Write the Fraction in Simplest Form 9 3/4÷4 1/8

$9 \frac{3}{4} \div 4 \frac{1}{8}$

Step 1

Convert $9 \frac{3}{4}$ to an improper fraction.

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

$(9 + \frac{3}{4}) \div 4 \frac{1}{8}$

Add $9$ and $\frac{3}{4}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(9 \cdot \frac{4}{4} + \frac{3}{4}) \div 4 \frac{1}{8}$

Combine $9$ and $\frac{4}{4}$ .

$(\frac{9 \cdot 4}{4} + \frac{3}{4}) \div 4 \frac{1}{8}$

Combine the numerators over the common denominator.

$\frac{9 \cdot 4 + 3}{4} \div 4 \frac{1}{8}$

Simplify the numerator.

Multiply $9$ by $4$ .

$\frac{36 + 3}{4} \div 4 \frac{1}{8}$

Add $36$ and $3$ .

$\frac{39}{4} \div 4 \frac{1}{8}$

Step 2

Convert $4 \frac{1}{8}$ to an improper fraction.

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

$\frac{39}{4} \div (4 + \frac{1}{8})$

Add $4$ and $\frac{1}{8}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{39}{4} \div (4 \cdot \frac{8}{8} + \frac{1}{8})$

Combine $4$ and $\frac{8}{8}$ .

$\frac{39}{4} \div (\frac{4 \cdot 8}{8} + \frac{1}{8})$

Combine the numerators over the common denominator.

$\frac{39}{4} \div \frac{4 \cdot 8 + 1}{8}$

Simplify the numerator.

Multiply $4$ by $8$ .

$\frac{39}{4} \div \frac{32 + 1}{8}$

Add $32$ and $1$ .

$\frac{39}{4} \div \frac{33}{8}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{39}{4} \cdot \frac{8}{33}$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $39$ .

$\frac{3 (13)}{4} \cdot \frac{8}{33}$

Factor $3$ out of $33$ .

$\frac{3 \cdot 13}{4} \cdot \frac{8}{3 \cdot 11}$

Cancel the common factor.

$\frac{3 \cdot 13}{4} \cdot \frac{8}{3 \cdot 11}$

Rewrite the expression.

$\frac{13}{4} \cdot \frac{8}{11}$

Step 5

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{13}{4} \cdot \frac{4 (2)}{11}$

Cancel the common factor.

$\frac{13}{4} \cdot \frac{4 \cdot 2}{11}$

Rewrite the expression.

$13 (\frac{2}{11})$

Step 6

Combine $13$ and $\frac{2}{11}$ .

$\frac{13 \cdot 2}{11}$

Step 7

Multiply $13$ by $2$ .

$\frac{26}{11}$

Write the Fraction in Simplest Form 9 3/4÷4 1/8

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