Solve x/2/frac{13{4}}=5/10/frac{15{20}}

$$\frac { \frac { x } { 2 } } { \frac { 13 } { 4 } } = \frac { \frac { 5 } { 10 } } { \frac { 15 } { 20 } }$$

Solve for x

$$x = \frac{13}{3} = 4\frac{1}{3} \approx 4.333333333$$

Steps for Solving Linear Equation

Divide \frac{5}{10} by \frac{15}{20} by multiplying \frac{5}{10} by the reciprocal of \frac{15}{20}.

$$\frac{\frac{x}{2}}{\frac{13}{4}}=\frac{5\times 20}{10\times 15}$$

Cancel out 2\times 5\times 5 in both numerator and denominator.

$$\frac{\frac{x}{2}}{\frac{13}{4}}=\frac{2}{3}$$

Multiply both sides by \frac{13}{4}.

$$\frac{x}{2}=\frac{2}{3}\times \frac{13}{4}$$

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$6x=8\times \frac{13}{4}$$

Express 8\times \frac{13}{4} as a single fraction.

$$6x=\frac{8\times 13}{4}$$

Multiply 8 and 13 to get 104.

$$6x=\frac{104}{4}$$

Divide 104 by 4 to get 26.

$$6x=26$$

Divide both sides by 6.

$$x=\frac{26}{6}$$

Reduce the fraction \frac{26}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{13}{3}$$