Divide 2 1/2÷3 5/8

$2 \frac{1}{2} \div 3 \frac{5}{8}$

Step 1

Convert $2 \frac{1}{2}$ to an improper fraction.

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

$(2 + \frac{1}{2}) \div 3 \frac{5}{8}$

Add $2$ and $\frac{1}{2}$ .

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

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \div 3 \frac{5}{8}$

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

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \div 3 \frac{5}{8}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} \div 3 \frac{5}{8}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} \div 3 \frac{5}{8}$

Add $4$ and $1$ .

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

Step 2

Convert $3 \frac{5}{8}$ to an improper fraction.

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

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

Add $3$ and $\frac{5}{8}$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $8$ .

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

Add $24$ and $5$ .

$\frac{5}{2} \div \frac{29}{8}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} \cdot \frac{8}{29}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{5}{2} \cdot \frac{2 (4)}{29}$

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 \cdot 4}{29}$

Rewrite the expression.

$5 (\frac{4}{29})$

Step 5

Combine $5$ and $\frac{4}{29}$ .

$\frac{5 \cdot 4}{29}$

Step 6

Multiply $5$ by $4$ .

$\frac{20}{29}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{20}{29}$

Decimal Form:

$0.68965517 \dots$

Divide 2 1/2÷3 5/8

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