Basic Math Examples

$(6 \frac{1}{3}) (2 \frac{2}{19}) \div \frac{5}{9}$

Step 1

Convert $6 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$(6 + \frac{1}{3}) (2 \frac{2}{19}) \div \frac{5}{9}$

Step 1.2

Add $6$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(6 \cdot \frac{3}{3} + \frac{1}{3}) (2 \frac{2}{19}) \div \frac{5}{9}$

Step 1.2.2

Combine $6$ and $\frac{3}{3}$ .

$(\frac{6 \cdot 3}{3} + \frac{1}{3}) (2 \frac{2}{19}) \div \frac{5}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 3 + 1}{3} (2 \frac{2}{19}) \div \frac{5}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $3$ .

$\frac{18 + 1}{3} (2 \frac{2}{19}) \div \frac{5}{9}$

Step 1.2.4.2

Add $18$ and $1$ .

$\frac{19}{3} (2 \frac{2}{19}) \div \frac{5}{9}$

Step 2

Convert $2 \frac{2}{19}$ to an improper fraction.

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Step 2.1

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

$\frac{19}{3} (2 + \frac{2}{19}) \div \frac{5}{9}$

Step 2.2

Add $2$ and $\frac{2}{19}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$\frac{19}{3} (2 \cdot \frac{19}{19} + \frac{2}{19}) \div \frac{5}{9}$

Step 2.2.2

Combine $2$ and $\frac{19}{19}$ .

$\frac{19}{3} (\frac{2 \cdot 19}{19} + \frac{2}{19}) \div \frac{5}{9}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{19}{3} \cdot \frac{2 \cdot 19 + 2}{19} \div \frac{5}{9}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $19$ .

$\frac{19}{3} \cdot \frac{38 + 2}{19} \div \frac{5}{9}$

Step 2.2.4.2

Add $38$ and $2$ .

$\frac{19}{3} \cdot \frac{40}{19} \div \frac{5}{9}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{19}{3} \cdot \frac{40}{19} \frac{9}{5}$

Step 4

Cancel the common factor of $19$ .

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Step 4.1

Cancel the common factor.

$\frac{19}{3} \cdot \frac{40}{19} \frac{9}{5}$

Step 4.2

Rewrite the expression.

$\frac{1}{3} \cdot 40 \frac{9}{5}$

Step 5

Combine $\frac{1}{3}$ and $40$ .

$\frac{40}{3} \cdot \frac{9}{5}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $40$ .

$\frac{5 (8)}{3} \cdot \frac{9}{5}$

Step 6.2

Cancel the common factor.

$\frac{5 \cdot 8}{3} \cdot \frac{9}{5}$

Step 6.3

Rewrite the expression.

$\frac{8}{3} \cdot 9$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Factor $3$ out of $9$ .

$\frac{8}{3} \cdot (3 (3))$

Step 7.2

Cancel the common factor.

$\frac{8}{3} \cdot (3 \cdot 3)$

Step 7.3

Rewrite the expression.

$8 \cdot 3$

Step 8

Multiply $8$ by $3$ .

$24$