Pre-Algebra Examples

$\frac{2}{5} + \frac{a}{3}$

Step 1

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

$\frac{2}{5} \cdot \frac{3}{3} + \frac{a}{3}$

Step 2

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

$\frac{2}{5} \cdot \frac{3}{3} + \frac{a}{3} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{2 \cdot 3}{5 \cdot 3} + \frac{a}{3} \cdot \frac{5}{5}$

Step 3.2

Multiply $5$ by $3$ .

$\frac{2 \cdot 3}{15} + \frac{a}{3} \cdot \frac{5}{5}$

Step 3.3

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

$\frac{2 \cdot 3}{15} + \frac{a \cdot 5}{3 \cdot 5}$

Step 3.4

Multiply $3$ by $5$ .

$\frac{2 \cdot 3}{15} + \frac{a \cdot 5}{15}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 \cdot 3 + a \cdot 5}{15}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $3$ .

$\frac{6 + a \cdot 5}{15}$

Step 5.2

Move $5$ to the left of $a$ .

$\frac{6 + 5 a}{15}$