Evaluate 6 3/4÷2 5/8

$6 \frac{3}{4} \div 2 \frac{5}{8}$

Step 1

Convert $6 \frac{3}{4}$ to an improper fraction.

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

$(6 + \frac{3}{4}) \div 2 \frac{5}{8}$

Add $6$ and $\frac{3}{4}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(6 \cdot \frac{4}{4} + \frac{3}{4}) \div 2 \frac{5}{8}$

Combine $6$ and $\frac{4}{4}$ .

$(\frac{6 \cdot 4}{4} + \frac{3}{4}) \div 2 \frac{5}{8}$

Combine the numerators over the common denominator.

$\frac{6 \cdot 4 + 3}{4} \div 2 \frac{5}{8}$

Simplify the numerator.

Multiply $6$ by $4$ .

$\frac{24 + 3}{4} \div 2 \frac{5}{8}$

Add $24$ and $3$ .

$\frac{27}{4} \div 2 \frac{5}{8}$

Step 2

Convert $2 \frac{5}{8}$ to an improper fraction.

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

$\frac{27}{4} \div (2 + \frac{5}{8})$

Add $2$ and $\frac{5}{8}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{27}{4} \div (2 \cdot \frac{8}{8} + \frac{5}{8})$

Combine $2$ and $\frac{8}{8}$ .

$\frac{27}{4} \div (\frac{2 \cdot 8}{8} + \frac{5}{8})$

Combine the numerators over the common denominator.

$\frac{27}{4} \div \frac{2 \cdot 8 + 5}{8}$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{27}{4} \div \frac{16 + 5}{8}$

Add $16$ and $5$ .

$\frac{27}{4} \div \frac{21}{8}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{27}{4} \cdot \frac{8}{21}$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$\frac{3 (9)}{4} \cdot \frac{8}{21}$

Factor $3$ out of $21$ .

$\frac{3 \cdot 9}{4} \cdot \frac{8}{3 \cdot 7}$

Cancel the common factor.

$\frac{3 \cdot 9}{4} \cdot \frac{8}{3 \cdot 7}$

Rewrite the expression.

$\frac{9}{4} \cdot \frac{8}{7}$

Step 5

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{9}{4} \cdot \frac{4 (2)}{7}$

Cancel the common factor.

$\frac{9}{4} \cdot \frac{4 \cdot 2}{7}$

Rewrite the expression.

$9 (\frac{2}{7})$

Step 6

Combine $9$ and $\frac{2}{7}$ .

$\frac{9 \cdot 2}{7}$

Step 7

Multiply $9$ by $2$ .

$\frac{18}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{18}{7}$

Decimal Form:

$2.\overline{571428}$

Mixed Number Form:

$2 \frac{4}{7}$

Evaluate 6 3/4÷2 5/8

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