Solve 3/4:t=5/16:4/9

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

Solve for t

$$t = \frac{16}{15} = 1\frac{1}{15} \approx 1.066666667$$

Steps for Solving Linear Equation

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

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

Divide \frac{5}{16} by \frac{4}{9} by multiplying \frac{5}{16} by the reciprocal of \frac{4}{9}.

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

Multiply \frac{5}{16} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{5\times 9}{16\times 4}.

$$\frac{3}{4}=t\times \frac{45}{64}$$

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

$$t\times \frac{45}{64}=\frac{3}{4}$$

Multiply both sides by \frac{64}{45}, the reciprocal of \frac{45}{64}.

$$t=\frac{3}{4}\times \frac{64}{45}$$

Multiply \frac{3}{4} times \frac{64}{45} by multiplying numerator times numerator and denominator times denominator.

$$t=\frac{3\times 64}{4\times 45}$$

Do the multiplications in the fraction \frac{3\times 64}{4\times 45}.

$$t=\frac{192}{180}$$

Reduce the fraction \frac{192}{180} to lowest terms by extracting and canceling out 12.

$$t=\frac{16}{15}$$