Solve 2:3:6=a:6:c

$$2 : 3 : 6 = a : 6 : c$$

Solve for a

$$a=\frac{2c}{3}$$

$$c\neq 0$$

Solution Steps

Multiply both sides of the equation by 6c, the least common multiple of 6,c.

$$c\times \frac{2}{3}=6\times \frac{a}{6}$$

Express 6\times \frac{a}{6} as a single fraction.

$$c\times \frac{2}{3}=\frac{6a}{6}$$

Cancel out 6 and 6.

$$c\times \frac{2}{3}=a$$

Swap sides so that all variable terms are on the left hand side.

$$a=c\times \frac{2}{3}$$

Solve for c

$$c=\frac{3a}{2}$$

$$a\neq 0$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6c, the least common multiple of 6,c.

$$c\times \frac{2}{3}=6\times \frac{a}{6}$$

Express 6\times \frac{a}{6} as a single fraction.

$$c\times \frac{2}{3}=\frac{6a}{6}$$

Cancel out 6 and 6.

$$c\times \frac{2}{3}=a$$

The equation is in standard form.

$$\frac{2}{3}c=a$$

Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{3}c}{\frac{2}{3}}=\frac{a}{\frac{2}{3}}$$

Dividing by \frac{2}{3} undoes the multiplication by \frac{2}{3}.

$$c=\frac{a}{\frac{2}{3}}$$

Divide a by \frac{2}{3} by multiplying a by the reciprocal of \frac{2}{3}.

$$c=\frac{3a}{2}$$

Variable c cannot be equal to 0.

$$c=\frac{3a}{2}\text{, }c\neq 0$$