Chapter 3 Algebraic Expressions II
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This document discusses algebraic expressions and terms. An algebraic term is the product of unknowns and numbers, with the coefficient being the other factors. Like terms have the same unknowns, while unlike terms do not. To multiply algebraic terms, multiply the signs, coefficients, and unknowns. To divide terms, write as a fraction and simplify by cancelling common unknowns in the numerator and denominator. An algebraic expression is a combination of terms using addition and subtraction.
Chapter 3 Algebraic Expressions II
- 2. An unknown is a letter that represents a quantity whose value is yet to be determined. Example : 𝑥,𝑦,𝑧,𝑎,𝑏,… An algebraic term in two or more unknowns is the product of unknowns and a number. Example: 5𝑎3 = 5 × 𝑎 ×𝑎 × 𝑎
- 3. The coefficient of an unknown in an algebraic term is the other factors in that algebraic term. Example: Algebraic term Coefficient of 10𝑚𝑛 𝑚 𝑖 𝑠 10𝑛 𝑛 𝑖 𝑠 10𝑚 𝑚𝑛 𝑖 𝑠 10
- 4. Like terms are algebraic terms with the same unknowns. Example: 1 5𝑥𝑦, 102𝑥𝑦, 𝑥𝑦 𝑎𝑟𝑒 𝑙 𝑖 𝑘 𝑒 𝑡𝑒𝑟𝑚𝑠 3 Unlike terms are algebraic terms with the same unknowns. Example: 5𝑥𝑦 , 3𝑥, 5𝑦 𝑎𝑟𝑒 𝑢𝑛𝑙 𝑖 𝑘 𝑒 𝑡𝑒𝑟𝑚𝑠
- 5. The product of algebraic terms is found by multiplying a) The signs (positive and negative) b) The coefficients c) The unknowns Example: 5𝑝𝑞 × −2𝑝 = − 5 × 2 × 𝑝 × 𝑝 × 𝑞 = −10𝑝2 𝑞
- 6. The quotient of two algebraic terms is written in the form of a fraction a) Simplify the coefficient if possible b) Crossing out the same unknowns both in the numerator and denominator. Example: 7𝑝2 𝑞 ÷ 8𝑝𝑞 7× 𝑝× 𝑝× 𝑞 = 8× 𝑝× 𝑞 7 = 𝑝 8
- 7. An algebraic expression is a combination of two or more algebraic terms by addition or subtraction operations. There is no ‘ =’ sign in an algebraic expression.