Evaluate (5/8+3/4)/(-2/3-5/6)

$\frac{\frac{5}{8} + \frac{3}{4}}{- \frac{2}{3} - \frac{5}{6}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $24$ .

Multiply $\frac{\frac{5}{8} + \frac{3}{4}}{- \frac{2}{3} - \frac{5}{6}}$ by $\frac{24}{24}$ .

$\frac{24}{24} \cdot \frac{\frac{5}{8} + \frac{3}{4}}{- \frac{2}{3} - \frac{5}{6}}$

Combine.

$\frac{24 (\frac{5}{8} + \frac{3}{4})}{24 (- \frac{2}{3} - \frac{5}{6})}$

Step 2

Apply the distributive property.

$\frac{24 (\frac{5}{8}) + 24 (\frac{3}{4})}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $8$ .

Factor $8$ out of $24$ .

$\frac{8 (3) \frac{5}{8} + 24 (\frac{3}{4})}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Cancel the common factor.

$\frac{8 \cdot 3 \frac{5}{8} + 24 (\frac{3}{4})}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Rewrite the expression.

$\frac{3 \cdot 5 + 24 (\frac{3}{4})}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Multiply $3$ by $5$ .

$\frac{15 + 24 (\frac{3}{4})}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Cancel the common factor of $4$ .

Factor $4$ out of $24$ .

$\frac{15 + 4 (6) \frac{3}{4}}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Cancel the common factor.

$\frac{15 + 4 \cdot 6 \frac{3}{4}}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Rewrite the expression.

$\frac{15 + 6 \cdot 3}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Multiply $6$ by $3$ .

$\frac{15 + 18}{24 (- \frac{2}{3}) + 24 (- \frac{5}{6})}$

Cancel the common factor of $3$ .

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

$\frac{15 + 18}{24 (\frac{- 2}{3}) + 24 (- \frac{5}{6})}$

Factor $3$ out of $24$ .

$\frac{15 + 18}{3 (8) \frac{- 2}{3} + 24 (- \frac{5}{6})}$

Cancel the common factor.

$\frac{15 + 18}{3 \cdot 8 \frac{- 2}{3} + 24 (- \frac{5}{6})}$

Rewrite the expression.

$\frac{15 + 18}{8 \cdot - 2 + 24 (- \frac{5}{6})}$

Multiply $8$ by $- 2$ .

$\frac{15 + 18}{- 16 + 24 (- \frac{5}{6})}$

Cancel the common factor of $6$ .

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

$\frac{15 + 18}{- 16 + 24 (\frac{- 5}{6})}$

Factor $6$ out of $24$ .

$\frac{15 + 18}{- 16 + 6 (4) \frac{- 5}{6}}$

Cancel the common factor.

$\frac{15 + 18}{- 16 + 6 \cdot 4 \frac{- 5}{6}}$

Rewrite the expression.

$\frac{15 + 18}{- 16 + 4 \cdot - 5}$

Multiply $4$ by $- 5$ .

$\frac{15 + 18}{- 16 - 20}$

Step 4

Reduce the expression by cancelling the common factors.

Add $15$ and $18$ .

$\frac{33}{- 16 - 20}$

Subtract $20$ from $- 16$ .

$\frac{33}{- 36}$

Cancel the common factor of $33$ and $- 36$ .

Factor $3$ out of $33$ .

$\frac{3 (11)}{- 36}$

Cancel the common factors.

Factor $3$ out of $- 36$ .

$\frac{3 \cdot 11}{3 \cdot - 12}$

Cancel the common factor.

$\frac{3 \cdot 11}{3 \cdot - 12}$

Rewrite the expression.

$\frac{11}{- 12}$

Move the negative in front of the fraction.

$- \frac{11}{12}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{11}{12}$

Decimal Form:

$- 0.91\overline{6}$

Evaluate (5/8+3/4)/(-2/3-5/6)

Related Questions

Support LCMGCF.com by disabling your adblocker.