Skill: Evaluate expressions with fractions

Explanation and Free Practice Resources

Evaluating expressions with fractions means interpreting a variable as a number, substituting given fractional, whole-number, or decimal values, and determining the resulting value while preserving parentheses and the order of operations. It includes adding, subtracting, multiplying, and dividing fractions accurately, recognizing that a fraction may represent a quantity or an operation, and distinguishing substitution from changing the expression’s structure; more advanced algebraic manipulation and generalized rational expressions are outside this scope.

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Detailed Explanation: Evaluate expressions with fractions

To evaluate an expression with fractions:

Substitute the given value for the variable.
Keep the parentheses and follow the order of operations.
Add, subtract, multiply, or divide the fractions carefully.
Simplify the final answer.

Example: Evaluate

\frac{5}{6}-2\left(x+\frac{1}{3}\right)

when

x=\frac{1}{2}.

Step 1: Substitute $\frac{1}{2}$ for $x$ :

\frac{5}{6}-2\left(\frac{1}{2}+\frac{1}{3}\right)

Step 2: Evaluate inside the parentheses. The least common denominator of $2$ and $3$ is $6$ :

\frac{1}{2}+\frac{1}{3} =\frac{3}{6}+\frac{2}{6} =\frac{5}{6}

Now the expression is

\frac{5}{6}-2\left(\frac{5}{6}\right).

Step 3: Multiply:

2\left(\frac{5}{6}\right)=\frac{10}{6}.

So the expression becomes

\frac{5}{6}-\frac{10}{6}.

Step 4: Subtract:

\frac{5}{6}-\frac{10}{6} =-\frac{5}{6}.

Therefore, the value of the expression is

\boxed{-\frac{5}{6}}.

Remember: substitution replaces the variable with its value, but it does not change the expression’s structure.

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Algebraic Function Variable Substitution - Fractional Terms

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