Algebra Examples

$\frac{2 \frac{4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$

Step 1

Convert $2 \frac{4}{9}$ to an improper fraction.

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Step 1.1

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

$\frac{2 + \frac{4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$

Step 1.2

Add $2$ and $\frac{4}{9}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2 \cdot \frac{9}{9} + \frac{4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$

Step 1.2.2

Combine $2$ and $\frac{9}{9}$ .

$\frac{\frac{2 \cdot 9}{9} + \frac{4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{\frac{2 \cdot 9 + 4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $9$ .

$\frac{\frac{18 + 4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$

Step 1.2.4.2

Add $18$ and $4$ .

$\frac{\frac{22}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$

Step 2

Convert $5 \frac{2}{3}$ to an improper fraction.

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Step 2.1

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

$\frac{\frac{22}{9} - (5 + \frac{2}{3})}{2 \frac{1}{3}}$

Step 2.2

Add $5$ and $\frac{2}{3}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{\frac{22}{9} - (5 \cdot \frac{3}{3} + \frac{2}{3})}{2 \frac{1}{3}}$

Step 2.2.2

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

$\frac{\frac{22}{9} - (\frac{5 \cdot 3}{3} + \frac{2}{3})}{2 \frac{1}{3}}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{\frac{22}{9} - \frac{5 \cdot 3 + 2}{3}}{2 \frac{1}{3}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $3$ .

$\frac{\frac{22}{9} - \frac{15 + 2}{3}}{2 \frac{1}{3}}$

Step 2.2.4.2

Add $15$ and $2$ .

$\frac{\frac{22}{9} - \frac{17}{3}}{2 \frac{1}{3}}$

Step 3

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

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Step 3.1

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

$\frac{\frac{22}{9} - \frac{17}{3}}{2 + \frac{1}{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{\frac{22}{9} - \frac{17}{3}}{2 \cdot \frac{3}{3} + \frac{1}{3}}$

Step 3.2.2

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

$\frac{\frac{22}{9} - \frac{17}{3}}{\frac{2 \cdot 3}{3} + \frac{1}{3}}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{\frac{22}{9} - \frac{17}{3}}{\frac{2 \cdot 3 + 1}{3}}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $3$ .

$\frac{\frac{22}{9} - \frac{17}{3}}{\frac{6 + 1}{3}}$

Step 3.2.4.2

Add $6$ and $1$ .

$\frac{\frac{22}{9} - \frac{17}{3}}{\frac{7}{3}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$(\frac{22}{9} - \frac{17}{3}) \frac{3}{7}$

Step 5

To write $- \frac{17}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{22}{9} - \frac{17}{3} \cdot \frac{3}{3}) \frac{3}{7}$

Step 6

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{17}{3}$ by $\frac{3}{3}$ .

$(\frac{22}{9} - \frac{17 \cdot 3}{3 \cdot 3}) \frac{3}{7}$

Step 6.2

Multiply $3$ by $3$ .

$(\frac{22}{9} - \frac{17 \cdot 3}{9}) \frac{3}{7}$

Step 7

Combine the numerators over the common denominator.

$\frac{22 - 17 \cdot 3}{9} \cdot \frac{3}{7}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $- 17$ by $3$ .

$\frac{22 - 51}{9} \cdot \frac{3}{7}$

Step 8.2

Subtract $51$ from $22$ .

$\frac{- 29}{9} \cdot \frac{3}{7}$

Step 9

Cancel the common factor of $3$ .

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Step 9.1

Factor $3$ out of $9$ .

$\frac{- 29}{3 (3)} \cdot \frac{3}{7}$

Step 9.2

Cancel the common factor.

$\frac{- 29}{3 \cdot 3} \cdot \frac{3}{7}$

Step 9.3

Rewrite the expression.

$\frac{- 29}{3} \cdot \frac{1}{7}$

Step 10

Multiply $\frac{- 29}{3}$ by $\frac{1}{7}$ .

$\frac{- 29}{3 \cdot 7}$

Step 11

Simplify the expression.

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Step 11.1

Multiply $3$ by $7$ .

$\frac{- 29}{21}$

Step 11.2

Move the negative in front of the fraction.

$- \frac{29}{21}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{29}{21}$

Decimal Form:

$- 1.\overline{380952}$

Mixed Number Form:

$- 1 \frac{8}{21}$