Algebra Examples

$- 3 (\frac{2}{15}) + \frac{3}{4}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ .

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Step 1.1.1

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{2}{15} + \frac{3}{4}$

Step 1.1.2

Factor $3$ out of $15$ .

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

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

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

Step 1.2

Rewrite $- 1 (\frac{2}{5})$ as $- (\frac{2}{5})$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{5}$ by $\frac{4}{4}$ .

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

Step 4.2

Multiply $5$ by $4$ .

$- \frac{2 \cdot 4}{20} + \frac{3}{4} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$- \frac{2 \cdot 4}{20} + \frac{3 \cdot 5}{4 \cdot 5}$

Step 4.4

Multiply $4$ by $5$ .

$- \frac{2 \cdot 4}{20} + \frac{3 \cdot 5}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 4 + 3 \cdot 5}{20}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 2$ by $4$ .

$\frac{- 8 + 3 \cdot 5}{20}$

Step 6.2

Multiply $3$ by $5$ .

$\frac{- 8 + 15}{20}$

Step 6.3

Add $- 8$ and $15$ .

$\frac{7}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{20}$

Decimal Form:

$0.35$