Pre-Algebra Examples

$\frac{2}{5} \cdot (d - 10) - \frac{2}{3} \cdot (d + 6)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{2}{5} d + \frac{2}{5} \cdot - 10 - \frac{2}{3} \cdot (d + 6)$

Step 1.2

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

$\frac{2 d}{5} + \frac{2}{5} \cdot - 10 - \frac{2}{3} \cdot (d + 6)$

Step 1.3

Cancel the common factor of $5$ .

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Step 1.3.1

Factor $5$ out of $- 10$ .

$\frac{2 d}{5} + \frac{2}{5} \cdot (5 (- 2)) - \frac{2}{3} \cdot (d + 6)$

Step 1.3.2

Cancel the common factor.

$\frac{2 d}{5} + \frac{2}{5} \cdot (5 \cdot - 2) - \frac{2}{3} \cdot (d + 6)$

Step 1.3.3

Rewrite the expression.

$\frac{2 d}{5} + 2 \cdot - 2 - \frac{2}{3} \cdot (d + 6)$

Step 1.4

Multiply $2$ by $- 2$ .

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

Step 1.5

Apply the distributive property.

$\frac{2 d}{5} - 4 - \frac{2}{3} d - \frac{2}{3} \cdot 6$

Step 1.6

Combine $d$ and $\frac{2}{3}$ .

$\frac{2 d}{5} - 4 - \frac{d \cdot 2}{3} - \frac{2}{3} \cdot 6$

Step 1.7

Cancel the common factor of $3$ .

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Step 1.7.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{2 d}{5} - 4 - \frac{d \cdot 2}{3} + \frac{- 2}{3} \cdot 6$

Step 1.7.2

Factor $3$ out of $6$ .

$\frac{2 d}{5} - 4 - \frac{d \cdot 2}{3} + \frac{- 2}{3} \cdot (3 (2))$

Step 1.7.3

Cancel the common factor.

$\frac{2 d}{5} - 4 - \frac{d \cdot 2}{3} + \frac{- 2}{3} \cdot (3 \cdot 2)$

Step 1.7.4

Rewrite the expression.

$\frac{2 d}{5} - 4 - \frac{d \cdot 2}{3} - 2 \cdot 2$

Step 1.8

Multiply $- 2$ by $2$ .

$\frac{2 d}{5} - 4 - \frac{d \cdot 2}{3} - 4$

Step 1.9

Move $2$ to the left of $d$ .

$\frac{2 d}{5} - 4 - \frac{2 d}{3} - 4$

Step 2

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

$\frac{2 d}{5} \cdot \frac{3}{3} - \frac{2 d}{3} - 4 - 4$

Step 3

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

$\frac{2 d}{5} \cdot \frac{3}{3} - \frac{2 d}{3} \cdot \frac{5}{5} - 4 - 4$

Step 4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2 d}{5}$ by $\frac{3}{3}$ .

$\frac{2 d \cdot 3}{5 \cdot 3} - \frac{2 d}{3} \cdot \frac{5}{5} - 4 - 4$

Step 4.2

Multiply $5$ by $3$ .

$\frac{2 d \cdot 3}{15} - \frac{2 d}{3} \cdot \frac{5}{5} - 4 - 4$

Step 4.3

Multiply $\frac{2 d}{3}$ by $\frac{5}{5}$ .

$\frac{2 d \cdot 3}{15} - \frac{2 d \cdot 5}{3 \cdot 5} - 4 - 4$

Step 4.4

Multiply $3$ by $5$ .

$\frac{2 d \cdot 3}{15} - \frac{2 d \cdot 5}{15} - 4 - 4$

Step 5

Combine the numerators over the common denominator.

$\frac{2 d \cdot 3 - 2 d \cdot 5}{15} - 4 - 4$

Step 6

Find the common denominator.

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Step 6.1

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

$\frac{2 d \cdot 3 - 2 d \cdot 5}{15} + \frac{- 4}{1} - 4$

Step 6.2

Multiply $\frac{- 4}{1}$ by $\frac{15}{15}$ .

$\frac{2 d \cdot 3 - 2 d \cdot 5}{15} + \frac{- 4}{1} \cdot \frac{15}{15} - 4$

Step 6.3

Multiply $\frac{- 4}{1}$ by $\frac{15}{15}$ .

$\frac{2 d \cdot 3 - 2 d \cdot 5}{15} + \frac{- 4 \cdot 15}{15} - 4$

Step 6.4

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

$\frac{2 d \cdot 3 - 2 d \cdot 5}{15} + \frac{- 4 \cdot 15}{15} + \frac{- 4}{1}$

Step 6.5

Multiply $\frac{- 4}{1}$ by $\frac{15}{15}$ .

$\frac{2 d \cdot 3 - 2 d \cdot 5}{15} + \frac{- 4 \cdot 15}{15} + \frac{- 4}{1} \cdot \frac{15}{15}$

Step 6.6

Multiply $\frac{- 4}{1}$ by $\frac{15}{15}$ .

$\frac{2 d \cdot 3 - 2 d \cdot 5}{15} + \frac{- 4 \cdot 15}{15} + \frac{- 4 \cdot 15}{15}$

Step 7

Combine the numerators over the common denominator.

$\frac{2 d \cdot 3 - 2 d \cdot 5 - 4 \cdot 15 - 4 \cdot 15}{15}$

Step 8

Simplify each term.

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Step 8.1

Multiply $3$ by $2$ .

$\frac{6 d - 2 d \cdot 5 - 4 \cdot 15 - 4 \cdot 15}{15}$

Step 8.2

Multiply $5$ by $- 2$ .

$\frac{6 d - 10 d - 4 \cdot 15 - 4 \cdot 15}{15}$

Step 8.3

Multiply $- 4$ by $15$ .

$\frac{6 d - 10 d - 60 - 4 \cdot 15}{15}$

Step 8.4

Multiply $- 4$ by $15$ .

$\frac{6 d - 10 d - 60 - 60}{15}$

Step 9

Simplify terms.

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Step 9.1

Subtract $10 d$ from $6 d$ .

$\frac{- 4 d - 60 - 60}{15}$

Step 9.2

Subtract $60$ from $- 60$ .

$\frac{- 4 d - 120}{15}$

Step 9.3

Factor $4$ out of $- 4 d - 120$ .

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Step 9.3.1

Factor $4$ out of $- 4 d$ .

$\frac{4 (- d) - 120}{15}$

Step 9.3.2

Factor $4$ out of $- 120$ .

$\frac{4 (- d) + 4 (- 30)}{15}$

Step 9.3.3

Factor $4$ out of $4 (- d) + 4 (- 30)$ .

$\frac{4 (- d - 30)}{15}$

Step 9.4

Factor $- 1$ out of $- d$ .

$\frac{4 (- (d) - 30)}{15}$

Step 9.5

Rewrite $- 30$ as $- 1 (30)$ .

$\frac{4 (- (d) - 1 (30))}{15}$

Step 9.6

Factor $- 1$ out of $- (d) - 1 (30)$ .

$\frac{4 (- (d + 30))}{15}$

Step 9.7

Simplify the expression.

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Step 9.7.1

Rewrite $- (d + 30)$ as $- 1 (d + 30)$ .

$\frac{4 (- 1 (d + 30))}{15}$

Step 9.7.2

Move the negative in front of the fraction.

$- \frac{4 (d + 30)}{15}$