Basic Math Examples

$\frac{125}{27} \cdot {(\frac{3}{5})}^{2} - \frac{5}{12}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{3}{5}$ .

$\frac{125}{27} \cdot \frac{3^{2}}{5^{2}} - \frac{5}{12}$

Step 1.2

Combine.

$\frac{125 \cdot 3^{2}}{27 \cdot 5^{2}} - \frac{5}{12}$

Step 1.3

Raise $3$ to the power of $2$ .

$\frac{125 \cdot 9}{27 \cdot 5^{2}} - \frac{5}{12}$

Step 1.4

Raise $5$ to the power of $2$ .

$\frac{125 \cdot 9}{27 \cdot 25} - \frac{5}{12}$

Step 1.5

Multiply $125$ by $9$ .

$\frac{1125}{27 \cdot 25} - \frac{5}{12}$

Step 1.6

Multiply $27$ by $25$ .

$\frac{1125}{675} - \frac{5}{12}$

Step 1.7

Cancel the common factor of $1125$ and $675$ .

Tap for more steps...

Step 1.7.1

Factor $225$ out of $1125$ .

$\frac{225 (5)}{675} - \frac{5}{12}$

Step 1.7.2

Cancel the common factors.

Tap for more steps...

Step 1.7.2.1

Factor $225$ out of $675$ .

$\frac{225 \cdot 5}{225 \cdot 3} - \frac{5}{12}$

Step 1.7.2.2

Cancel the common factor.

$\frac{225 \cdot 5}{225 \cdot 3} - \frac{5}{12}$

Step 1.7.2.3

Rewrite the expression.

$\frac{5}{3} - \frac{5}{12}$

Step 2

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{3} \cdot \frac{4}{4} - \frac{5}{12}$

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

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

$\frac{5 \cdot 4}{3 \cdot 4} - \frac{5}{12}$

Step 3.2

Multiply $3$ by $4$ .

$\frac{5 \cdot 4}{12} - \frac{5}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 - 5}{12}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $5$ by $4$ .

$\frac{20 - 5}{12}$

Step 5.2

Subtract $5$ from $20$ .

$\frac{15}{12}$

Step 6

Cancel the common factor of $15$ and $12$ .

Tap for more steps...

Step 6.1

Factor $3$ out of $15$ .

$\frac{3 (5)}{12}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 5}{3 \cdot 4}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 5}{3 \cdot 4}$

Step 6.2.3

Rewrite the expression.

$\frac{5}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$