1 / 25

Basic Algibra in Computational Mathematics

Basic Algibra in Computational Mathematics

Kaveesha1
Download Presentation

Basic Algibra in Computational Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1. Basic Concepts of Algebra By : H. F. K. M. Fonseka M.Sc. in IT (in Reading) , UOM B.Sc. (Special in Computer Science), SEUSL 5/28/2025 1

  2. Content 1. Introduction to Algebraic Expressions 2. Basic Operations with Algebraic Expressions 3. Laws of Exponents 4. Solving Linear Equations 5/28/2025 2

  3. Algebraic Expressions • An algebraic expression is a mathematical phrase that includes numbers, variables, and operations. Ex : ?? + ? • Components: • Numbers (constants) • Variables (Ex: x, y) • Operations (+, -, ×, ÷) 5/28/2025 3

  4. Introduction to Terms, Coefficients, Variables, and Constants • Term: A part of an expression separated by + , –, * or / Ex: 3x + 5 • Coefficient: The numerical part of a term with a variable Ex: 3 in 3x • Variable: A symbol representing an unknown value Ex: x • Constant: A fixed number without variables Ex: 5 5/28/2025 4

  5. Practice Problems Considering the given equations, identify the terms. 1. 5? + 3? 2. 7? − 3 3. 6? + 8 4. 2?2+ 2 5. 3?3+ 2?2+ 3? + 3 5/28/2025 5

  6. Simplifying Expressions • The Combining terms must have the same variables raised to the same powers. • Combine them under mathematical operations. • Example: • 4? + 3? = ?? • 2? + 5 − 3? + 1 = −? + ? 5/28/2025 6

  7. Practice Problems Simplify ➔ 1. 5? + 2? – 3 2. 2? + 4? − ? + 6? 3. (3? + 4) + (2? − 5) 4. 7? − 3 = 5? 5. 6? + 8 = 5 5/28/2025 7

  8. Basic Operations • Four basic operations on algebraic expressions: - Addition - Subtraction - Multiplication - Division - These operations follow algebraic rules and involve combining like terms, applying distributive law, and simplifying. 5/28/2025 8

  9. Addition and Subtraction of Algebraic Terms • Combine the terms: • 3x + 5x = 8x • 4a - 2a = 2a Example: (2? + 3) + (4? − 5) = 6? − 2 • Always group the terms before simplify. 5/28/2025 9

  10. Multiplication and Division of Algebraic Terms Multiply and divide the coefficients, when applicable. • ? × ? = ?? • 2? × 3? = 6?? • 6?? ÷ 3? = 2? • (2?)(3?) = 6?? • (4?²?) ÷ (2?) = 2?? 5/28/2025 10

  11. Distributive Property • The distributive property allows multiplying a single term by terms inside parentheses: • a(b + c) = ab + ac • Example: 3(x + 2) = 3x + 6 • Use it to simplify expressions before combining the terms. 5/28/2025 11

  12. Introduction to Exponents • Exponents represent repeated multiplication. Example: ?³ = ? × ? × ? • Base → : The number being multiplied • Exponent → : How many times the base is multiplied by itself • Example: 2⁴ = 2 × 2 × 2 × 2 = 16 Exponent 24 Base 5/28/2025 12

  13. Laws of Exponents 1. Product Rule: ?ᵐ × ?ⁿ = ?ᵐ⁺ⁿ 2. Quotient Rule: ?ᵐ ?ⁿ= ?ᵐ⁻ⁿ,? ≠ 0 3. Power Rule: ?ᵐ ⁿ = ??∗? Examples: • 3² × 3⁴ = 3⁶ 56 52= 5⁴ • (2³)² = 2⁶ • 5/28/2025 13

  14. Zero & Negative Powers • Zero Exponent: ?⁰ = 1 (??? ? ≠ 0) • Negative Exponent: ?⁻ⁿ = 1 / ?ⁿ • Examples: • 4⁰ = 1 • 2⁻³ = 1 / 8 5/28/2025 14

  15. Simplify: ?3?−2 2 ? ?−1 • Steps: 1. Expand the numerator: ?⁶ ?⁻⁴ 2. Divide: ?6 ? ?−4 ?−1= ?⁻³ = ?⁵ 3. Final Answer: ?5 ?3 5/28/2025 15

  16. Practice Problems ?3⋅?−22 ?.?−1 • (3²)³ = ? • a⁵ / a² = ? • x⁰ = ? • 2⁻² = ? = ? • 3 ?2⋅?−3 (?4⋅?−2)= ? • 2 ?−1⋅?2 (?−3⋅?) ?4⋅?−13 ?2⋅?2 ?−2⋅?32 ?−1⋅?−4= ? = ? • = ? • • 5/28/2025 16

  17. Linear Equations • A linear equation is an equation that makes a straight line when graphed. y • Standard form: ?? + ? = ? ? = ? • The variable (usually x) has an exponent of 1. 0 x ??= ? 5/28/2025 17

  18. Solving One-Variable Equations: Step by Step Steps: 1. Rearrange the variables and all constants for the both sides. 2. Simplify both sides (if needed). 3. Use inverse operations to isolate the variable. 4. Solve for the variable. Example: • 2? + 3 = 11 subtract 3 from both sides, 2? + 3 − 3 = 11 – 3 2? = 8 divide both sides by 2, 2? 2=8 ? = ? 2 5/28/2025 18

  19. Inverse Operations • Inverse operations undo each other: • Addition ↔ Subtraction • Multiplication ↔ Division • Used to isolate the variable in an equation. Example: • ? + 5 = 9 → ? = 9 − 5 = 4 • 3? = 12 → ? = 12 ÷ 3 = 4 5/28/2025 19

  20. Practice Problems Find the value of the variable that makes the equation true. 1. 7? + 8 = 5? 2. 3? + 5 = 2? + 1 3. 4 + 8? = 3 – 8? 4. 10? + 7 = 5? 5/28/2025 20

  21. ???????????? • After solving, substitute the value back into the original equation. • If both sides are equal, the solution is correct. Example: • Equation: 2? + 3 = 11 • Solution: ? = 4 • Check: 2(4) + 3 = 8 + 3 = 11 ✓ 5/28/2025 21

  22. Practice Problems Check your answers by substitution! 1. x + 7 = 10 → x = ? 2. 5x = 20 → x = ? 3. 3x - 4 = 8 → x = ? 4. 4 + 8? = 3 – 8? → x = ? 5. 10? + 7 = 5? → x = ? 5/28/2025 ICBT , International Diploma in IT 22

  23. Summary • Linear equations have one variable. • Use inverse operations to isolate the variable. • Always check your solution by substitution. 5/28/2025 23

  24. 5/28/2025 24

More Related