Algebra Examples

$\frac{1}{4} (8 m - 4 n) + \frac{1}{3} (6 m + 3 n)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{4} (8 m) + \frac{1}{4} (- 4 n) + \frac{1}{3} \cdot (6 m + 3 n)$

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Factor $4$ out of $8 m$ .

$\frac{1}{4} (4 (2 m)) + \frac{1}{4} (- 4 n) + \frac{1}{3} \cdot (6 m + 3 n)$

Step 1.2.2

Cancel the common factor.

$\frac{1}{4} (4 (2 m)) + \frac{1}{4} (- 4 n) + \frac{1}{3} \cdot (6 m + 3 n)$

Step 1.2.3

Rewrite the expression.

$2 m + \frac{1}{4} (- 4 n) + \frac{1}{3} \cdot (6 m + 3 n)$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $- 4 n$ .

$2 m + \frac{1}{4} (4 (- n)) + \frac{1}{3} \cdot (6 m + 3 n)$

Step 1.3.2

Cancel the common factor.

$2 m + \frac{1}{4} (4 (- n)) + \frac{1}{3} \cdot (6 m + 3 n)$

Step 1.3.3

Rewrite the expression.

$2 m - n + \frac{1}{3} \cdot (6 m + 3 n)$

Step 1.4

Apply the distributive property.

$2 m - n + \frac{1}{3} (6 m) + \frac{1}{3} (3 n)$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $6 m$ .

$2 m - n + \frac{1}{3} (3 (2 m)) + \frac{1}{3} (3 n)$

Step 1.5.2

Cancel the common factor.

$2 m - n + \frac{1}{3} (3 (2 m)) + \frac{1}{3} (3 n)$

Step 1.5.3

Rewrite the expression.

$2 m - n + 2 m + \frac{1}{3} (3 n)$

Step 1.6

Cancel the common factor of $3$ .

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Step 1.6.1

Factor $3$ out of $3 n$ .

$2 m - n + 2 m + \frac{1}{3} (3 (n))$

Step 1.6.2

Cancel the common factor.

$2 m - n + 2 m + \frac{1}{3} (3 n)$

Step 1.6.3

Rewrite the expression.

$2 m - n + 2 m + n$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $2 m - n + 2 m + n$ .

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Step 2.1.1

Add $- n$ and $n$ .

$2 m + 2 m + 0$

Step 2.1.2

Add $2 m + 2 m$ and $0$ .

$2 m + 2 m$

Step 2.2

Add $2 m$ and $2 m$ .

$4 m$