Divide (3/4)÷7 1/2

$\frac{3}{4} \div 7 \frac{1}{2}$

Step 1

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

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

$\frac{3}{4} \div (7 + \frac{1}{2})$

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

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

$\frac{3}{4} \div (7 \cdot \frac{2}{2} + \frac{1}{2})$

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

$\frac{3}{4} \div (\frac{7 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{3}{4} \div \frac{7 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply $7$ by $2$ .

$\frac{3}{4} \div \frac{14 + 1}{2}$

Add $14$ and $1$ .

$\frac{3}{4} \div \frac{15}{2}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{4} \cdot \frac{2}{15}$

Step 3

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$\frac{3}{4} \cdot \frac{2}{3 (5)}$

Cancel the common factor.

$\frac{3}{4} \cdot \frac{2}{3 \cdot 5}$

Rewrite the expression.

$\frac{1}{4} \cdot \frac{2}{5}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{1}{2 (2)} \cdot \frac{2}{5}$

Cancel the common factor.

$\frac{1}{2 \cdot 2} \cdot \frac{2}{5}$

Rewrite the expression.

$\frac{1}{2} \cdot \frac{1}{5}$

Step 5

Multiply $\frac{1}{2}$ by $\frac{1}{5}$ .

$\frac{1}{2 \cdot 5}$

Step 6

Multiply $2$ by $5$ .

$\frac{1}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{10}$

Decimal Form:

$0.1$

Divide (3/4)÷7 1/2

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