Algebra Examples

$\frac{1}{4} b = - \frac{3}{5} c$

Step 1

Multiply each term in $\frac{1}{4} b = - \frac{3}{5} c$ by $4$ to eliminate the fractions.

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Step 1.1

Multiply each term in $\frac{1}{4} b = - \frac{3}{5} c$ by $4$ .

$\frac{1}{4} b \cdot 4 = - \frac{3}{5} c \cdot 4$

Step 1.2

Simplify the left side.

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Step 1.2.1

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

$\frac{b}{4} \cdot 4 = - \frac{3}{5} c \cdot 4$

Step 1.2.2

Cancel the common factor of $4$ .

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Step 1.2.2.1

Cancel the common factor.

$\frac{b}{4} \cdot 4 = - \frac{3}{5} c \cdot 4$

Step 1.2.2.2

Rewrite the expression.

$b = - \frac{3}{5} c \cdot 4$

Step 1.3

Simplify the right side.

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Step 1.3.1

Combine $c$ and $\frac{3}{5}$ .

$b = - \frac{c \cdot 3}{5} \cdot 4$

Step 1.3.2

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

$b = - \frac{3 \cdot c}{5} \cdot 4$

Step 1.3.3

Multiply $- \frac{3 c}{5} \cdot 4$ .

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Step 1.3.3.1

Multiply $4$ by $- 1$ .

$b = - 4 \frac{3 c}{5}$

Step 1.3.3.2

Combine $- 4$ and $\frac{3 c}{5}$ .

$b = \frac{- 4 (3 c)}{5}$

Step 1.3.3.3

Multiply $3$ by $- 4$ .

$b = \frac{- 12 c}{5}$

Step 1.3.4

Move the negative in front of the fraction.

$b = - \frac{12 c}{5}$

Step 2

Since the equation can be written in the form $y = k x$ , $y$ varies directly with $x$ and $k$ . The constant of variation, $k$ , is $- \frac{12}{5}$ .

$- \frac{12}{5}$