Percentages

  • Increase and Decrease Calculations:
    • Increase a number by a percentage:
      Increase 25 by 40%:40×25100=10\text{Increase } 25\text{ by } 40\%: \frac{40 \times 25}{100} = 10
      So, new value is 25+10=3525 + 10 = 35.
    • Decrease a number by a percentage:
      Decrease 150 by 20%:20×150100=30\text{Decrease } 150\text{ by } 20\%: \frac{20 \times 150}{100} = 30
      So, new value is 150−30=120150 - 30 = 120.

Algebraic Expressions

  • Rules for Like Terms:
    • Like terms: terms with exact same variables and exponents.
    • Example of like terms: 20c,5c,6c20c, 5c, 6c.
  • Combining Like Terms:
    • Example: 2x+5c+6x=8x+5c2x + 5c + 6x = 8x + 5c.
    • Maintain order (alphabetical).

Simplification of Algebraic Expressions

  • Basic Addition and Multiplication:
    • Example: x+x+x=3xx + x + x = 3x.
    • E.g., 2x+3x+x=6x2x + 3x + x = 6x.
  • Combination of variables:
    • Keep track of coefficients.
    • Simplifying expressions with mixed variables.

Multiplication of Algebraic Expressions

  • Multiplying Monomials:
    • Step 1: Multiply coefficients.
    • Step 2: Apply the law of exponents for variables.
    • Example:
    • (−7x)(−4y)=28xy(-7x)(-4y) = 28xy.

Operations Involving Monomials

  • Using distributive property for multiplication:
    • Example:
    • Simplifying combinations such as 50c3+10x250c^3 + 10x^2 or others using laws of exponents.
  • Exponent Basics:
    • Use laws of exponents when multiplying or dividing terms.