Evaluate 3/4+(1/6)÷(2/5)

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

Step 1

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

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

Multiply $\frac{1}{6} \cdot \frac{5}{2}$ .

Multiply $\frac{1}{6}$ by $\frac{5}{2}$ .

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

Multiply $6$ by $2$ .

$\frac{3}{4} + \frac{5}{12}$

Step 2

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

$\frac{3}{4} \cdot \frac{3}{3} + \frac{5}{12}$

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 \cdot 3}{4 \cdot 3} + \frac{5}{12}$

Multiply $4$ by $3$ .

$\frac{3 \cdot 3}{12} + \frac{5}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 5}{12}$

Step 5

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 + 5}{12}$

Add $9$ and $5$ .

$\frac{14}{12}$

Step 6

Cancel the common factor of $14$ and $12$ .

Factor $2$ out of $14$ .

$\frac{2 (7)}{12}$

Cancel the common factors.

Factor $2$ out of $12$ .

$\frac{2 \cdot 7}{2 \cdot 6}$

Cancel the common factor.

$\frac{2 \cdot 7}{2 \cdot 6}$

Rewrite the expression.

$\frac{7}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{6}$

Decimal Form:

$1.1\overline{6}$

Mixed Number Form:

$1 \frac{1}{6}$

Evaluate 3/4+(1/6)÷(2/5)

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