Evaluate 5/6+(1/3)/(6/7)

$\frac{5}{6} + \frac{\frac{1}{3}}{\frac{6}{7}}$

Step 1

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{6} + \frac{1}{3} \cdot \frac{7}{6}$

Multiply $\frac{1}{3} \cdot \frac{7}{6}$ .

Multiply $\frac{1}{3}$ by $\frac{7}{6}$ .

$\frac{5}{6} + \frac{7}{3 \cdot 6}$

Multiply $3$ by $6$ .

$\frac{5}{6} + \frac{7}{18}$

Step 2

To write $\frac{5}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{6} \cdot \frac{3}{3} + \frac{7}{18}$

Step 3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{6}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{6 \cdot 3} + \frac{7}{18}$

Multiply $6$ by $3$ .

$\frac{5 \cdot 3}{18} + \frac{7}{18}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 7}{18}$

Step 5

Simplify the numerator.

Multiply $5$ by $3$ .

$\frac{15 + 7}{18}$

Add $15$ and $7$ .

$\frac{22}{18}$

Step 6

Cancel the common factor of $22$ and $18$ .

Factor $2$ out of $22$ .

$\frac{2 (11)}{18}$

Cancel the common factors.

Factor $2$ out of $18$ .

$\frac{2 \cdot 11}{2 \cdot 9}$

Cancel the common factor.

$\frac{2 \cdot 11}{2 \cdot 9}$

Rewrite the expression.

$\frac{11}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{9}$

Decimal Form:

$1.\overline{2}$

Mixed Number Form:

$1 \frac{2}{9}$

Evaluate 5/6+(1/3)/(6/7)

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