Step 4

Simplify the numerator.

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Step 4.1

Factor $5$ out of $5 (a + 12) - 5 a \cdot 6$ .

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Step 4.1.1

Factor $5$ out of $- 5 a \cdot 6$ .

$\frac{5 (a + 12) + 5 (- a \cdot 6)}{6} + 11$

Step 4.1.2

Factor $5$ out of $5 (a + 12) + 5 (- a \cdot 6)$ .

$\frac{5 (a + 12 - a \cdot 6)}{6} + 11$

Step 4.2

Multiply $6$ by $- 1$ .

$\frac{5 (a + 12 - 6 a)}{6} + 11$

Step 4.3

Subtract $6 a$ from $a$ .

$\frac{5 (- 5 a + 12)}{6} + 11$

Step 5

To write $11$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{5 (- 5 a + 12)}{6} + 11 \cdot \frac{6}{6}$

Step 6

Simplify terms.

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Step 6.1

Combine $11$ and $\frac{6}{6}$ .

$\frac{5 (- 5 a + 12)}{6} + \frac{11 \cdot 6}{6}$

Step 6.2

Combine the numerators over the common denominator.

$\frac{5 (- 5 a + 12) + 11 \cdot 6}{6}$

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$\frac{5 (- 5 a) + 5 \cdot 12 + 11 \cdot 6}{6}$

Step 7.2

Multiply $- 5$ by $5$ .

$\frac{- 25 a + 5 \cdot 12 + 11 \cdot 6}{6}$

Step 7.3

Multiply $5$ by $12$ .

$\frac{- 25 a + 60 + 11 \cdot 6}{6}$

Step 7.4

Multiply $11$ by $6$ .

$\frac{- 25 a + 60 + 66}{6}$

Step 7.5

Add $60$ and $66$ .

$\frac{- 25 a + 126}{6}$

Step 8

Simplify with factoring out.

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Step 8.1

Factor $- 1$ out of $- 25 a$ .

$\frac{- (25 a) + 126}{6}$

Step 8.2

Rewrite $126$ as $- 1 (- 126)$ .

$\frac{- (25 a) - 1 (- 126)}{6}$

Step 8.3

Factor $- 1$ out of $- (25 a) - 1 (- 126)$ .

$\frac{- (25 a - 126)}{6}$

Step 8.4

Simplify the expression.

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Step 8.4.1

Rewrite $- (25 a - 126)$ as $- 1 (25 a - 126)$ .

$\frac{- 1 (25 a - 126)}{6}$

Step 8.4.2

Move the negative in front of the fraction.

$- \frac{25 a - 126}{6}$