Basic Math Examples

$\frac{2 a}{3 b} + \frac{1 b}{5 a}$

Step 1

Multiply $b$ by $1$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

$\frac{2 a (5 a)}{3 b (5 a)} + \frac{b}{5 a} \cdot \frac{3 b}{3 b}$

Step 4.2

Multiply $5$ by $3$ .

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

Step 4.3

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

$\frac{2 a (5 a)}{15 b a} + \frac{b (3 b)}{5 a (3 b)}$

Step 4.4

Multiply $3$ by $5$ .

$\frac{2 a (5 a)}{15 b a} + \frac{b (3 b)}{15 a b}$

Step 4.5

Reorder the factors of $15 b a$ .

$\frac{2 a (5 a)}{15 a b} + \frac{b (3 b)}{15 a b}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 a (5 a) + b (3 b)}{15 a b}$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite using the commutative property of multiplication.

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

Step 6.2

Multiply $a$ by $a$ by adding the exponents.

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Step 6.2.1

Move $a$ .

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

Step 6.2.2

Multiply $a$ by $a$ .

$\frac{2 \cdot 5 a^{2} + b (3 b)}{15 a b}$

Step 6.3

Multiply $2$ by $5$ .

$\frac{10 a^{2} + b (3 b)}{15 a b}$

Step 6.4

Rewrite using the commutative property of multiplication.

$\frac{10 a^{2} + 3 b \cdot b}{15 a b}$

Step 6.5

Multiply $b$ by $b$ by adding the exponents.

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Step 6.5.1

Move $b$ .

$\frac{10 a^{2} + 3 (b \cdot b)}{15 a b}$

Step 6.5.2

Multiply $b$ by $b$ .

$\frac{10 a^{2} + 3 b^{2}}{15 a b}$