Pre-Algebra Examples

$\frac{3 m}{2 n} + \frac{5 n}{4 m}$

Step 1

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

$\frac{3 m}{2 n} \cdot \frac{2 m}{2 m} + \frac{5 n}{4 m}$

Step 2

To write $\frac{5 n}{4 m}$ as a fraction with a common denominator, multiply by $\frac{n}{n}$ .

$\frac{3 m}{2 n} \cdot \frac{2 m}{2 m} + \frac{5 n}{4 m} \cdot \frac{n}{n}$

Step 3

Write each expression with a common denominator of $4 n m$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3 m}{2 n}$ by $\frac{2 m}{2 m}$ .

$\frac{3 m (2 m)}{2 n (2 m)} + \frac{5 n}{4 m} \cdot \frac{n}{n}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{3 m (2 m)}{4 n m} + \frac{5 n}{4 m} \cdot \frac{n}{n}$

Step 3.3

Multiply $\frac{5 n}{4 m}$ by $\frac{n}{n}$ .

$\frac{3 m (2 m)}{4 n m} + \frac{5 n \cdot n}{4 m n}$

Step 3.4

Reorder the factors of $4 n m$ .

$\frac{3 m (2 m)}{4 m n} + \frac{5 n \cdot n}{4 m n}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 m (2 m) + 5 n \cdot n}{4 m n}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{3 \cdot 2 m \cdot m + 5 n \cdot n}{4 m n}$

Step 5.2

Multiply $m$ by $m$ by adding the exponents.

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Step 5.2.1

Move $m$ .

$\frac{3 \cdot 2 (m \cdot m) + 5 n \cdot n}{4 m n}$

Step 5.2.2

Multiply $m$ by $m$ .

$\frac{3 \cdot 2 m^{2} + 5 n \cdot n}{4 m n}$

Step 5.3

Multiply $3$ by $2$ .

$\frac{6 m^{2} + 5 n \cdot n}{4 m n}$

Step 5.4

Multiply $n$ by $n$ by adding the exponents.

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Step 5.4.1

Move $n$ .

$\frac{6 m^{2} + 5 (n \cdot n)}{4 m n}$

Step 5.4.2

Multiply $n$ by $n$ .

$\frac{6 m^{2} + 5 n^{2}}{4 m n}$