Basic Math Examples

$4 \frac{1}{2} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 1

Convert $4 \frac{1}{2}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$4 + \frac{1}{2} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 1.2

Add $4$ and $\frac{1}{2}$ .

Tap for more steps...

Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 \cdot \frac{2}{2} + \frac{1}{2} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 1.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{4 \cdot 2}{2} + \frac{1}{2} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 1}{2} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $4$ by $2$ .

$\frac{8 + 1}{2} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 1.2.4.2

Add $8$ and $1$ .

$\frac{9}{2} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Multiply $\frac{9}{2}$ by $\frac{\frac{2 \cdot 24}{5}}{\frac{2 \cdot 24}{5}}$ .

$\frac{9}{2} \cdot \frac{\frac{2 \cdot 24}{5}}{\frac{2 \cdot 24}{5}} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 2.2

Multiply $\frac{9}{2}$ by $\frac{\frac{2 \cdot 24}{5}}{\frac{2 \cdot 24}{5}}$ .

$\frac{9 \frac{2 \cdot 24}{5}}{2 \frac{2 \cdot 24}{5}} - \frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} - \frac{3}{4}$

Step 2.3

Multiply $\frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5}$ by $\frac{4}{4}$ .

$\frac{9 \frac{2 \cdot 24}{5}}{2 \frac{2 \cdot 24}{5}} - (\frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5} \cdot \frac{4}{4}) - \frac{3}{4}$

Step 2.4

Multiply $\frac{52}{5} \cdot (- \frac{15}{13}) \div \frac{24}{5}$ by $\frac{4}{4}$ .

$\frac{9 \frac{2 \cdot 24}{5}}{2 \frac{2 \cdot 24}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{24}{5} \cdot 4} - \frac{3}{4}$

Step 2.5

Multiply $\frac{3}{4}$ by $\frac{\frac{24}{5}}{\frac{24}{5}}$ .

$\frac{9 \frac{2 \cdot 24}{5}}{2 \frac{2 \cdot 24}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{24}{5} \cdot 4} - (\frac{3}{4} \cdot \frac{\frac{24}{5}}{\frac{24}{5}})$

Step 2.6

Multiply $\frac{3}{4}$ by $\frac{\frac{24}{5}}{\frac{24}{5}}$ .

$\frac{9 \frac{2 \cdot 24}{5}}{2 \frac{2 \cdot 24}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{24}{5} \cdot 4} - \frac{3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 2.7

Multiply $2$ by $24$ .

$\frac{9 \frac{2 \cdot 24}{5}}{2 (\frac{48}{5})} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{24}{5} \cdot 4} - \frac{3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 2.8

Combine $2$ and $\frac{48}{5}$ .

$\frac{9 \frac{2 \cdot 24}{5}}{\frac{2 \cdot 48}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{24}{5} \cdot 4} - \frac{3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 2.9

Multiply $2$ by $48$ .

$\frac{9 \frac{2 \cdot 24}{5}}{\frac{96}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{24}{5} \cdot 4} - \frac{3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 2.10

Reorder the factors of $\frac{24}{5} \cdot 4$ .

$\frac{9 \frac{2 \cdot 24}{5}}{\frac{96}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{4 (\frac{24}{5})} - \frac{3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 2.11

Combine $4$ and $\frac{24}{5}$ .

$\frac{9 \frac{2 \cdot 24}{5}}{\frac{96}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{4 \cdot 24}{5}} - \frac{3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 2.12

Multiply $4$ by $24$ .

$\frac{9 \frac{2 \cdot 24}{5}}{\frac{96}{5}} - \frac{\frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{96}{5}} - \frac{3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 \frac{2 \cdot 24}{5} - \frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply $2$ by $24$ .

$\frac{9 (\frac{48}{5}) - \frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.2

Multiply $9 (\frac{48}{5})$ .

Tap for more steps...

Step 4.2.1

Combine $9$ and $\frac{48}{5}$ .

$\frac{\frac{9 \cdot 48}{5} - \frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.2.2

Multiply $9$ by $48$ .

$\frac{\frac{432}{5} - \frac{52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.3

Cancel the common factor of $13$ .

Tap for more steps...

Step 4.3.1

Move the leading negative in $- \frac{52}{5}$ into the numerator.

$\frac{\frac{432}{5} + \frac{- 52}{5} \cdot (- \frac{15}{13}) \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.3.2

Move the leading negative in $- \frac{15}{13}$ into the numerator.

$\frac{\frac{432}{5} + \frac{- 52}{5} \cdot \frac{- 15}{13} \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.3.3

Factor $13$ out of $- 52$ .

$\frac{\frac{432}{5} + \frac{13 (- 4)}{5} \cdot \frac{- 15}{13} \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.3.4

Cancel the common factor.

$\frac{\frac{432}{5} + \frac{13 \cdot - 4}{5} \cdot \frac{- 15}{13} \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.3.5

Rewrite the expression.

$\frac{\frac{432}{5} + \frac{- 4}{5} \cdot - 15 \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.4

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.4.1

Factor $5$ out of $- 15$ .

$\frac{\frac{432}{5} + \frac{- 4}{5} \cdot (5 (- 3)) \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.4.2

Cancel the common factor.

$\frac{\frac{432}{5} + \frac{- 4}{5} \cdot (5 \cdot - 3) \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.4.3

Rewrite the expression.

$\frac{\frac{432}{5} - 4 \cdot - 3 \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.5

Multiply $- 4$ by $- 3$ .

$\frac{\frac{432}{5} + 12 \cdot 4}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 4.6

Multiply $12$ by $4$ .

$\frac{\frac{432}{5} + 48}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 5

To write $48$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{\frac{432}{5} + 48 \cdot \frac{5}{5}}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 6

Combine $48$ and $\frac{5}{5}$ .

$\frac{\frac{432}{5} + \frac{48 \cdot 5}{5}}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 7

Combine the numerators over the common denominator.

$\frac{\frac{432 + 48 \cdot 5}{5}}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 8

Simplify the numerator.

Tap for more steps...

Step 8.1

Multiply $48$ by $5$ .

$\frac{\frac{432 + 240}{5}}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 8.2

Add $432$ and $240$ .

$\frac{\frac{672}{5}}{\frac{96}{5}} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9

Simplify each term.

Tap for more steps...

Step 9.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{672}{5} \cdot \frac{5}{96} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9.2

Cancel the common factor of $96$ .

Tap for more steps...

Step 9.2.1

Factor $96$ out of $672$ .

$\frac{96 (7)}{5} \cdot \frac{5}{96} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9.2.2

Cancel the common factor.

$\frac{96 \cdot 7}{5} \cdot \frac{5}{96} + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9.2.3

Rewrite the expression.

$\frac{7}{5} \cdot 5 + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9.3

Cancel the common factor of $5$ .

Tap for more steps...

Step 9.3.1

Cancel the common factor.

$\frac{7}{5} \cdot 5 + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9.3.2

Rewrite the expression.

$7 + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9.4

Cancel the common factor of $\frac{24}{5}$ .

Tap for more steps...

Step 9.4.1

Cancel the common factor.

$7 + \frac{- 3 (\frac{24}{5})}{4 (\frac{24}{5})}$

Step 9.4.2

Rewrite the expression.

$7 + \frac{- 3}{4}$

Step 9.5

Move the negative in front of the fraction.

$7 - \frac{3}{4}$

Step 10

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$7 \cdot \frac{4}{4} - \frac{3}{4}$

Step 11

Combine $7$ and $\frac{4}{4}$ .

$\frac{7 \cdot 4}{4} - \frac{3}{4}$

Step 12

Combine the numerators over the common denominator.

$\frac{7 \cdot 4 - 3}{4}$

Step 13

Simplify the numerator.

Tap for more steps...

Step 13.1

Multiply $7$ by $4$ .

$\frac{28 - 3}{4}$

Step 13.2

Subtract $3$ from $28$ .

$\frac{25}{4}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{4}$

Decimal Form:

$6.25$

Mixed Number Form:

$6 \frac{1}{4}$