Basic Math Examples

$4 \frac{4}{9} \div 1 \frac{1}{5}$

Step 1

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

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Step 1.1

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

$(4 + \frac{4}{9}) \div 1 \frac{1}{5}$

Step 1.2

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

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Step 1.2.1

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

$(4 \cdot \frac{9}{9} + \frac{4}{9}) \div 1 \frac{1}{5}$

Step 1.2.2

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

$(\frac{4 \cdot 9}{9} + \frac{4}{9}) \div 1 \frac{1}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 9 + 4}{9} \div 1 \frac{1}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $9$ .

$\frac{36 + 4}{9} \div 1 \frac{1}{5}$

Step 1.2.4.2

Add $36$ and $4$ .

$\frac{40}{9} \div 1 \frac{1}{5}$

Step 2

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

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Step 2.1

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

$\frac{40}{9} \div (1 + \frac{1}{5})$

Step 2.2

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

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

$\frac{40}{9} \div (\frac{5}{5} + \frac{1}{5})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{40}{9} \div \frac{5 + 1}{5}$

Step 2.2.3

Add $5$ and $1$ .

$\frac{40}{9} \div \frac{6}{5}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{40}{9} \cdot \frac{5}{6}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $40$ .

$\frac{2 (20)}{9} \cdot \frac{5}{6}$

Step 4.2

Factor $2$ out of $6$ .

$\frac{2 \cdot 20}{9} \cdot \frac{5}{2 \cdot 3}$

Step 4.3

Cancel the common factor.

$\frac{2 \cdot 20}{9} \cdot \frac{5}{2 \cdot 3}$

Step 4.4

Rewrite the expression.

$\frac{20}{9} \cdot \frac{5}{3}$

Step 5

Multiply $\frac{20}{9}$ by $\frac{5}{3}$ .

$\frac{20 \cdot 5}{9 \cdot 3}$

Step 6

Multiply.

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Step 6.1

Multiply $20$ by $5$ .

$\frac{100}{9 \cdot 3}$

Step 6.2

Multiply $9$ by $3$ .

$\frac{100}{27}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{100}{27}$

Decimal Form:

$3.\overline{703}$

Mixed Number Form:

$3 \frac{19}{27}$