Evaluate 1/3+(5/6)÷(4/7)

$\frac{1}{3} + \frac{5}{6} \div \frac{4}{7}$

Step 1

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{3} + \frac{5}{6} \cdot \frac{7}{4}$

Multiply $\frac{5}{6} \cdot \frac{7}{4}$ .

Multiply $\frac{5}{6}$ by $\frac{7}{4}$ .

$\frac{1}{3} + \frac{5 \cdot 7}{6 \cdot 4}$

Multiply $5$ by $7$ .

$\frac{1}{3} + \frac{35}{6 \cdot 4}$

Multiply $6$ by $4$ .

$\frac{1}{3} + \frac{35}{24}$

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{3} \cdot \frac{8}{8} + \frac{35}{24}$

Step 3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{8}{8}$ .

$\frac{8}{3 \cdot 8} + \frac{35}{24}$

Multiply $3$ by $8$ .

$\frac{8}{24} + \frac{35}{24}$

Step 4

Combine the numerators over the common denominator.

$\frac{8 + 35}{24}$

Step 5

Add $8$ and $35$ .

$\frac{43}{24}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{43}{24}$

Decimal Form:

$1.791\overline{6}$

Mixed Number Form:

$1 \frac{19}{24}$