Basic Math Examples

9 \frac{5}{9} - 6 \frac{5}{6}

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

Step 1

Convert

9 \frac{5}{9}

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

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

Step 1.2

Add

9

$9$ and

\frac{5}{9}

$\frac{5}{9}$ .

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Step 1.2.1

To write

9

$9$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

9 \cdot \frac{9}{9} + \frac{5}{9} - 6 \frac{5}{6}

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

Step 1.2.2

Combine

9

$9$ and

\frac{9}{9}

$\frac{9}{9}$ .

\frac{9 \cdot 9}{9} + \frac{5}{9} - 6 \frac{5}{6}

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

Step 1.2.3

Combine the numerators over the common denominator.

\frac{9 \cdot 9 + 5}{9} - 6 \frac{5}{6}

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

9

$9$ by

9

$9$ .

\frac{81 + 5}{9} - 6 \frac{5}{6}

$\frac{81 + 5}{9} - 6 \frac{5}{6}$

Step 1.2.4.2

Add

81

$81$ and

5

$5$ .

\frac{86}{9} - 6 \frac{5}{6}

$\frac{86}{9} - 6 \frac{5}{6}$

\frac{86}{9} - 6 \frac{5}{6}

$\frac{86}{9} - 6 \frac{5}{6}$

\frac{86}{9} - 6 \frac{5}{6}

$\frac{86}{9} - 6 \frac{5}{6}$

\frac{86}{9} - 6 \frac{5}{6}

$\frac{86}{9} - 6 \frac{5}{6}$

Step 2

Convert

6 \frac{5}{6}

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

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Step 2.1

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

\frac{86}{9} - (6 + \frac{5}{6})

$\frac{86}{9} - (6 + \frac{5}{6})$

Step 2.2

Add

6

$6$ and

\frac{5}{6}

$\frac{5}{6}$ .

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Step 2.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{6}{6}

$\frac{6}{6}$ .

\frac{86}{9} - (6 \cdot \frac{6}{6} + \frac{5}{6})

$\frac{86}{9} - (6 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine

6

$6$ and

\frac{6}{6}

$\frac{6}{6}$ .

\frac{86}{9} - (\frac{6 \cdot 6}{6} + \frac{5}{6})

$\frac{86}{9} - (\frac{6 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{86}{9} - \frac{6 \cdot 6 + 5}{6}

$\frac{86}{9} - \frac{6 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

6

$6$ by

6

$6$ .

\frac{86}{9} - \frac{36 + 5}{6}

$\frac{86}{9} - \frac{36 + 5}{6}$

Step 2.2.4.2

Add

36

$36$ and

5

$5$ .

\frac{86}{9} - \frac{41}{6}

$\frac{86}{9} - \frac{41}{6}$

\frac{86}{9} - \frac{41}{6}

$\frac{86}{9} - \frac{41}{6}$

\frac{86}{9} - \frac{41}{6}

$\frac{86}{9} - \frac{41}{6}$

\frac{86}{9} - \frac{41}{6}

$\frac{86}{9} - \frac{41}{6}$

Step 3

To write

\frac{86}{9}

$\frac{86}{9}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{86}{9} \cdot \frac{2}{2} - \frac{41}{6}

$\frac{86}{9} \cdot \frac{2}{2} - \frac{41}{6}$

Step 4

To write

- \frac{41}{6}

$- \frac{41}{6}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{86}{9} \cdot \frac{2}{2} - \frac{41}{6} \cdot \frac{3}{3}

$\frac{86}{9} \cdot \frac{2}{2} - \frac{41}{6} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

18

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

1

$1$ .

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Step 5.1

Multiply

\frac{86}{9}

$\frac{86}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{86 \cdot 2}{9 \cdot 2} - \frac{41}{6} \cdot \frac{3}{3}

$\frac{86 \cdot 2}{9 \cdot 2} - \frac{41}{6} \cdot \frac{3}{3}$

Step 5.2

Multiply

9

$9$ by

2

$2$ .

\frac{86 \cdot 2}{18} - \frac{41}{6} \cdot \frac{3}{3}

$\frac{86 \cdot 2}{18} - \frac{41}{6} \cdot \frac{3}{3}$

Step 5.3

Multiply

\frac{41}{6}

$\frac{41}{6}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{86 \cdot 2}{18} - \frac{41 \cdot 3}{6 \cdot 3}

$\frac{86 \cdot 2}{18} - \frac{41 \cdot 3}{6 \cdot 3}$

Step 5.4

Multiply

6

$6$ by

3

$3$ .

\frac{86 \cdot 2}{18} - \frac{41 \cdot 3}{18}

$\frac{86 \cdot 2}{18} - \frac{41 \cdot 3}{18}$

\frac{86 \cdot 2}{18} - \frac{41 \cdot 3}{18}

$\frac{86 \cdot 2}{18} - \frac{41 \cdot 3}{18}$

Step 6

Combine the numerators over the common denominator.

\frac{86 \cdot 2 - 41 \cdot 3}{18}

$\frac{86 \cdot 2 - 41 \cdot 3}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

86

$86$ by

2

$2$ .

\frac{172 - 41 \cdot 3}{18}

$\frac{172 - 41 \cdot 3}{18}$

Step 7.2

Multiply

- 41

$- 41$ by

3

$3$ .

\frac{172 - 123}{18}

$\frac{172 - 123}{18}$

Step 7.3

Subtract

123

$123$ from

172

$172$ .

\frac{49}{18}

$\frac{49}{18}$

\frac{49}{18}

$\frac{49}{18}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{49}{18}

$\frac{49}{18}$

Decimal Form:

2.7\overline{2}

$2.7\overline{2}$

Mixed Number Form:

2 \frac{13}{18}

$2 \frac{13}{18}$