Math with Mr. J: Writing Algebraic Expressions

Overview

• Topic: Writing algebraic expressions with variables.
• Focus: Expressions with one and two operations.
• Importance: Understanding algebraic expressions lays a solid foundation for algebra and math in general.
• Key Skill: Recognizing keywords to apply correct operations and problem-solving skills.

Expressions with One Operation

Multiplication

• Example 1: Product of 9 and m
  • Keyword: Product (indicates multiplication)
  • Correct notation:
    • 9m (number next to a variable represents multiplication)
    • 9 * m (using an asterisk)
    • 9 (\cdot) m (using a filled circle)
    • 9(m) (using parentheses)
  • Avoid: Using 'x' for multiplication (could be confused with a variable)*

Division

• Example 2: Number x divided by 12
  • Division can be represented by:
    • x ÷ 12
    • x/12 (using a slash)

Subtraction

• Example 3: Seven less than r
  • Keyword: Less than (switch the order)
  • Notation: r - 7

Addition

• Example 4: Sum of w and 55
  • Keyword: Sum (indicates addition)
  • Notation: w + 55

More Subtraction

• Example 5: Difference of c and 38
  • Keyword: Difference (subtraction, order does not switch)
  • Notation: c - 38

Additional Addition

• Example 6: Number y increased by 10
  • Keyword: Increased (indicates addition)
  • Notation: y + 10

More Multiplication

• Example 7: 21 times a number g
  • Notation: 21g

Division Again

• Example 8: Quotient of 46 and x
  • Keyword: Quotient (indicates division)
  • Division as a fraction: (\frac{46}{x})

Expressions with Two Operations

Example 1

• Phrase: Sum of a number x and 8, then multiply by 10
  • Break it down:
    • First, the sum: x + 8
    • Use parentheses to show order: (x + 8)
    • Multiply by 10: (x + 8) * 10
  • Alternatively: 10(x + 8)
  • Incorrect: x + 8 * 10 (due to order of operations)

Example 2

• Phrase: Quotient of 25 and a number y, increased by a number m
  • Division first: (\frac{25}{y}) or (25 ÷ y)
  • Increased by m: (\frac{25}{y} + m)
  • Parentheses not necessary due to order of operations.

Example 3

• Phrase: Subtract a number w from 81, then divide by 2
  • Subtraction first: 81 - w
  • Divide by 2: (\frac{81-w}{2}) or (81 - w) ÷ 2

Example 4

• Phrase: 5 times the difference of 33 and a number x
  • Difference first: 33 - x
  • Multiply by 5: 5(33 - x)

Conclusion

• Double-check algebraic expressions to ensure they match the original phrase and follow the order of operations.
• Understanding how to correctly translate phrases into algebraic expressions is crucial for proficiency in algebra.