Solve 5/6:x=3/4:2/5

$$\frac { 5 } { 6 } : x = \frac { 3 } { 4 } : \frac { 2 } { 5 }$$

Solve for x

$$x=\frac{4}{9}\approx 0.444444444$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\frac{5}{6}=x\times \frac{\frac{3}{4}}{\frac{2}{5}}$$

Divide \frac{3}{4} by \frac{2}{5} by multiplying \frac{3}{4} by the reciprocal of \frac{2}{5}.

$$\frac{5}{6}=x\times \frac{3}{4}\times \frac{5}{2}$$

Multiply \frac{3}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}=x\times \frac{3\times 5}{4\times 2}$$

Do the multiplications in the fraction \frac{3\times 5}{4\times 2}.

$$\frac{5}{6}=x\times \frac{15}{8}$$

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

$$x\times \frac{15}{8}=\frac{5}{6}$$

Multiply both sides by \frac{8}{15}, the reciprocal of \frac{15}{8}.

$$x=\frac{5}{6}\times \frac{8}{15}$$

Multiply \frac{5}{6} times \frac{8}{15} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{5\times 8}{6\times 15}$$

Do the multiplications in the fraction \frac{5\times 8}{6\times 15}.

$$x=\frac{40}{90}$$

Reduce the fraction \frac{40}{90} to lowest terms by extracting and canceling out 10.

$$x=\frac{4}{9}$$