Basic Math Examples

2 \frac{1}{9} - \frac{7}{6}

$2 \frac{1}{9} - \frac{7}{6}$

Step 1

Convert

2 \frac{1}{9}

$2 \frac{1}{9}$ to an improper fraction.

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Step 1.1

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

2 + \frac{1}{9} - \frac{7}{6}

$2 + \frac{1}{9} - \frac{7}{6}$

Step 1.2

Add

2

$2$ and

\frac{1}{9}

$\frac{1}{9}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

2 \cdot \frac{9}{9} + \frac{1}{9} - \frac{7}{6}

$2 \cdot \frac{9}{9} + \frac{1}{9} - \frac{7}{6}$

Step 1.2.2

Combine

2

$2$ and

\frac{9}{9}

$\frac{9}{9}$ .

\frac{2 \cdot 9}{9} + \frac{1}{9} - \frac{7}{6}

$\frac{2 \cdot 9}{9} + \frac{1}{9} - \frac{7}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 9 + 1}{9} - \frac{7}{6}

$\frac{2 \cdot 9 + 1}{9} - \frac{7}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

9

$9$ .

\frac{18 + 1}{9} - \frac{7}{6}

$\frac{18 + 1}{9} - \frac{7}{6}$

Step 1.2.4.2

Add

18

$18$ and

1

$1$ .

\frac{19}{9} - \frac{7}{6}

$\frac{19}{9} - \frac{7}{6}$

\frac{19}{9} - \frac{7}{6}

$\frac{19}{9} - \frac{7}{6}$

\frac{19}{9} - \frac{7}{6}

$\frac{19}{9} - \frac{7}{6}$

\frac{19}{9} - \frac{7}{6}

$\frac{19}{9} - \frac{7}{6}$

Step 2

To write

\frac{19}{9}

$\frac{19}{9}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{19}{9} \cdot \frac{2}{2} - \frac{7}{6}

$\frac{19}{9} \cdot \frac{2}{2} - \frac{7}{6}$

Step 3

To write

- \frac{7}{6}

$- \frac{7}{6}$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{19}{9} \cdot \frac{2}{2} - \frac{7}{6} \cdot \frac{3}{3}

$\frac{19}{9} \cdot \frac{2}{2} - \frac{7}{6} \cdot \frac{3}{3}$

Step 4

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 4.1

Multiply

\frac{19}{9}

$\frac{19}{9}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{19 \cdot 2}{9 \cdot 2} - \frac{7}{6} \cdot \frac{3}{3}

$\frac{19 \cdot 2}{9 \cdot 2} - \frac{7}{6} \cdot \frac{3}{3}$

Step 4.2

Multiply

9

$9$ by

2

$2$ .

\frac{19 \cdot 2}{18} - \frac{7}{6} \cdot \frac{3}{3}

$\frac{19 \cdot 2}{18} - \frac{7}{6} \cdot \frac{3}{3}$

Step 4.3

Multiply

\frac{7}{6}

$\frac{7}{6}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{19 \cdot 2}{18} - \frac{7 \cdot 3}{6 \cdot 3}

$\frac{19 \cdot 2}{18} - \frac{7 \cdot 3}{6 \cdot 3}$

Step 4.4

Multiply

6

$6$ by

3

$3$ .

\frac{19 \cdot 2}{18} - \frac{7 \cdot 3}{18}

$\frac{19 \cdot 2}{18} - \frac{7 \cdot 3}{18}$

\frac{19 \cdot 2}{18} - \frac{7 \cdot 3}{18}

$\frac{19 \cdot 2}{18} - \frac{7 \cdot 3}{18}$

Step 5

Combine the numerators over the common denominator.

$\frac{19 \cdot 2 - 7 \cdot 3}{18}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$19$ by

$2$ .

$\frac{38 - 7 \cdot 3}{18}$

Step 6.2

Multiply

$- 7$ by

$3$ .

$\frac{38 - 21}{18}$

Step 6.3

Subtract

$21$ from

$38$ .

$\frac{17}{18}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{18}$

Decimal Form:

$0.9\overline{4}$