Basic Math Examples

$n - \frac{1}{3} = \frac{2}{5}$

Step 1

Add $\frac{1}{3}$ to both sides of the equation.

$n = \frac{2}{5} + \frac{1}{3}$

Step 2

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

$n = \frac{2}{5} \cdot \frac{3}{3} + \frac{1}{3}$

Step 3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$n = \frac{2}{5} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{5}{5}$

Step 4

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

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Step 4.1

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

$n = \frac{2 \cdot 3}{5 \cdot 3} + \frac{1}{3} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $3$ .

$n = \frac{2 \cdot 3}{15} + \frac{1}{3} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$n = \frac{2 \cdot 3}{15} + \frac{5}{3 \cdot 5}$

Step 4.4

Multiply $3$ by $5$ .

$n = \frac{2 \cdot 3}{15} + \frac{5}{15}$

Step 5

Combine the numerators over the common denominator.

$n = \frac{2 \cdot 3 + 5}{15}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $2$ by $3$ .

$n = \frac{6 + 5}{15}$

Step 6.2

Add $6$ and $5$ .

$n = \frac{11}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$n = \frac{11}{15}$

Decimal Form:

$n = 0.7\overline{3}$