Basic Math Examples

5 \frac{1}{3} \div 2 \frac{2}{3}

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

Step 1

Convert

$5 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add

$5$ and

$\frac{1}{3}$ .

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Step 1.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

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

Step 1.2.2

Combine

$5$ and

$\frac{3}{3}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$5$ by

$3$ .

$\frac{15 + 1}{3} \div 2 \frac{2}{3}$

Step 1.2.4.2

Add

$15$ and

$1$ .

$\frac{16}{3} \div 2 \frac{2}{3}$

Step 2

Convert

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

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Step 2.1

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

$\frac{16}{3} \div (2 + \frac{2}{3})$

Step 2.2

Add

$2$ and

$\frac{2}{3}$ .

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Step 2.2.1

To write

$2$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{16}{3} \div (2 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

Combine

$2$ and

$\frac{3}{3}$ .

$\frac{16}{3} \div (\frac{2 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{16}{3} \div \frac{2 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$3$ .

$\frac{16}{3} \div \frac{6 + 2}{3}$

Step 2.2.4.2

Add

$6$ and

$2$ .

$\frac{16}{3} \div \frac{8}{3}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$\frac{16}{3} \cdot \frac{3}{8}$

Step 4

Cancel the common factor of

$8$ .

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Step 4.1

Factor

$8$ out of

$16$ .

$\frac{8 (2)}{3} \cdot \frac{3}{8}$

Step 4.2

Cancel the common factor.

$\frac{8 \cdot 2}{3} \cdot \frac{3}{8}$

Step 4.3

Rewrite the expression.

$\frac{2}{3} \cdot 3$

Step 5

Cancel the common factor of

$3$ .

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Step 5.1

Cancel the common factor.

$\frac{2}{3} \cdot 3$

Step 5.2

Rewrite the expression.

$2$