Evaluate (1/6+5/8)÷(7/12-1/6)

$(\frac{1}{6} + \frac{5}{8}) \div (\frac{7}{12} - \frac{1}{6})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{1}{6} + \frac{5}{8}}{\frac{7}{12} - \frac{1}{6}}$

Step 2

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

Multiply $\frac{\frac{1}{6} + \frac{5}{8}}{\frac{7}{12} - \frac{1}{6}}$ by $\frac{24}{24}$ .

$\frac{24}{24} \cdot \frac{\frac{1}{6} + \frac{5}{8}}{\frac{7}{12} - \frac{1}{6}}$

Combine.

$\frac{24 (\frac{1}{6} + \frac{5}{8})}{24 (\frac{7}{12} - \frac{1}{6})}$

Step 3

Apply the distributive property.

$\frac{24 (\frac{1}{6}) + 24 (\frac{5}{8})}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Step 4

Simplify by cancelling.

Cancel the common factor of $6$ .

Factor $6$ out of $24$ .

$\frac{6 (4) \frac{1}{6} + 24 (\frac{5}{8})}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Cancel the common factor.

$\frac{6 \cdot 4 \frac{1}{6} + 24 (\frac{5}{8})}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Rewrite the expression.

$\frac{4 + 24 (\frac{5}{8})}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Cancel the common factor of $8$ .

Factor $8$ out of $24$ .

$\frac{4 + 8 (3) \frac{5}{8}}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Cancel the common factor.

$\frac{4 + 8 \cdot 3 \frac{5}{8}}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Rewrite the expression.

$\frac{4 + 3 \cdot 5}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Multiply $3$ by $5$ .

$\frac{4 + 15}{24 (\frac{7}{12}) + 24 (- \frac{1}{6})}$

Cancel the common factor of $12$ .

Factor $12$ out of $24$ .

$\frac{4 + 15}{12 (2) \frac{7}{12} + 24 (- \frac{1}{6})}$

Cancel the common factor.

$\frac{4 + 15}{12 \cdot 2 \frac{7}{12} + 24 (- \frac{1}{6})}$

Rewrite the expression.

$\frac{4 + 15}{2 \cdot 7 + 24 (- \frac{1}{6})}$

Multiply $2$ by $7$ .

$\frac{4 + 15}{14 + 24 (- \frac{1}{6})}$

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$\frac{4 + 15}{14 + 24 (\frac{- 1}{6})}$

Factor $6$ out of $24$ .

$\frac{4 + 15}{14 + 6 (4) \frac{- 1}{6}}$

Cancel the common factor.

$\frac{4 + 15}{14 + 6 \cdot 4 \frac{- 1}{6}}$

Rewrite the expression.

$\frac{4 + 15}{14 + 4 \cdot - 1}$

Multiply $4$ by $- 1$ .

$\frac{4 + 15}{14 - 4}$

Step 5

Simplify by adding and subtracting.

Add $4$ and $15$ .

$\frac{19}{14 - 4}$

Subtract $4$ from $14$ .

$\frac{19}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{10}$

Decimal Form:

$1.9$

Mixed Number Form:

$1 \frac{9}{10}$

Evaluate (1/6+5/8)÷(7/12-1/6)

Related Questions