Ctrl+k

Evaluate expressions with fractions

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.

Detailed Explanation: Evaluate expressions with fractions

To evaluate an expression with fractions:

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

Example: Evaluate

56−2(x+13)\frac{5}{6}-2\left(x+\frac{1}{3}\right)

when

x=12.x=\frac{1}{2}.

Step 1: Substitute 12\frac{1}{2} for xx:

56−2(12+13)\frac{5}{6}-2\left(\frac{1}{2}+\frac{1}{3}\right)

Step 2: Evaluate inside the parentheses. The least common denominator of 22 and 33 is 66:

12+13=36+26=56\frac{1}{2}+\frac{1}{3} =\frac{3}{6}+\frac{2}{6} =\frac{5}{6}

Now the expression is

56−2(56).\frac{5}{6}-2\left(\frac{5}{6}\right).

Step 3: Multiply:

2(56)=106.2\left(\frac{5}{6}\right)=\frac{10}{6}.

So the expression becomes

56−106.\frac{5}{6}-\frac{10}{6}.

Step 4: Subtract:

56−106=−56.\frac{5}{6}-\frac{10}{6} =-\frac{5}{6}.

Therefore, the value of the expression is

−56.\boxed{-\frac{5}{6}}.

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

Learn by doing: Evaluate expressions with fractions

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Algebraic Function Variable Substitution - Fractional Terms

      ?