Simplifying Expressions with Rational Coefficients
Simplifying expressions with rational coefficients means combining like terms where the coefficients are fractions or decimals. For example, 1/2 x + 3/4 x = (1/2 + 3/4) x = (2/4 + 3/4) x = 5/4 x. The process is identical to combining integer like terms, but requires fraction arithmetic for the coefficients. This 6th grade algebra skill from enVision Mathematics Grade 6 is essential for solving equations with fractional coefficients and forms the foundation for all polynomial simplification in algebra.
Key Concepts
The process for combining like terms is the same for rational coefficients (fractions and decimals). Use the Distributive Property to add or subtract the coefficients, and keep the variable part unchanged: $ax + bx = (a+b)x$.
Common Questions
How do you simplify expressions with rational (fraction) coefficients?
Combine like terms by adding or subtracting their fractional coefficients. For 1/2 x + 3/4 x: find LCD = 4, giving 2/4 x + 3/4 x = 5/4 x.
What are like terms in an algebraic expression?
Like terms have the same variable raised to the same power. 3x and 5x are like terms; 3x and 3x squared are not. You can only add or subtract like terms.
What is a rational coefficient?
A rational coefficient is a fraction or integer (any number that can be expressed as a ratio of two integers). In 2/3 x, the coefficient is 2/3.
What grade simplifies expressions with rational coefficients?
This is a 6th grade algebra skill in enVision Mathematics Grade 6, building on fraction arithmetic and introducing algebraic simplification.
How do you combine terms with decimal coefficients?
Add or subtract the decimal coefficients directly. For 0.5x + 1.2x = 1.7x. Decimal coefficients follow the same rules as integer coefficients.
What is the first step when simplifying an expression with multiple terms?
Identify all like terms (same variable and power). Group them together. Then add or subtract their coefficients using the appropriate fraction or decimal arithmetic.