Divide 5 1/4÷(3/4)

$5 \frac{1}{4} \div \frac{3}{4}$

Step 1

Convert $5 \frac{1}{4}$ to an improper fraction.

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

$(5 + \frac{1}{4}) \div \frac{3}{4}$

Add $5$ and $\frac{1}{4}$ .

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(5 \cdot \frac{4}{4} + \frac{1}{4}) \div \frac{3}{4}$

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

$(\frac{5 \cdot 4}{4} + \frac{1}{4}) \div \frac{3}{4}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + 1}{4} \div \frac{3}{4}$

Simplify the numerator.

Multiply $5$ by $4$ .

$\frac{20 + 1}{4} \div \frac{3}{4}$

Add $20$ and $1$ .

$\frac{21}{4} \div \frac{3}{4}$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{21}{4} \cdot \frac{4}{3}$

Step 3

Cancel the common factor of $3$ .

Factor $3$ out of $21$ .

$\frac{3 (7)}{4} \cdot \frac{4}{3}$

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$7$