Solve {l}{1/y+1/10+2/1}{+1/4}

$$\left. \begin{array} { l } { \frac { 1 } { y } + \frac { 1 } { 10 } + \frac { 2 } { 1 } } \\ { + \frac { 1 } { 4 } } \end{array} \right.$$

Evaluate

$$\frac{47}{20}+\frac{1}{y}$$

Solution Steps

Anything divided by one gives itself.

$$\frac{1}{y}+\frac{1}{10}+2+\frac{1}{4}$$

Convert 2 to fraction \frac{20}{10}.

$$\frac{1}{y}+\frac{1}{10}+\frac{20}{10}+\frac{1}{4}$$

Since \frac{1}{10} and \frac{20}{10} have the same denominator, add them by adding their numerators.

$$\frac{1}{y}+\frac{1+20}{10}+\frac{1}{4}$$

Add 1 and 20 to get 21.

$$\frac{1}{y}+\frac{21}{10}+\frac{1}{4}$$

Least common multiple of 10 and 4 is 20. Convert \frac{21}{10} and \frac{1}{4} to fractions with denominator 20.

$$\frac{1}{y}+\frac{42}{20}+\frac{5}{20}$$

Since \frac{42}{20} and \frac{5}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{y}+\frac{42+5}{20}$$

Add 42 and 5 to get 47.

$$\frac{1}{y}+\frac{47}{20}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and 20 is 20y. Multiply \frac{1}{y} times \frac{20}{20}. Multiply \frac{47}{20} times \frac{y}{y}.

$$\frac{20}{20y}+\frac{47y}{20y}$$

Since \frac{20}{20y} and \frac{47y}{20y} have the same denominator, add them by adding their numerators.

$$\frac{20+47y}{20y}$$

Factor

$$\frac{47y+20}{20y}$$