Write the Fraction in Simplest Form 8 2/3÷1 7/9

$8 \frac{2}{3} \div 1 \frac{7}{9}$

Step 1

Convert $8 \frac{2}{3}$ to an improper fraction.

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

$(8 + \frac{2}{3}) \div 1 \frac{7}{9}$

Add $8$ and $\frac{2}{3}$ .

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

$(8 \cdot \frac{3}{3} + \frac{2}{3}) \div 1 \frac{7}{9}$

Combine $8$ and $\frac{3}{3}$ .

$(\frac{8 \cdot 3}{3} + \frac{2}{3}) \div 1 \frac{7}{9}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 3 + 2}{3} \div 1 \frac{7}{9}$

Simplify the numerator.

Multiply $8$ by $3$ .

$\frac{24 + 2}{3} \div 1 \frac{7}{9}$

Add $24$ and $2$ .

$\frac{26}{3} \div 1 \frac{7}{9}$

Step 2

Convert $1 \frac{7}{9}$ to an improper fraction.

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

$\frac{26}{3} \div (1 + \frac{7}{9})$

Add $1$ and $\frac{7}{9}$ .

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

$\frac{26}{3} \div (\frac{9}{9} + \frac{7}{9})$

Combine the numerators over the common denominator.

$\frac{26}{3} \div \frac{9 + 7}{9}$

Add $9$ and $7$ .

$\frac{26}{3} \div \frac{16}{9}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{26}{3} \cdot \frac{9}{16}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $26$ .

$\frac{2 (13)}{3} \cdot \frac{9}{16}$

Factor $2$ out of $16$ .

$\frac{2 \cdot 13}{3} \cdot \frac{9}{2 \cdot 8}$

Cancel the common factor.

$\frac{2 \cdot 13}{3} \cdot \frac{9}{2 \cdot 8}$

Rewrite the expression.

$\frac{13}{3} \cdot \frac{9}{8}$

Step 5

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{13}{3} \cdot \frac{3 (3)}{8}$

Cancel the common factor.

$\frac{13}{3} \cdot \frac{3 \cdot 3}{8}$

Rewrite the expression.

$13 (\frac{3}{8})$

Step 6

Combine $13$ and $\frac{3}{8}$ .

$\frac{13 \cdot 3}{8}$

Step 7

Multiply $13$ by $3$ .

$\frac{39}{8}$

Write the Fraction in Simplest Form 8 2/3÷1 7/9

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