Basic Math Examples

$\frac{(\frac{7}{24}) - (- \frac{9}{8})}{1 + (\frac{7}{24}) (- \frac{9}{8})}$

Step 1

Multiply the numerator and denominator of the fraction by $24$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{7}{24} - - \frac{9}{8}}{1 + \frac{7}{24} (- \frac{9}{8})}$ by $\frac{24}{24}$ .

$\frac{24}{24} \cdot \frac{\frac{7}{24} - - \frac{9}{8}}{1 + \frac{7}{24} (- \frac{9}{8})}$

Step 1.2

Combine.

$\frac{24 (\frac{7}{24} - - \frac{9}{8})}{24 (1 + \frac{7}{24} (- \frac{9}{8}))}$

Step 2

Apply the distributive property.

$\frac{24 (\frac{7}{24}) + 24 (- - \frac{9}{8})}{24 \cdot 1 + 24 (\frac{7}{24} (- \frac{9}{8}))}$

Step 3

Cancel the common factor of $24$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{24 (\frac{7}{24}) + 24 (- - \frac{9}{8})}{24 \cdot 1 + 24 (\frac{7}{24} (- \frac{9}{8}))}$

Step 3.2

Rewrite the expression.

$\frac{7 + 24 (- - \frac{9}{8})}{24 \cdot 1 + 24 (\frac{7}{24} (- \frac{9}{8}))}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply $- - \frac{9}{8}$ .

Tap for more steps...

Step 4.1.1

Multiply $- 1$ by $- 1$ .

$\frac{7 + 24 (1 (\frac{9}{8}))}{24 \cdot 1 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 4.1.2

Multiply $\frac{9}{8}$ by $1$ .

$\frac{7 + 24 (\frac{9}{8})}{24 \cdot 1 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 4.2

Cancel the common factor of $8$ .

Tap for more steps...

Step 4.2.1

Factor $8$ out of $24$ .

$\frac{7 + 8 (3) \frac{9}{8}}{24 \cdot 1 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 4.2.2

Cancel the common factor.

$\frac{7 + 8 \cdot 3 \frac{9}{8}}{24 \cdot 1 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 4.2.3

Rewrite the expression.

$\frac{7 + 3 \cdot 9}{24 \cdot 1 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 4.3

Multiply $3$ by $9$ .

$\frac{7 + 27}{24 \cdot 1 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 4.4

Add $7$ and $27$ .

$\frac{34}{24 \cdot 1 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Multiply $24$ by $1$ .

$\frac{34}{24 + 24 (\frac{7}{24}) (- \frac{9}{8})}$

Step 5.2

Cancel the common factor of $8$ .

Tap for more steps...

Step 5.2.1

Move the leading negative in $- \frac{9}{8}$ into the numerator.

$\frac{34}{24 + 24 (\frac{7}{24}) \frac{- 9}{8}}$

Step 5.2.2

Factor $8$ out of $24 (\frac{7}{24})$ .

$\frac{34}{24 + 8 (3 (\frac{7}{24})) \frac{- 9}{8}}$

Step 5.2.3

Cancel the common factor.

$\frac{34}{24 + 8 (3 (\frac{7}{24})) \frac{- 9}{8}}$

Step 5.2.4

Rewrite the expression.

$\frac{34}{24 + 3 (\frac{7}{24}) \cdot - 9}$

Step 5.3

Combine $3$ and $\frac{7}{24}$ .

$\frac{34}{24 + \frac{3 \cdot 7}{24} \cdot - 9}$

Step 5.4

Multiply $3$ by $7$ .

$\frac{34}{24 + \frac{21}{24} \cdot - 9}$

Step 5.5

Combine $\frac{21}{24}$ and $- 9$ .

$\frac{34}{24 + \frac{21 \cdot - 9}{24}}$

Step 5.6

Multiply $21$ by $- 9$ .

$\frac{34}{24 + \frac{- 189}{24}}$

Step 5.7

Cancel the common factor of $- 189$ and $24$ .

Tap for more steps...

Step 5.7.1

Factor $3$ out of $- 189$ .

$\frac{34}{24 + \frac{3 (- 63)}{24}}$

Step 5.7.2

Cancel the common factors.

Tap for more steps...

Step 5.7.2.1

Factor $3$ out of $24$ .

$\frac{34}{24 + \frac{3 \cdot - 63}{3 \cdot 8}}$

Step 5.7.2.2

Cancel the common factor.

$\frac{34}{24 + \frac{3 \cdot - 63}{3 \cdot 8}}$

Step 5.7.2.3

Rewrite the expression.

$\frac{34}{24 + \frac{- 63}{8}}$

Step 5.8

Move the negative in front of the fraction.

$\frac{34}{24 - \frac{63}{8}}$

Step 5.9

To write $24$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{34}{24 \cdot \frac{8}{8} - \frac{63}{8}}$

Step 5.10

Combine $24$ and $\frac{8}{8}$ .

$\frac{34}{\frac{24 \cdot 8}{8} - \frac{63}{8}}$

Step 5.11

Combine the numerators over the common denominator.

$\frac{34}{\frac{24 \cdot 8 - 63}{8}}$

Step 5.12

Simplify the numerator.

Tap for more steps...

Step 5.12.1

Multiply $24$ by $8$ .

$\frac{34}{\frac{192 - 63}{8}}$

Step 5.12.2

Subtract $63$ from $192$ .

$\frac{34}{\frac{129}{8}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$34 (\frac{8}{129})$

Step 7

Multiply $34 (\frac{8}{129})$ .

Tap for more steps...

Step 7.1

Combine $34$ and $\frac{8}{129}$ .

$\frac{34 \cdot 8}{129}$

Step 7.2

Multiply $34$ by $8$ .

$\frac{272}{129}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{272}{129}$

Decimal Form:

$2.10852713 \dots$

Mixed Number Form:

$2 \frac{14}{129}$