Adding and Subtracting Like Terms
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to add and subtract like terms in algebraic expressions. Students identify terms with the same variable and exponent, then add or subtract their coefficients to simplify the expression into fewer terms.
Key Concepts
Property To add like terms: Add the numerical coefficients of the terms. Do not change the variable factors of the terms. To subtract like terms: Subtract the numerical coefficients of the terms. Do not change the variable factors of the terms. Replacing an expression by a simpler equivalent one is called simplifying the expression.
Examples To simplify $7b + 4b$, we add the coefficients: $(7+4)b = 11b$. We have combined the like terms into a single, simpler term. To simplify $12k ( 3k)$, we subtract the coefficients: $(12 ( 3))k = (12+3)k = 15k$. The variable factor $k$ remains unchanged. We cannot simplify $8p + 5q$ because $8p$ and $5q$ are not like terms. Their variable factors are different.
Explanation When combining like terms, you only perform the operation on their coefficients. The variable part just tells you what 'family' of terms you're counting. It's like adding 4 apples and 5 apples to get 9 apples.
Common Questions
How do you add like terms?
Identify terms with the same variable and exponent, then add or subtract their coefficients. The variable part stays the same. For example, 4x + 3x = 7x.
Can you add 3x and 3x^2?
No. 3x and 3x^2 are not like terms because the exponents are different. You cannot combine them by adding.
How do you subtract like terms?
Subtract the coefficients of the like terms. For example, 8y - 5y = 3y.
What happens to unlike terms when simplifying?
Unlike terms cannot be combined—leave them as separate terms in the simplified expression.
Where is adding and subtracting like terms taught?
This skill is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.