Simplify 6 2/5÷1 13/15

$6 \frac{2}{5} \div 1 \frac{13}{15}$

Step 1

Convert $6 \frac{2}{5}$ to an improper fraction.

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

$(6 + \frac{2}{5}) \div 1 \frac{13}{15}$

Add $6$ and $\frac{2}{5}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(6 \cdot \frac{5}{5} + \frac{2}{5}) \div 1 \frac{13}{15}$

Combine $6$ and $\frac{5}{5}$ .

$(\frac{6 \cdot 5}{5} + \frac{2}{5}) \div 1 \frac{13}{15}$

Combine the numerators over the common denominator.

$\frac{6 \cdot 5 + 2}{5} \div 1 \frac{13}{15}$

Simplify the numerator.

Multiply $6$ by $5$ .

$\frac{30 + 2}{5} \div 1 \frac{13}{15}$

Add $30$ and $2$ .

$\frac{32}{5} \div 1 \frac{13}{15}$

Step 2

Convert $1 \frac{13}{15}$ to an improper fraction.

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

$\frac{32}{5} \div (1 + \frac{13}{15})$

Add $1$ and $\frac{13}{15}$ .

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

$\frac{32}{5} \div (\frac{15}{15} + \frac{13}{15})$

Combine the numerators over the common denominator.

$\frac{32}{5} \div \frac{15 + 13}{15}$

Add $15$ and $13$ .

$\frac{32}{5} \div \frac{28}{15}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{32}{5} \cdot \frac{15}{28}$

Step 4

Cancel the common factor of $4$ .

Factor $4$ out of $32$ .

$\frac{4 (8)}{5} \cdot \frac{15}{28}$

Factor $4$ out of $28$ .

$\frac{4 \cdot 8}{5} \cdot \frac{15}{4 \cdot 7}$

Cancel the common factor.

$\frac{4 \cdot 8}{5} \cdot \frac{15}{4 \cdot 7}$

Rewrite the expression.

$\frac{8}{5} \cdot \frac{15}{7}$

Step 5

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$\frac{8}{5} \cdot \frac{5 (3)}{7}$

Cancel the common factor.

$\frac{8}{5} \cdot \frac{5 \cdot 3}{7}$

Rewrite the expression.

$8 (\frac{3}{7})$

Step 6

Combine $8$ and $\frac{3}{7}$ .

$\frac{8 \cdot 3}{7}$

Step 7

Multiply $8$ by $3$ .

$\frac{24}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{24}{7}$

Decimal Form:

$3.\overline{428571}$

Mixed Number Form:

$3 \frac{3}{7}$

Simplify 6 2/5÷1 13/15

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