Divide 1 6/7÷5 3/4

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

Step 1

Convert $1 \frac{6}{7}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

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

Add $1$ and $\frac{6}{7}$ .

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $7$ and $6$ .

$\frac{13}{7} \div 5 \frac{3}{4}$

Step 2

Convert $5 \frac{3}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{13}{7} \div (5 + \frac{3}{4})$

Add $5$ and $\frac{3}{4}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{13}{7} \div (5 \cdot \frac{4}{4} + \frac{3}{4})$

Combine $5$ and $\frac{4}{4}$ .

$\frac{13}{7} \div (\frac{5 \cdot 4}{4} + \frac{3}{4})$

Combine the numerators over the common denominator.

$\frac{13}{7} \div \frac{5 \cdot 4 + 3}{4}$

Simplify the numerator.

Multiply $5$ by $4$ .

$\frac{13}{7} \div \frac{20 + 3}{4}$

Add $20$ and $3$ .

$\frac{13}{7} \div \frac{23}{4}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{13}{7} \cdot \frac{4}{23}$

Step 4

Multiply $\frac{13}{7} \cdot \frac{4}{23}$ .

Multiply $\frac{13}{7}$ by $\frac{4}{23}$ .

$\frac{13 \cdot 4}{7 \cdot 23}$

Multiply $13$ by $4$ .

$\frac{52}{7 \cdot 23}$

Multiply $7$ by $23$ .

$\frac{52}{161}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{52}{161}$

Decimal Form:

$0.32298136 \dots$