Exam Questions – Addition & subtraction

Exam Questions – Addition & subtraction

Algebra – Addition & Subtraction of Terms

Concept Overview

  • In algebra, terms can be added or subtracted just like regular numbers.
  • Addition and subtraction in algebra follow the same rules, but the variables add an extra layer of complexity.

Types of Terms for Addition & Subtraction

  • A term in an algebraic expression can be a standalone number, a variable (like x or y), or a combination of the two. The terms are usually separated by plus (+) or minus (-) signs.
  • Like terms are terms whose variables (and their powers/exponents) are the same. For example, 2x and 5x are like terms because they both contain the same variable, x.
  • Unlike terms contain differing variables or differing powers of the same variable. For instance, 2x and 3y are unlike terms.

Addition and Subtraction Rules

  • Addition and subtraction in algebra occur directly between like terms.
  • When adding or subtracting like terms, combine their coefficients (the numbers in front of the variable). For example, 2x + 3x equals 5x.
  • Unlike terms cannot be added or subtracted directly because they do not refer to the same quantity or entity.

Examples

  • For example, consider the expression: 3x + 5 - 2x + 7. Here, 3x and -2x are like terms and can be combined to give x. Also, 5 and 7 are like terms that combine to give 12. Hence, the simplified expression is: x + 12.
  • In the expression 4x - 3y + 2x - 5y, the like terms are 4x and 2x which combine to give 6x. The terms -3y and -5y combine to give -8y. Thus, the simplified expression is 6x - 8y.

Practical Application

  • Understanding how to add and subtract terms in algebra is fundamental to solving equations and simplification of expressions.
  • Regular practice will enhance confidence and improve problem-solving ability.

Conclusion

  • Master the addition and subtraction of algebraic terms by identifying like terms and combining them effectively.
  • Remember, unlike terms cannot be added or subtracted directly. Continue practising and applying these concepts to improve your ability.