Basic Math Examples

$\frac{2}{3} A + \frac{1}{5} A = \frac{8}{15}$

Step 1

Simplify $\frac{2}{3} A + \frac{1}{5} A$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{2}{3}$ and $A$ .

$\frac{2 A}{3} + \frac{1}{5} A = \frac{8}{15}$

Step 1.1.2

Combine $\frac{1}{5}$ and $A$ .

$\frac{2 A}{3} + \frac{A}{5} = \frac{8}{15}$

Step 1.2

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

$\frac{2 A}{3} \cdot \frac{5}{5} + \frac{A}{5} = \frac{8}{15}$

Step 1.3

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

$\frac{2 A}{3} \cdot \frac{5}{5} + \frac{A}{5} \cdot \frac{3}{3} = \frac{8}{15}$

Step 1.4

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

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Step 1.4.1

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

$\frac{2 A \cdot 5}{3 \cdot 5} + \frac{A}{5} \cdot \frac{3}{3} = \frac{8}{15}$

Step 1.4.2

Multiply $3$ by $5$ .

$\frac{2 A \cdot 5}{15} + \frac{A}{5} \cdot \frac{3}{3} = \frac{8}{15}$

Step 1.4.3

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

$\frac{2 A \cdot 5}{15} + \frac{A \cdot 3}{5 \cdot 3} = \frac{8}{15}$

Step 1.4.4

Multiply $5$ by $3$ .

$\frac{2 A \cdot 5}{15} + \frac{A \cdot 3}{15} = \frac{8}{15}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 A \cdot 5 + A \cdot 3}{15} = \frac{8}{15}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

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

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Step 1.6.1.1

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

$\frac{A (2 \cdot 5) + A \cdot 3}{15} = \frac{8}{15}$

Step 1.6.1.2

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

$\frac{A (2 \cdot 5) + A (3)}{15} = \frac{8}{15}$

Step 1.6.1.3

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

$\frac{A (2 \cdot 5 + 3)}{15} = \frac{8}{15}$

Step 1.6.2

Multiply $2$ by $5$ .

$\frac{A (10 + 3)}{15} = \frac{8}{15}$

Step 1.6.3

Add $10$ and $3$ .

$\frac{A \cdot 13}{15} = \frac{8}{15}$

Step 1.7

Move $13$ to the left of $A$ .

$\frac{13 A}{15} = \frac{8}{15}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$13 A = 8$

Step 3

Divide each term in $13 A = 8$ by $13$ and simplify.

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Step 3.1

Divide each term in $13 A = 8$ by $13$ .

$\frac{13 A}{13} = \frac{8}{13}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $13$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{13 A}{13} = \frac{8}{13}$

Step 3.2.1.2

Divide $A$ by $1$ .

$A = \frac{8}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$A = \frac{8}{13}$

Decimal Form:

$A = 0.\overline{615384}$