Question

Evaluate each expression if $w=6,x=0.4,y=\frac{1}{2},$and $z=-3$

$\frac{1}{y}+\frac{1}{w}$

Short answer

Expression $\frac{1}{y}+\frac{1}{w}$ results into$\frac{13}{6}$

Step-by-step solution

- Order of simplification

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

- Substitute given values

Substitute $\frac{1}{2}$for $y$, 6 for $w$into given expression

$\frac{1}{y}+\frac{1}{w}=\frac{1}{\frac{1}{2}}+\frac{1}{6}$

- Simplify  112+16

First take reciprocal of$y$and $w$, then take least common multiple of denominator and perform fraction addition as shown below

Reciprocal of$\frac{1}{2}$is$\frac{2}{1}$and of 6 is $\frac{1}{6}$

Least common multiple of 1 and 6 is 6

localid="1646745673704" $\begin{array}{c}\frac{1}{\frac{1}{2}}+\frac{1}{6}=\frac{2}{1}+\frac{1}{6}\\ =\frac{12+1}{6}\\ =\frac{13}{6}\end{array}$

Thus, value of$\frac{1}{y}+\frac{1}{w}$is $\frac{13}{6}$