Write the Fraction in Simplest Form 7 1/2÷2 5/8

$7 \frac{1}{2} \div 2 \frac{5}{8}$

Step 1

Convert $7 \frac{1}{2}$ to an improper fraction.

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

$(7 + \frac{1}{2}) \div 2 \frac{5}{8}$

Add $7$ and $\frac{1}{2}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(7 \cdot \frac{2}{2} + \frac{1}{2}) \div 2 \frac{5}{8}$

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

$(\frac{7 \cdot 2}{2} + \frac{1}{2}) \div 2 \frac{5}{8}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 1}{2} \div 2 \frac{5}{8}$

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{14 + 1}{2} \div 2 \frac{5}{8}$

Add $14$ and $1$ .

$\frac{15}{2} \div 2 \frac{5}{8}$

Step 2

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

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

$\frac{15}{2} \div (2 + \frac{5}{8})$

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

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

$\frac{15}{2} \div (2 \cdot \frac{8}{8} + \frac{5}{8})$

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

$\frac{15}{2} \div (\frac{2 \cdot 8}{8} + \frac{5}{8})$

Combine the numerators over the common denominator.

$\frac{15}{2} \div \frac{2 \cdot 8 + 5}{8}$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{15}{2} \div \frac{16 + 5}{8}$

Add $16$ and $5$ .

$\frac{15}{2} \div \frac{21}{8}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{15}{2} \cdot \frac{8}{21}$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$\frac{3 (5)}{2} \cdot \frac{8}{21}$

Factor $3$ out of $21$ .

$\frac{3 \cdot 5}{2} \cdot \frac{8}{3 \cdot 7}$

Cancel the common factor.

$\frac{3 \cdot 5}{2} \cdot \frac{8}{3 \cdot 7}$

Rewrite the expression.

$\frac{5}{2} \cdot \frac{8}{7}$

Step 5

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{5}{2} \cdot \frac{2 (4)}{7}$

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 \cdot 4}{7}$

Rewrite the expression.

$5 (\frac{4}{7})$

Step 6

Combine $5$ and $\frac{4}{7}$ .

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

Step 7

Multiply $5$ by $4$ .

$\frac{20}{7}$

Write the Fraction in Simplest Form 7 1/2÷2 5/8

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