Basic Math Examples

$4 \frac{4}{5} \div 2 \frac{2}{3} - {(1 \frac{1}{3})}^{2}$

Step 1

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

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Step 1.1

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

$(4 + \frac{4}{5}) \div 2 \frac{2}{3} - {(1 \frac{1}{3})}^{2}$

Step 1.2

Add $4$ and $\frac{4}{5}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(4 \cdot \frac{5}{5} + \frac{4}{5}) \div 2 \frac{2}{3} - {(1 \frac{1}{3})}^{2}$

Step 1.2.2

Combine $4$ and $\frac{5}{5}$ .

$(\frac{4 \cdot 5}{5} + \frac{4}{5}) \div 2 \frac{2}{3} - {(1 \frac{1}{3})}^{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 5 + 4}{5} \div 2 \frac{2}{3} - {(1 \frac{1}{3})}^{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $5$ .

$\frac{20 + 4}{5} \div 2 \frac{2}{3} - {(1 \frac{1}{3})}^{2}$

Step 1.2.4.2

Add $20$ and $4$ .

$\frac{24}{5} \div 2 \frac{2}{3} - {(1 \frac{1}{3})}^{2}$

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.

$\frac{24}{5} \div (2 + \frac{2}{3}) - {(1 \frac{1}{3})}^{2}$

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 $\frac{3}{3}$ .

$\frac{24}{5} \div (2 \cdot \frac{3}{3} + \frac{2}{3}) - {(1 \frac{1}{3})}^{2}$

Step 2.2.2

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

$\frac{24}{5} \div (\frac{2 \cdot 3}{3} + \frac{2}{3}) - {(1 \frac{1}{3})}^{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{24}{5} \div \frac{2 \cdot 3 + 2}{3} - {(1 \frac{1}{3})}^{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $3$ .

$\frac{24}{5} \div \frac{6 + 2}{3} - {(1 \frac{1}{3})}^{2}$

Step 2.2.4.2

Add $6$ and $2$ .

$\frac{24}{5} \div \frac{8}{3} - {(1 \frac{1}{3})}^{2}$

Step 3

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

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Step 3.1

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

$\frac{24}{5} \div \frac{8}{3} - {(1 + \frac{1}{3})}^{2}$

Step 3.2

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

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Step 3.2.1

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

$\frac{24}{5} \div \frac{8}{3} - {(\frac{3}{3} + \frac{1}{3})}^{2}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{24}{5} \div \frac{8}{3} - {(\frac{3 + 1}{3})}^{2}$

Step 3.2.3

Add $3$ and $1$ .

$\frac{24}{5} \div \frac{8}{3} - {(\frac{4}{3})}^{2}$

Step 4

Simplify each term.

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Step 4.1

To divide by a fraction, multiply by its reciprocal.

$\frac{24}{5} \cdot \frac{3}{8} - {(\frac{4}{3})}^{2}$

Step 4.2

Cancel the common factor of $8$ .

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Step 4.2.1

Factor $8$ out of $24$ .

$\frac{8 (3)}{5} \cdot \frac{3}{8} - {(\frac{4}{3})}^{2}$

Step 4.2.2

Cancel the common factor.

$\frac{8 \cdot 3}{5} \cdot \frac{3}{8} - {(\frac{4}{3})}^{2}$

Step 4.2.3

Rewrite the expression.

$\frac{3}{5} \cdot 3 - {(\frac{4}{3})}^{2}$

Step 4.3

Combine $\frac{3}{5}$ and $3$ .

$\frac{3 \cdot 3}{5} - {(\frac{4}{3})}^{2}$

Step 4.4

Multiply $3$ by $3$ .

$\frac{9}{5} - {(\frac{4}{3})}^{2}$

Step 4.5

Apply the product rule to $\frac{4}{3}$ .

$\frac{9}{5} - \frac{4^{2}}{3^{2}}$

Step 4.6

Raise $4$ to the power of $2$ .

$\frac{9}{5} - \frac{16}{3^{2}}$

Step 4.7

Raise $3$ to the power of $2$ .

$\frac{9}{5} - \frac{16}{9}$

Step 5

To write $\frac{9}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{9}{5} \cdot \frac{9}{9} - \frac{16}{9}$

Step 6

To write $- \frac{16}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{5} \cdot \frac{9}{9} - \frac{16}{9} \cdot \frac{5}{5}$

Step 7

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

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

$\frac{9 \cdot 9}{5 \cdot 9} - \frac{16}{9} \cdot \frac{5}{5}$

Step 7.2

Multiply $5$ by $9$ .

$\frac{9 \cdot 9}{45} - \frac{16}{9} \cdot \frac{5}{5}$

Step 7.3

Multiply $\frac{16}{9}$ by $\frac{5}{5}$ .

$\frac{9 \cdot 9}{45} - \frac{16 \cdot 5}{9 \cdot 5}$

Step 7.4

Multiply $9$ by $5$ .

$\frac{9 \cdot 9}{45} - \frac{16 \cdot 5}{45}$

Step 8

Combine the numerators over the common denominator.

$\frac{9 \cdot 9 - 16 \cdot 5}{45}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $9$ by $9$ .

$\frac{81 - 16 \cdot 5}{45}$

Step 9.2

Multiply $- 16$ by $5$ .

$\frac{81 - 80}{45}$

Step 9.3

Subtract $80$ from $81$ .

$\frac{1}{45}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{45}$

Decimal Form:

$0.0\overline{2}$