Basic Math Examples

$\frac{5 c}{2 d} + \frac{5 c}{3 d}$

Step 1

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

$\frac{5 c}{2 d} \cdot \frac{3}{3} + \frac{5 c}{3 d}$

Step 2

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

$\frac{5 c}{2 d} \cdot \frac{3}{3} + \frac{5 c}{3 d} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $6 d$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 c}{2 d}$ by $\frac{3}{3}$ .

$\frac{5 c \cdot 3}{2 d \cdot 3} + \frac{5 c}{3 d} \cdot \frac{2}{2}$

Step 3.2

Multiply $3$ by $2$ .

$\frac{5 c \cdot 3}{6 d} + \frac{5 c}{3 d} \cdot \frac{2}{2}$

Step 3.3

Multiply $\frac{5 c}{3 d}$ by $\frac{2}{2}$ .

$\frac{5 c \cdot 3}{6 d} + \frac{5 c \cdot 2}{3 d \cdot 2}$

Step 3.4

Multiply $2$ by $3$ .

$\frac{5 c \cdot 3}{6 d} + \frac{5 c \cdot 2}{6 d}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 c \cdot 3 + 5 c \cdot 2}{6 d}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $5 c$ out of $5 c \cdot 3 + 5 c \cdot 2$ .

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Step 5.1.1

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

$\frac{5 c (3) + 5 c \cdot 2}{6 d}$

Step 5.1.2

Factor $5 c$ out of $5 c \cdot 2$ .

$\frac{5 c (3) + 5 c (2)}{6 d}$

Step 5.1.3

Factor $5 c$ out of $5 c (3) + 5 c (2)$ .

$\frac{5 c (3 + 2)}{6 d}$

Step 5.2

Add $3$ and $2$ .

$\frac{5 c \cdot 5}{6 d}$

Step 5.3

Multiply $5$ by $5$ .

$\frac{25 c}{6 d}$