Finite Math Examples

$\frac{3}{35 p} + \frac{7}{25 p^{2}}$

Step 1

To write $\frac{3}{35 p}$ as a fraction with a common denominator, multiply by $\frac{5 p}{5 p}$ .

$\frac{3}{35 p} \cdot \frac{5 p}{5 p} + \frac{7}{25 p^{2}}$

Step 2

To write $\frac{7}{25 p^{2}}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3}{35 p} \cdot \frac{5 p}{5 p} + \frac{7}{25 p^{2}} \cdot \frac{7}{7}$

Step 3

Write each expression with a common denominator of $175 p^{2}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.1

Multiply $\frac{3}{35 p}$ by $\frac{5 p}{5 p}$ .

$\frac{3 (5 p)}{35 p (5 p)} + \frac{7}{25 p^{2}} \cdot \frac{7}{7}$

Step 3.2

Multiply $5$ by $35$ .

$\frac{3 (5 p)}{175 p \cdot p} + \frac{7}{25 p^{2}} \cdot \frac{7}{7}$

Step 3.3

Raise $p$ to the power of $1$ .

$\frac{3 (5 p)}{175 (p^{1} p)} + \frac{7}{25 p^{2}} \cdot \frac{7}{7}$

Step 3.4

Raise $p$ to the power of $1$ .

$\frac{3 (5 p)}{175 (p^{1} p^{1})} + \frac{7}{25 p^{2}} \cdot \frac{7}{7}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 (5 p)}{175 p^{1 + 1}} + \frac{7}{25 p^{2}} \cdot \frac{7}{7}$

Step 3.6

Add $1$ and $1$ .

$\frac{3 (5 p)}{175 p^{2}} + \frac{7}{25 p^{2}} \cdot \frac{7}{7}$

Step 3.7

Multiply $\frac{7}{25 p^{2}}$ by $\frac{7}{7}$ .

$\frac{3 (5 p)}{175 p^{2}} + \frac{7 \cdot 7}{25 p^{2} \cdot 7}$

Step 3.8

Multiply $7$ by $25$ .

$\frac{3 (5 p)}{175 p^{2}} + \frac{7 \cdot 7}{175 p^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 (5 p) + 7 \cdot 7}{175 p^{2}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $3$ by $5$ .

$\frac{15 p + 7 \cdot 7}{175 p^{2}}$

Step 5.2

Multiply $7$ by $7$ .

$\frac{15 p + 49}{175 p^{2}}$