Simplify 4 2/5÷1 1/10

$4 \frac{2}{5} \div 1 \frac{1}{10}$

Step 1

Convert

$4 \frac{2}{5}$ to an improper fraction.

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

$(4 + \frac{2}{5}) \div 1 \frac{1}{10}$

Add

$4$ and

$\frac{2}{5}$ .

To write

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

$\frac{5}{5}$ .

$(4 \cdot \frac{5}{5} + \frac{2}{5}) \div 1 \frac{1}{10}$

Combine

$4$ and

$\frac{5}{5}$ .

$(\frac{4 \cdot 5}{5} + \frac{2}{5}) \div 1 \frac{1}{10}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 + 2}{5} \div 1 \frac{1}{10}$

Simplify the numerator.

Multiply

$4$ by

$5$ .

$\frac{20 + 2}{5} \div 1 \frac{1}{10}$

Add

$20$ and

$2$ .

$\frac{22}{5} \div 1 \frac{1}{10}$

Step 2

Convert

$1 \frac{1}{10}$ to an improper fraction.

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

$\frac{22}{5} \div (1 + \frac{1}{10})$

Add

$1$ and

$\frac{1}{10}$ .

Write

$1$ as a fraction with a common denominator.

$\frac{22}{5} \div (\frac{10}{10} + \frac{1}{10})$

Combine the numerators over the common denominator.

$\frac{22}{5} \div \frac{10 + 1}{10}$

Add

$10$ and

$1$ .

$\frac{22}{5} \div \frac{11}{10}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{22}{5} \cdot \frac{10}{11}$

Step 4

Cancel the common factor of

$11$ .

Factor

$11$ out of

$22$ .

$\frac{11 (2)}{5} \cdot \frac{10}{11}$

Cancel the common factor.

$\frac{11 \cdot 2}{5} \cdot \frac{10}{11}$

Rewrite the expression.

$\frac{2}{5} \cdot 10$

Step 5

Cancel the common factor of

$5$ .

Factor

$5$ out of

$10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 \cdot 2$

Step 6

Multiply

$2$ by

$2$ .

$4$

Simplify 4 2/5÷1 1/10

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