Basic Math Examples

- \frac{9}{7} - \frac{11}{9}

$- \frac{9}{7} - \frac{11}{9}$

Step 1

To write

- \frac{9}{7}

$- \frac{9}{7}$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

- \frac{9}{7} \cdot \frac{9}{9} - \frac{11}{9}

$- \frac{9}{7} \cdot \frac{9}{9} - \frac{11}{9}$

Step 2

To write

- \frac{11}{9}

$- \frac{11}{9}$ as a fraction with a common denominator, multiply by

\frac{7}{7}

$\frac{7}{7}$ .

- \frac{9}{7} \cdot \frac{9}{9} - \frac{11}{9} \cdot \frac{7}{7}

$- \frac{9}{7} \cdot \frac{9}{9} - \frac{11}{9} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of

63

$63$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{9}{7}

$\frac{9}{7}$ by

\frac{9}{9}

$\frac{9}{9}$ .

- \frac{9 \cdot 9}{7 \cdot 9} - \frac{11}{9} \cdot \frac{7}{7}

$- \frac{9 \cdot 9}{7 \cdot 9} - \frac{11}{9} \cdot \frac{7}{7}$

Step 3.2

Multiply

7

$7$ by

9

$9$ .

- \frac{9 \cdot 9}{63} - \frac{11}{9} \cdot \frac{7}{7}

$- \frac{9 \cdot 9}{63} - \frac{11}{9} \cdot \frac{7}{7}$

Step 3.3

Multiply

\frac{11}{9}

$\frac{11}{9}$ by

\frac{7}{7}

$\frac{7}{7}$ .

- \frac{9 \cdot 9}{63} - \frac{11 \cdot 7}{9 \cdot 7}

$- \frac{9 \cdot 9}{63} - \frac{11 \cdot 7}{9 \cdot 7}$

Step 3.4

Multiply

9

$9$ by

7

$7$ .

- \frac{9 \cdot 9}{63} - \frac{11 \cdot 7}{63}

$- \frac{9 \cdot 9}{63} - \frac{11 \cdot 7}{63}$

- \frac{9 \cdot 9}{63} - \frac{11 \cdot 7}{63}

$- \frac{9 \cdot 9}{63} - \frac{11 \cdot 7}{63}$

Step 4

Combine the numerators over the common denominator.

\frac{- 9 \cdot 9 - 11 \cdot 7}{63}

$\frac{- 9 \cdot 9 - 11 \cdot 7}{63}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

- 9

$- 9$ by

9

$9$ .

\frac{- 81 - 11 \cdot 7}{63}

$\frac{- 81 - 11 \cdot 7}{63}$

Step 5.2

Multiply

- 11

$- 11$ by

7

$7$ .

\frac{- 81 - 77}{63}

$\frac{- 81 - 77}{63}$

Step 5.3

Subtract

77

$77$ from

- 81

$- 81$ .

\frac{- 158}{63}

$\frac{- 158}{63}$

\frac{- 158}{63}

$\frac{- 158}{63}$

Step 6

Move the negative in front of the fraction.

- \frac{158}{63}

$- \frac{158}{63}$

Step 7

The result can be shown in multiple forms.

Exact Form:

- \frac{158}{63}

$- \frac{158}{63}$

Decimal Form:

- 2. ¯ ¯¯¯¯¯¯¯¯¯¯ ¯ 507936

$- 2.\overline{507936}$

Mixed Number Form:

- 2 \frac{32}{63}

$- 2 \frac{32}{63}$