Write the Fraction in Simplest Form 6 3/7÷1 13/14

$6 \frac{3}{7} \div 1 \frac{13}{14}$

Step 1

Convert $6 \frac{3}{7}$ to an improper fraction.

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

$(6 + \frac{3}{7}) \div 1 \frac{13}{14}$

Add $6$ and $\frac{3}{7}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(6 \cdot \frac{7}{7} + \frac{3}{7}) \div 1 \frac{13}{14}$

Combine $6$ and $\frac{7}{7}$ .

$(\frac{6 \cdot 7}{7} + \frac{3}{7}) \div 1 \frac{13}{14}$

Combine the numerators over the common denominator.

$\frac{6 \cdot 7 + 3}{7} \div 1 \frac{13}{14}$

Simplify the numerator.

Multiply $6$ by $7$ .

$\frac{42 + 3}{7} \div 1 \frac{13}{14}$

Add $42$ and $3$ .

$\frac{45}{7} \div 1 \frac{13}{14}$

Step 2

Convert $1 \frac{13}{14}$ to an improper fraction.

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

$\frac{45}{7} \div (1 + \frac{13}{14})$

Add $1$ and $\frac{13}{14}$ .

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

$\frac{45}{7} \div (\frac{14}{14} + \frac{13}{14})$

Combine the numerators over the common denominator.

$\frac{45}{7} \div \frac{14 + 13}{14}$

Add $14$ and $13$ .

$\frac{45}{7} \div \frac{27}{14}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{45}{7} \cdot \frac{14}{27}$

Step 4

Cancel the common factor of $9$ .

Factor $9$ out of $45$ .

$\frac{9 (5)}{7} \cdot \frac{14}{27}$

Factor $9$ out of $27$ .

$\frac{9 \cdot 5}{7} \cdot \frac{14}{9 \cdot 3}$

Cancel the common factor.

$\frac{9 \cdot 5}{7} \cdot \frac{14}{9 \cdot 3}$

Rewrite the expression.

$\frac{5}{7} \cdot \frac{14}{3}$

Step 5

Cancel the common factor of $7$ .

Factor $7$ out of $14$ .

$\frac{5}{7} \cdot \frac{7 (2)}{3}$

Cancel the common factor.

$\frac{5}{7} \cdot \frac{7 \cdot 2}{3}$

Rewrite the expression.

$5 (\frac{2}{3})$

Step 6

Combine $5$ and $\frac{2}{3}$ .

$\frac{5 \cdot 2}{3}$

Step 7

Multiply $5$ by $2$ .

$\frac{10}{3}$

Write the Fraction in Simplest Form 6 3/7÷1 13/14

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