Simplify Expressions With Fractional Coefficients

Simplifying expressions with fractional coefficients

When terms have fractional coefficients, the goal is still to combine like terms. Like terms must have the same variable part, such as the same letter and the same exponent. Only the coefficients change.

1) Identify like terms

Group terms that match exactly in their variable part. For example, terms like (\frac{1}{2}x) and (\frac{3}{4}x) are like terms, but (\frac{1}{2}x) and (\frac{1}{2}x^2) are not.

2) Add or subtract the coefficients

Keep the variable part unchanged and work only with the fractions. If the coefficients have different denominators, find a common denominator first.

Example: [ \frac{1}{3}x+\frac{2}{5}x =\left(\frac{5}{15}+\frac{6}{15}\right)x =\frac{11}{15}x ]

3) Simplify the result

Reduce the fraction if possible and write the final coefficient in simplest form.

4) Check your work

A good check is to substitute a simple number for the variable and compare the value before and after simplifying. The expression should give the same result.

Common tip

If there are constants mixed in, combine them separately from the variable terms. Keep an eye on negative fractions and subtraction signs.