Mathematics » Introducing Fractions » Add and Subtract Fractions with Different Denominators

Evaluating Variable Expressions with Fractions

Evaluating Variable Expressions with Fractions

We have evaluated expressions before, but now we can also evaluate expressions with fractions. Remember, to evaluate an expression, we substitute the value of the variable into the expression and then simplify.

Example

Evaluate \(x+\frac{1}{3}\) when

  1. \(x=-\frac{1}{3}\)
  2. \(x=-\frac{3}{4}.\)

Solution

To evaluate \(x+\frac{1}{3}\) when \(x=-\frac{1}{3},\) substitute \(-\frac{1}{3}\) for \(x\) in the expression.

 \(x+\frac{1}{3}\)
Evaluating Variable Expressions with FractionsEvaluating Variable Expressions with Fractions
Simplify.\(0\)

To evaluate \(x+\frac{1}{3}\) when \(x=-\frac{3}{4},\) we substitute \(-\frac{3}{4}\) for \(x\) in the expression.

 \(x+\frac{1}{3}\)
Evaluating Variable Expressions with FractionsEvaluating Variable Expressions with Fractions
Rewrite as equivalent fractions with the LCD, 12.\(-\frac{3·3}{4·3}+\frac{1·4}{3·4}\)
Simplify the numerators and denominators.\(-\frac{9}{12}+\frac{4}{12}\)
Add.\(-\frac{5}{12}\)

Example

Evaluate \(y-\frac{5}{6}\) when \(y=-\frac{2}{3}.\)

Solution

We substitute \(-\frac{2}{3}\) for \(y\) in the expression.

 \(y-\frac{5}{6}\)
Evaluating Variable Expressions with FractionsEvaluating Variable Expressions with Fractions
Rewrite as equivalent fractions with the LCD, 6.\(-\frac{4}{6}-\frac{5}{6}\)
Subtract.\(-\frac{9}{6}\)
Simplify.\(-\frac{3}{2}\)

Example

Evaluate \(2{x}^{2}y\) when \(x=\frac{1}{4}\) and \(y=-\frac{2}{3}.\)

Solution

Substitute the values into the expression. In \(2{x}^{2}y,\) the exponent applies only to \(x.\)

 Evaluating Variable Expressions with Fractions
Evaluating Variable Expressions with FractionsEvaluating Variable Expressions with Fractions
Simplify exponents first.Evaluating Variable Expressions with Fractions
Multiply. The product will be negative.Evaluating Variable Expressions with Fractions
Simplify.Evaluating Variable Expressions with Fractions
Remove the common factors.Evaluating Variable Expressions with Fractions
Simplify.Evaluating Variable Expressions with Fractions

Example

Evaluate \(\frac{p+q}{r}\) when \(p=-4,q=-2,\) and \(r=8.\)

Solution

We substitute the values into the expression and simplify.

 \(\frac{p+q}{r}\)
Evaluating Variable Expressions with FractionsEvaluating Variable Expressions with Fractions
Add in the numerator first.\(-\frac{6}{8}\)
Simplify.\(-\frac{3}{4}\)

[Attributions and Licenses]


This is a lesson from the tutorial, Introducing Fractions and you are encouraged to log in or register, so that you can track your progress.

Log In

Do NOT follow this link or you will be banned from the site!