Solve 1/6x+1/y/frac{frac{1{3}x}{1/5y}}

$$\frac { \frac { 1 } { 6 } x + \frac { 1 } { y } } { \frac { \frac { 1 } { 3 } x } { \frac { 1 } { 5 } y } }$$

Evaluate

$$\frac{y}{10}+\frac{3}{5x}$$

Short Solution Steps

Divide \frac{1}{6}x+\frac{1}{y} by \frac{\frac{1}{3}x}{\frac{1}{5}y} by multiplying \frac{1}{6}x+\frac{1}{y} by the reciprocal of \frac{\frac{1}{3}x}{\frac{1}{5}y}.

$$\frac{\left(\frac{1}{6}x+\frac{1}{y}\right)\times \frac{1}{5}y}{\frac{1}{3}x}$$

Use the distributive property to multiply \frac{1}{6}x+\frac{1}{y} by \frac{1}{5}.

$$\frac{\left(\frac{1}{6}x\times \frac{1}{5}+\frac{1}{y}\times \frac{1}{5}\right)y}{\frac{1}{3}x}$$

Multiply \frac{1}{6} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{1\times 1}{6\times 5}x+\frac{1}{y}\times \frac{1}{5}\right)y}{\frac{1}{3}x}$$

Do the multiplications in the fraction \frac{1\times 1}{6\times 5}.

$$\frac{\left(\frac{1}{30}x+\frac{1}{y}\times \frac{1}{5}\right)y}{\frac{1}{3}x}$$

Multiply \frac{1}{y} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{1}{30}x+\frac{1}{y\times 5}\right)y}{\frac{1}{3}x}$$

Use the distributive property to multiply \frac{1}{30}x+\frac{1}{y\times 5} by y.

$$\frac{\frac{1}{30}xy+\frac{1}{y\times 5}y}{\frac{1}{3}x}$$

Express \frac{1}{y\times 5}y as a single fraction.

$$\frac{\frac{1}{30}xy+\frac{y}{y\times 5}}{\frac{1}{3}x}$$

Cancel out y in both numerator and denominator.

$$\frac{\frac{1}{30}xy+\frac{1}{5}}{\frac{1}{3}x}$$

Expand

$$\frac{y}{10}+\frac{3}{5x}$$

Short Solution Steps

Divide \frac{1}{6}x+\frac{1}{y} by \frac{\frac{1}{3}x}{\frac{1}{5}y} by multiplying \frac{1}{6}x+\frac{1}{y} by the reciprocal of \frac{\frac{1}{3}x}{\frac{1}{5}y}.

$$\frac{\left(\frac{1}{6}x+\frac{1}{y}\right)\times \frac{1}{5}y}{\frac{1}{3}x}$$

Use the distributive property to multiply \frac{1}{6}x+\frac{1}{y} by \frac{1}{5}.

$$\frac{\left(\frac{1}{6}x\times \frac{1}{5}+\frac{1}{y}\times \frac{1}{5}\right)y}{\frac{1}{3}x}$$

Multiply \frac{1}{6} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{1\times 1}{6\times 5}x+\frac{1}{y}\times \frac{1}{5}\right)y}{\frac{1}{3}x}$$

Do the multiplications in the fraction \frac{1\times 1}{6\times 5}.

$$\frac{\left(\frac{1}{30}x+\frac{1}{y}\times \frac{1}{5}\right)y}{\frac{1}{3}x}$$

Multiply \frac{1}{y} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{1}{30}x+\frac{1}{y\times 5}\right)y}{\frac{1}{3}x}$$

Use the distributive property to multiply \frac{1}{30}x+\frac{1}{y\times 5} by y.

$$\frac{\frac{1}{30}xy+\frac{1}{y\times 5}y}{\frac{1}{3}x}$$

Express \frac{1}{y\times 5}y as a single fraction.

$$\frac{\frac{1}{30}xy+\frac{y}{y\times 5}}{\frac{1}{3}x}$$

Cancel out y in both numerator and denominator.

$$\frac{\frac{1}{30}xy+\frac{1}{5}}{\frac{1}{3}x}$$