Simplify Expressions With Decimal Coefficients

Simplifying expressions with decimal coefficients

When an expression has like terms, you can combine them by adding or subtracting their coefficients, even if those coefficients are decimals.

1) Identify like terms

Like terms have the same variable part. For example, terms with just x can be combined with other x terms, and terms with x^2 can only be combined with other x^2 terms.

2) Add or subtract the decimal coefficients

Keep the variable part the same and combine only the numbers in front.

• 2.5x + 1.3x = (2.5 + 1.3)x = 3.8x
• 7.2y - 0.6y = (7.2 - 0.6)y = 6.6y

3) Watch signs carefully

If a term is being subtracted, the coefficient changes sign when you combine terms. Write the decimal operation clearly to avoid mistakes.

4) Simplify the final expression

After combining all like terms, write the result in its simplest form. If there are no like terms left, the expression is already simplified.

Quick check

Re-read the original expression and make sure:

• every combined group had the same variable part,
• the decimal arithmetic is correct,
• no like terms were missed.

If possible, substitute a simple value for the variable in both the original and simplified expressions to see whether they match.