Basic Math Examples

$\frac{1}{2} \cdot (5 a - 6) - \frac{1}{3} \cdot (9 a - 15) + 1$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{2} (5 a) + \frac{1}{2} \cdot - 6 - \frac{1}{3} \cdot (9 a - 15) + 1$

Step 1.2

Multiply $\frac{1}{2} (5 a)$ .

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Step 1.2.1

Combine $5$ and $\frac{1}{2}$ .

$\frac{5}{2} a + \frac{1}{2} \cdot - 6 - \frac{1}{3} \cdot (9 a - 15) + 1$

Step 1.2.2

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

$\frac{5 a}{2} + \frac{1}{2} \cdot - 6 - \frac{1}{3} \cdot (9 a - 15) + 1$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $- 6$ .

$\frac{5 a}{2} + \frac{1}{2} \cdot (2 (- 3)) - \frac{1}{3} \cdot (9 a - 15) + 1$

Step 1.3.2

Cancel the common factor.

$\frac{5 a}{2} + \frac{1}{2} \cdot (2 \cdot - 3) - \frac{1}{3} \cdot (9 a - 15) + 1$

Step 1.3.3

Rewrite the expression.

$\frac{5 a}{2} - 3 - \frac{1}{3} \cdot (9 a - 15) + 1$

Step 1.4

Apply the distributive property.

$\frac{5 a}{2} - 3 - \frac{1}{3} (9 a) - \frac{1}{3} \cdot - 15 + 1$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{5 a}{2} - 3 + \frac{- 1}{3} (9 a) - \frac{1}{3} \cdot - 15 + 1$

Step 1.5.2

Factor $3$ out of $9 a$ .

$\frac{5 a}{2} - 3 + \frac{- 1}{3} (3 (3 a)) - \frac{1}{3} \cdot - 15 + 1$

Step 1.5.3

Cancel the common factor.

$\frac{5 a}{2} - 3 + \frac{- 1}{3} (3 (3 a)) - \frac{1}{3} \cdot - 15 + 1$

Step 1.5.4

Rewrite the expression.

$\frac{5 a}{2} - 3 - 1 (3 a) - \frac{1}{3} \cdot - 15 + 1$

Step 1.6

Multiply $3$ by $- 1$ .

$\frac{5 a}{2} - 3 - 3 a - \frac{1}{3} \cdot - 15 + 1$

Step 1.7

Cancel the common factor of $3$ .

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Step 1.7.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{5 a}{2} - 3 - 3 a + \frac{- 1}{3} \cdot - 15 + 1$

Step 1.7.2

Factor $3$ out of $- 15$ .

$\frac{5 a}{2} - 3 - 3 a + \frac{- 1}{3} \cdot (3 (- 5)) + 1$

Step 1.7.3

Cancel the common factor.

$\frac{5 a}{2} - 3 - 3 a + \frac{- 1}{3} \cdot (3 \cdot - 5) + 1$

Step 1.7.4

Rewrite the expression.

$\frac{5 a}{2} - 3 - 3 a - 1 \cdot - 5 + 1$

Step 1.8

Multiply $- 1$ by $- 5$ .

$\frac{5 a}{2} - 3 - 3 a + 5 + 1$

Step 2

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

$\frac{5 a}{2} - 3 a \cdot \frac{2}{2} - 3 + 5 + 1$

Step 3

Combine $- 3 a$ and $\frac{2}{2}$ .

$\frac{5 a}{2} + \frac{- 3 a \cdot 2}{2} - 3 + 5 + 1$

Step 4

Combine the numerators over the common denominator.

$\frac{5 a - 3 a \cdot 2}{2} - 3 + 5 + 1$

Step 5

Find the common denominator.

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Step 5.1

Write $- 3$ as a fraction with denominator $1$ .

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3}{1} + 5 + 1$

Step 5.2

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

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3}{1} \cdot \frac{2}{2} + 5 + 1$

Step 5.3

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

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + 5 + 1$

Step 5.4

Write $5$ as a fraction with denominator $1$ .

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{5}{1} + 1$

Step 5.5

Multiply $\frac{5}{1}$ by $\frac{2}{2}$ .

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{5}{1} \cdot \frac{2}{2} + 1$

Step 5.6

Multiply $\frac{5}{1}$ by $\frac{2}{2}$ .

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{5 \cdot 2}{2} + 1$

Step 5.7

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

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{5 \cdot 2}{2} + \frac{1}{1}$

Step 5.8

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{5 \cdot 2}{2} + \frac{1}{1} \cdot \frac{2}{2}$

Step 5.9

Multiply $\frac{1}{1}$ by $\frac{2}{2}$ .

$\frac{5 a - 3 a \cdot 2}{2} + \frac{- 3 \cdot 2}{2} + \frac{5 \cdot 2}{2} + \frac{2}{2}$

Step 6

Combine the numerators over the common denominator.

$\frac{5 a - 3 a \cdot 2 - 3 \cdot 2 + 5 \cdot 2 + 2}{2}$

Step 7

Simplify each term.

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Step 7.1

Multiply $2$ by $- 3$ .

$\frac{5 a - 6 a - 3 \cdot 2 + 5 \cdot 2 + 2}{2}$

Step 7.2

Multiply $- 3$ by $2$ .

$\frac{5 a - 6 a - 6 + 5 \cdot 2 + 2}{2}$

Step 7.3

Multiply $5$ by $2$ .

$\frac{5 a - 6 a - 6 + 10 + 2}{2}$

Step 8

Simplify terms.

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Step 8.1

Subtract $6 a$ from $5 a$ .

$\frac{- a - 6 + 10 + 2}{2}$

Step 8.2

Simplify by adding numbers.

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Step 8.2.1

Add $- 6$ and $10$ .

$\frac{- a + 4 + 2}{2}$

Step 8.2.2

Add $4$ and $2$ .

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

Step 8.3

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

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

Step 8.4

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

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

Step 8.5

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

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

Step 8.6

Simplify the expression.

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Step 8.6.1

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

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

Step 8.6.2

Move the negative in front of the fraction.

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