Basic Math Examples

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

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

Move the leading negative in $- \frac{3}{4}$ into the numerator.

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

Step 1.1.2

Factor $3$ out of $- 3$ .

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

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $4$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.3

Move the negative in front of the fraction.

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

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

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

Step 1.4.2

Move the leading negative in $- \frac{5}{6}$ into the numerator.

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

Step 1.4.3

Factor $3$ out of $- 3$ .

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

Step 1.4.4

Factor $3$ out of $6$ .

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

Step 1.4.5

Cancel the common factor.

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

Step 1.4.6

Rewrite the expression.

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

Step 1.5

Multiply $\frac{- 1}{4}$ by $\frac{- 5}{2}$ .

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

Step 1.6

Multiply $- 1$ by $- 5$ .

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

Step 1.7

Multiply $4$ by $2$ .

$- \frac{1}{2} + \frac{5}{8}$

Step 2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{1}{2} \cdot \frac{4}{4} + \frac{5}{8}$

Step 3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

$- \frac{4}{2 \cdot 4} + \frac{5}{8}$

Step 3.2

Multiply $2$ by $4$ .

$- \frac{4}{8} + \frac{5}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 4 + 5}{8}$

Step 5

Add $- 4$ and $5$ .

$\frac{1}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$