Basic Math Examples

$9 \frac{4}{9} - 3 \frac{7}{9}$

Step 1

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

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Step 1.1

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

$9 + \frac{4}{9} - 3 \frac{7}{9}$

Step 1.2

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

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Step 1.2.1

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

$9 \cdot \frac{9}{9} + \frac{4}{9} - 3 \frac{7}{9}$

Step 1.2.2

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

$\frac{9 \cdot 9}{9} + \frac{4}{9} - 3 \frac{7}{9}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{9 \cdot 9 + 4}{9} - 3 \frac{7}{9}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $9$ by $9$ .

$\frac{81 + 4}{9} - 3 \frac{7}{9}$

Step 1.2.4.2

Add $81$ and $4$ .

$\frac{85}{9} - 3 \frac{7}{9}$

Step 2

Convert $3 \frac{7}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{85}{9} - (3 + \frac{7}{9})$

Step 2.2

Add $3$ and $\frac{7}{9}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{85}{9} - (3 \cdot \frac{9}{9} + \frac{7}{9})$

Step 2.2.2

Combine $3$ and $\frac{9}{9}$ .

$\frac{85}{9} - (\frac{3 \cdot 9}{9} + \frac{7}{9})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{85}{9} - \frac{3 \cdot 9 + 7}{9}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $9$ .

$\frac{85}{9} - \frac{27 + 7}{9}$

Step 2.2.4.2

Add $27$ and $7$ .

$\frac{85}{9} - \frac{34}{9}$

Step 3

Combine the numerators over the common denominator.

$\frac{85 - 34}{9}$

Step 4

Subtract $34$ from $85$ .

$\frac{51}{9}$

Step 5

Cancel the common factor of $51$ and $9$ .

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Step 5.1

Factor $3$ out of $51$ .

$\frac{3 (17)}{9}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $9$ .

$\frac{3 \cdot 17}{3 \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{3 \cdot 17}{3 \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{17}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{3}$

Decimal Form:

$5.\overline{6}$

Mixed Number Form:

$5 \frac{2}{3}$