Basic Math Examples

$8 \frac{1}{9} - 4 \frac{5}{6}$

Step 1

Convert

$8 \frac{1}{9}$ to an improper fraction.

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Step 1.1

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

$8 + \frac{1}{9} - 4 \frac{5}{6}$

Step 1.2

Add

$8$ and

$\frac{1}{9}$ .

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Step 1.2.1

To write

$8$ as a fraction with a common denominator, multiply by

$\frac{9}{9}$ .

$8 \cdot \frac{9}{9} + \frac{1}{9} - 4 \frac{5}{6}$

Step 1.2.2

Combine

$8$ and

$\frac{9}{9}$ .

$\frac{8 \cdot 9}{9} + \frac{1}{9} - 4 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 9 + 1}{9} - 4 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$8$ by

$9$ .

$\frac{72 + 1}{9} - 4 \frac{5}{6}$

Step 1.2.4.2

Add

$72$ and

$1$ .

$\frac{73}{9} - 4 \frac{5}{6}$

Step 2

Convert

$4 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{73}{9} - (4 + \frac{5}{6})$

Step 2.2

Add

$4$ and

$\frac{5}{6}$ .

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Step 2.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$\frac{73}{9} - (4 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine

$4$ and

$\frac{6}{6}$ .

$\frac{73}{9} - (\frac{4 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{73}{9} - \frac{4 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$4$ by

$6$ .

$\frac{73}{9} - \frac{24 + 5}{6}$

Step 2.2.4.2

Add

$24$ and

$5$ .

$\frac{73}{9} - \frac{29}{6}$

Step 3

To write

$\frac{73}{9}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{73}{9} \cdot \frac{2}{2} - \frac{29}{6}$

Step 4

To write

$- \frac{29}{6}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{73}{9} \cdot \frac{2}{2} - \frac{29}{6} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

$18$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{73}{9}$ by

$\frac{2}{2}$ .

$\frac{73 \cdot 2}{9 \cdot 2} - \frac{29}{6} \cdot \frac{3}{3}$

Step 5.2

Multiply

$9$ by

$2$ .

$\frac{73 \cdot 2}{18} - \frac{29}{6} \cdot \frac{3}{3}$

Step 5.3

Multiply

$\frac{29}{6}$ by

$\frac{3}{3}$ .

$\frac{73 \cdot 2}{18} - \frac{29 \cdot 3}{6 \cdot 3}$

Step 5.4

Multiply

$6$ by

$3$ .

$\frac{73 \cdot 2}{18} - \frac{29 \cdot 3}{18}$

Step 6

Combine the numerators over the common denominator.

$\frac{73 \cdot 2 - 29 \cdot 3}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$73$ by

$2$ .

$\frac{146 - 29 \cdot 3}{18}$

Step 7.2

Multiply

$- 29$ by

$3$ .

$\frac{146 - 87}{18}$

Step 7.3

Subtract

$87$ from

$146$ .

$\frac{59}{18}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{18}$

Decimal Form:

$3.2\overline{7}$

Mixed Number Form:

$3 \frac{5}{18}$