Algebra Examples

$\frac{1}{4} k + \frac{1}{4} m - \frac{2}{3} k + \frac{5}{9} m$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{4}$ and $k$ .

$\frac{k}{4} + \frac{1}{4} m - \frac{2}{3} k + \frac{5}{9} m$

Step 1.2

Combine $\frac{1}{4}$ and $m$ .

$\frac{k}{4} + \frac{m}{4} - \frac{2}{3} k + \frac{5}{9} m$

Step 1.3

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

$\frac{k}{4} + \frac{m}{4} - \frac{k \cdot 2}{3} + \frac{5}{9} m$

Step 1.4

Move $2$ to the left of $k$ .

$\frac{k}{4} + \frac{m}{4} - \frac{2 \cdot k}{3} + \frac{5}{9} m$

Step 1.5

Combine $\frac{5}{9}$ and $m$ .

$\frac{k}{4} + \frac{m}{4} - \frac{2 k}{3} + \frac{5 m}{9}$

Step 2

Combine the numerators over the common denominator.

$\frac{k + m}{4} - \frac{2 k}{3} + \frac{5 m}{9}$

Step 3

To write $\frac{k + m}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{k + m}{4} \cdot \frac{3}{3} - \frac{2 k}{3} + \frac{5 m}{9}$

Step 4

To write $- \frac{2 k}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{k + m}{4} \cdot \frac{3}{3} - \frac{2 k}{3} \cdot \frac{4}{4} + \frac{5 m}{9}$

Step 5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{k + m}{4}$ by $\frac{3}{3}$ .

$\frac{(k + m) \cdot 3}{4 \cdot 3} - \frac{2 k}{3} \cdot \frac{4}{4} + \frac{5 m}{9}$

Step 5.2

Multiply $4$ by $3$ .

$\frac{(k + m) \cdot 3}{12} - \frac{2 k}{3} \cdot \frac{4}{4} + \frac{5 m}{9}$

Step 5.3

Multiply $\frac{2 k}{3}$ by $\frac{4}{4}$ .

$\frac{(k + m) \cdot 3}{12} - \frac{2 k \cdot 4}{3 \cdot 4} + \frac{5 m}{9}$

Step 5.4

Multiply $3$ by $4$ .

$\frac{(k + m) \cdot 3}{12} - \frac{2 k \cdot 4}{12} + \frac{5 m}{9}$

Step 6

Combine the numerators over the common denominator.

$\frac{(k + m) \cdot 3 - 2 k \cdot 4}{12} + \frac{5 m}{9}$

Step 7

Simplify the numerator.

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Step 7.1

Apply the distributive property.

$\frac{k \cdot 3 + m \cdot 3 - 2 k \cdot 4}{12} + \frac{5 m}{9}$

Step 7.2

Move $3$ to the left of $k$ .

$\frac{3 \cdot k + m \cdot 3 - 2 k \cdot 4}{12} + \frac{5 m}{9}$

Step 7.3

Move $3$ to the left of $m$ .

$\frac{3 \cdot k + 3 \cdot m - 2 k \cdot 4}{12} + \frac{5 m}{9}$

Step 7.4

Multiply $3$ by $m$ .

$\frac{3 k + 3 m - 2 k \cdot 4}{12} + \frac{5 m}{9}$

Step 7.5

Multiply $4$ by $- 2$ .

$\frac{3 k + 3 m - 8 k}{12} + \frac{5 m}{9}$

Step 7.6

Subtract $8 k$ from $3 k$ .

$\frac{- 5 k + 3 m}{12} + \frac{5 m}{9}$

Step 8

To write $\frac{- 5 k + 3 m}{12}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- 5 k + 3 m}{12} \cdot \frac{3}{3} + \frac{5 m}{9}$

Step 9

To write $\frac{5 m}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{- 5 k + 3 m}{12} \cdot \frac{3}{3} + \frac{5 m}{9} \cdot \frac{4}{4}$

Step 10

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 10.1

Multiply $\frac{- 5 k + 3 m}{12}$ by $\frac{3}{3}$ .

$\frac{(- 5 k + 3 m) \cdot 3}{12 \cdot 3} + \frac{5 m}{9} \cdot \frac{4}{4}$

Step 10.2

Multiply $12$ by $3$ .

$\frac{(- 5 k + 3 m) \cdot 3}{36} + \frac{5 m}{9} \cdot \frac{4}{4}$

Step 10.3

Multiply $\frac{5 m}{9}$ by $\frac{4}{4}$ .

$\frac{(- 5 k + 3 m) \cdot 3}{36} + \frac{5 m \cdot 4}{9 \cdot 4}$

Step 10.4

Multiply $9$ by $4$ .

$\frac{(- 5 k + 3 m) \cdot 3}{36} + \frac{5 m \cdot 4}{36}$

Step 11

Combine the numerators over the common denominator.

$\frac{(- 5 k + 3 m) \cdot 3 + 5 m \cdot 4}{36}$

Step 12

Simplify the numerator.

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Step 12.1

Apply the distributive property.

$\frac{- 5 k \cdot 3 + 3 m \cdot 3 + 5 m \cdot 4}{36}$

Step 12.2

Multiply $3$ by $- 5$ .

$\frac{- 15 k + 3 m \cdot 3 + 5 m \cdot 4}{36}$

Step 12.3

Multiply $3$ by $3$ .

$\frac{- 15 k + 9 m + 5 m \cdot 4}{36}$

Step 12.4

Multiply $4$ by $5$ .

$\frac{- 15 k + 9 m + 20 m}{36}$

Step 12.5

Add $9 m$ and $20 m$ .

$\frac{- 15 k + 29 m}{36}$

Step 13

Simplify with factoring out.

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Step 13.1

Factor $- 1$ out of $- 15 k$ .

$\frac{- (15 k) + 29 m}{36}$

Step 13.2

Factor $- 1$ out of $29 m$ .

$\frac{- (15 k) - (- 29 m)}{36}$

Step 13.3

Factor $- 1$ out of $- (15 k) - (- 29 m)$ .

$\frac{- (15 k - 29 m)}{36}$

Step 13.4

Simplify the expression.

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Step 13.4.1

Rewrite $- (15 k - 29 m)$ as $- 1 (15 k - 29 m)$ .

$\frac{- 1 (15 k - 29 m)}{36}$

Step 13.4.2

Move the negative in front of the fraction.

$- \frac{15 k - 29 m}{36}$