Simplify 4 5/8÷3 1/2

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

Step 1

Convert

$4 \frac{5}{8}$ to an improper fraction.

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

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

Add

$4$ and

$\frac{5}{8}$ .

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{8}{8}$ .

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

Combine

$4$ and

$\frac{8}{8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$4$ by

$8$ .

$\frac{32 + 5}{8} \div 3 \frac{1}{2}$

Add

$32$ and

$5$ .

$\frac{37}{8} \div 3 \frac{1}{2}$

Step 2

Convert

$3 \frac{1}{2}$ to an improper fraction.

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

$\frac{37}{8} \div (3 + \frac{1}{2})$

Add

$3$ and

$\frac{1}{2}$ .

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{37}{8} \div (3 \cdot \frac{2}{2} + \frac{1}{2})$

Combine

$3$ and

$\frac{2}{2}$ .

$\frac{37}{8} \div (\frac{3 \cdot 2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{37}{8} \div \frac{3 \cdot 2 + 1}{2}$

Simplify the numerator.

Multiply

$3$ by

$2$ .

$\frac{37}{8} \div \frac{6 + 1}{2}$

Add

$6$ and

$1$ .

$\frac{37}{8} \div \frac{7}{2}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{37}{8} \cdot \frac{2}{7}$

Step 4

Cancel the common factor of

$2$ .

Factor

$2$ out of

$8$ .

$\frac{37}{2 (4)} \cdot \frac{2}{7}$

Cancel the common factor.

$\frac{37}{2 \cdot 4} \cdot \frac{2}{7}$

Rewrite the expression.

$\frac{37}{4} \cdot \frac{1}{7}$

Step 5

Multiply

$\frac{37}{4}$ by

$\frac{1}{7}$ .

$\frac{37}{4 \cdot 7}$

Step 6

Multiply

$4$ by

$7$ .

$\frac{37}{28}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{37}{28}$

Decimal Form:

$1.32142857 \dots$

Mixed Number Form:

$1 \frac{9}{28}$

Simplify 4 5/8÷3 1/2

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