Basic Math Examples

$8 \frac{2}{3} \cdot 2 \frac{1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 1

Convert $8 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$(8 + \frac{2}{3}) \cdot 2 \frac{1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 1.2

Add $8$ and $\frac{2}{3}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(8 \cdot \frac{3}{3} + \frac{2}{3}) \cdot 2 \frac{1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 1.2.2

Combine $8$ and $\frac{3}{3}$ .

$(\frac{8 \cdot 3}{3} + \frac{2}{3}) \cdot 2 \frac{1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 3 + 2}{3} \cdot 2 \frac{1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $3$ .

$\frac{24 + 2}{3} \cdot 2 \frac{1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 1.2.4.2

Add $24$ and $2$ .

$\frac{26}{3} \cdot 2 \frac{1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 2

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{26}{3} \cdot (2 + \frac{1}{4}) \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 2.2

Add $2$ and $\frac{1}{4}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{26}{3} \cdot (2 \cdot \frac{4}{4} + \frac{1}{4}) \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 2.2.2

Combine $2$ and $\frac{4}{4}$ .

$\frac{26}{3} \cdot (\frac{2 \cdot 4}{4} + \frac{1}{4}) \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{26}{3} \cdot \frac{2 \cdot 4 + 1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$\frac{26}{3} \cdot \frac{8 + 1}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 2.2.4.2

Add $8$ and $1$ .

$\frac{26}{3} \cdot \frac{9}{4} \div 3 \frac{1}{2} \div 2 \frac{1}{3}$

Step 3

Convert $3 \frac{1}{2}$ to an improper fraction.

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Step 3.1

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

$\frac{26}{3} \cdot \frac{9}{4} \div (3 + \frac{1}{2}) \div 2 \frac{1}{3}$

Step 3.2

Add $3$ and $\frac{1}{2}$ .

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{26}{3} \cdot \frac{9}{4} \div (3 \cdot \frac{2}{2} + \frac{1}{2}) \div 2 \frac{1}{3}$

Step 3.2.2

Combine $3$ and $\frac{2}{2}$ .

$\frac{26}{3} \cdot \frac{9}{4} \div (\frac{3 \cdot 2}{2} + \frac{1}{2}) \div 2 \frac{1}{3}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{3 \cdot 2 + 1}{2} \div 2 \frac{1}{3}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $2$ .

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{6 + 1}{2} \div 2 \frac{1}{3}$

Step 3.2.4.2

Add $6$ and $1$ .

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \div 2 \frac{1}{3}$

Step 4

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 4.1

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

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \div (2 + \frac{1}{3})$

Step 4.2

Add $2$ and $\frac{1}{3}$ .

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Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \div (2 \cdot \frac{3}{3} + \frac{1}{3})$

Step 4.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \div (\frac{2 \cdot 3}{3} + \frac{1}{3})$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \div \frac{2 \cdot 3 + 1}{3}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $2$ by $3$ .

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \div \frac{6 + 1}{3}$

Step 4.2.4.2

Add $6$ and $1$ .

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \div \frac{7}{3}$

Step 5

To divide by a fraction, multiply by its reciprocal.

$\frac{26}{3} \cdot \frac{9}{4} \div \frac{7}{2} \cdot \frac{3}{7}$

Step 6

To divide by a fraction, multiply by its reciprocal.

$\frac{26}{3} \cdot \frac{9}{4} \frac{2}{7} \frac{3}{7}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $26$ .

$\frac{2 (13)}{3} \cdot \frac{9}{4} \frac{2}{7} \frac{3}{7}$

Step 7.2

Factor $2$ out of $4$ .

$\frac{2 \cdot 13}{3} \cdot \frac{9}{2 \cdot 2} \frac{2}{7} \frac{3}{7}$

Step 7.3

Cancel the common factor.

$\frac{2 \cdot 13}{3} \cdot \frac{9}{2 \cdot 2} \frac{2}{7} \frac{3}{7}$

Step 7.4

Rewrite the expression.

$\frac{13}{3} \cdot \frac{9}{2} \frac{2}{7} \frac{3}{7}$

Step 8

Cancel the common factor of $3$ .

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Step 8.1

Factor $3$ out of $9$ .

$\frac{13}{3} \cdot \frac{3 (3)}{2} \frac{2}{7} \frac{3}{7}$

Step 8.2

Cancel the common factor.

$\frac{13}{3} \cdot \frac{3 \cdot 3}{2} \frac{2}{7} \frac{3}{7}$

Step 8.3

Rewrite the expression.

$13 \cdot \frac{3}{2} \frac{2}{7} \frac{3}{7}$

Step 9

Combine $13$ and $\frac{3}{2}$ .

$\frac{13 \cdot 3}{2} \cdot \frac{2}{7} \frac{3}{7}$

Step 10

Multiply $13$ by $3$ .

$\frac{39}{2} \cdot \frac{2}{7} \frac{3}{7}$

Step 11

Cancel the common factor of $2$ .

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Step 11.1

Cancel the common factor.

$\frac{39}{2} \cdot \frac{2}{7} \frac{3}{7}$

Step 11.2

Rewrite the expression.

$39 (\frac{1}{7}) \frac{3}{7}$

Step 12

Combine $39$ and $\frac{1}{7}$ .

$\frac{39}{7} \cdot \frac{3}{7}$

Step 13

Multiply $\frac{39}{7} \cdot \frac{3}{7}$ .

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Step 13.1

Multiply $\frac{39}{7}$ by $\frac{3}{7}$ .

$\frac{39 \cdot 3}{7 \cdot 7}$

Step 13.2

Multiply $39$ by $3$ .

$\frac{117}{7 \cdot 7}$

Step 13.3

Multiply $7$ by $7$ .

$\frac{117}{49}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{117}{49}$

Decimal Form:

$2.38775510 \dots$

Mixed Number Form:

$2 \frac{19}{49}$