Solve 5/6:3/16=x:9/4

$$\frac { 5 } { 6 } : \frac { 3 } { 16 } = x : \frac { 9 } { 4 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Divide \frac{5}{6} by \frac{3}{16} by multiplying \frac{5}{6} by the reciprocal of \frac{3}{16}.

$$\frac{5}{6}\times \frac{16}{3}=\frac{x}{\frac{9}{4}}$$

Multiply \frac{5}{6} times \frac{16}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 16}{6\times 3}=\frac{x}{\frac{9}{4}}$$

Do the multiplications in the fraction \frac{5\times 16}{6\times 3}.

$$\frac{80}{18}=\frac{x}{\frac{9}{4}}$$

Reduce the fraction \frac{80}{18} to lowest terms by extracting and canceling out 2.

$$\frac{40}{9}=\frac{x}{\frac{9}{4}}$$

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

$$\frac{x}{\frac{9}{4}}=\frac{40}{9}$$

Multiply both sides by \frac{9}{4}.

$$x=\frac{40}{9}\times \frac{9}{4}$$

Multiply \frac{40}{9} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{40\times 9}{9\times 4}$$

Cancel out 9 in both numerator and denominator.

$$x=\frac{40}{4}$$

Divide 40 by 4 to get 10.

$$x=10$$