Pre-Algebra Examples

$\frac{6}{5 m} + \frac{3}{7 m^{2}}$

Step 1

To write $\frac{6}{5 m}$ as a fraction with a common denominator, multiply by $\frac{7 m}{7 m}$ .

$\frac{6}{5 m} \cdot \frac{7 m}{7 m} + \frac{3}{7 m^{2}}$

Step 2

To write $\frac{3}{7 m^{2}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6}{5 m} \cdot \frac{7 m}{7 m} + \frac{3}{7 m^{2}} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $35 m^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{5 m}$ by $\frac{7 m}{7 m}$ .

$\frac{6 (7 m)}{5 m (7 m)} + \frac{3}{7 m^{2}} \cdot \frac{5}{5}$

Step 3.2

Multiply $7$ by $5$ .

$\frac{6 (7 m)}{35 m \cdot m} + \frac{3}{7 m^{2}} \cdot \frac{5}{5}$

Step 3.3

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

$\frac{6 (7 m)}{35 (m^{1} m)} + \frac{3}{7 m^{2}} \cdot \frac{5}{5}$

Step 3.4

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

$\frac{6 (7 m)}{35 (m^{1} m^{1})} + \frac{3}{7 m^{2}} \cdot \frac{5}{5}$

Step 3.5

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

$\frac{6 (7 m)}{35 m^{1 + 1}} + \frac{3}{7 m^{2}} \cdot \frac{5}{5}$

Step 3.6

Add $1$ and $1$ .

$\frac{6 (7 m)}{35 m^{2}} + \frac{3}{7 m^{2}} \cdot \frac{5}{5}$

Step 3.7

Multiply $\frac{3}{7 m^{2}}$ by $\frac{5}{5}$ .

$\frac{6 (7 m)}{35 m^{2}} + \frac{3 \cdot 5}{7 m^{2} \cdot 5}$

Step 3.8

Multiply $5$ by $7$ .

$\frac{6 (7 m)}{35 m^{2}} + \frac{3 \cdot 5}{35 m^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 (7 m) + 3 \cdot 5}{35 m^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $3$ out of $6 \cdot 7 m + 3 \cdot 5$ .

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Step 5.1.1

Factor $3$ out of $6 \cdot 7 m$ .

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

Step 5.1.2

Factor $3$ out of $3 \cdot 5$ .

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

Step 5.1.3

Factor $3$ out of $3 (2 \cdot 7 m) + 3 (5)$ .

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

Step 5.2

Multiply $2$ by $7$ .

$\frac{3 (14 m + 5)}{35 m^{2}}$