Q49. - Algebra 2

Question

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

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

Step-by-Step Solution

Answer

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

Step 1 - 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.

Step 2 - Substitute given values

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

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

Step 3 - Simplify 1 1 2 + 1 6

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

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

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