Translating English Phrases into Algebraic Expressions

Variables and Expressions

  • A variable is a letter that represents an unknown number.
  • An expression is a combination of operations on numbers and variables.
  • Algebraic expressions translate English phrases using numbers, variables, and mathematical symbols (+, -, ×, ÷).

Key Phrases and Operations

  • The table in the video demonstrates common key phrases and their corresponding mathematical operations.
  • Equality relationships involve equations, which are covered later.

Translating English Phrases

  • Use x to represent the unknown number in the following examples.

Product of 12 and a Number

  • "Product" indicates multiplication.
  • The expression is 12 * x or simply 12x. No other symbols like parentheses or dots are needed.
  • Avoid the x times symbol to prevent confusion.

Sum of a Number and Four Divided by Two

  • "Sum" indicates addition, and "divided by" indicates division.
  • First, add a number and four: x + 4.
  • Then, divide the entire sum by two.
  • Two ways to represent this:
    • (x + 4) / 2
    • \frac{x + 4}{2} (preferred for clarity)
  • Using a fraction makes it clearer that addition happens before division.

Quotient of 10 and a Number Plus Seven

  • "Quotient" indicates division, and "plus" indicates addition.
  • Divide 10 by a number: \frac{10}{x}.
  • Then, add seven to the result: \frac{10}{x} + 7.
  • While \frac{10}{x} + 7 is not technically wrong, the fractional representation is clearer.

18 Subtracted from Three Times a Number

  • "Times" indicates multiplication, and "subtracted from" indicates subtraction.
  • First, find three times a number: 3x.
  • Then, subtract 18 from that result: 3x - 18.

25% of a Number

  • "Of" can indicate multiplication, especially with percentages or fractions.
  • Convert the percentage to a decimal before writing the expression: 25% = 0.25.
  • The expression is 0.25 * x or simply 0.25x.
  • To convert a percentage to a decimal, divide by 100 (move the decimal point two places to the left).

Ratio of 32 and a Number

  • "Ratio" indicates division.
  • Divide 32 by a number: \frac{32}{x}.
  • While 32 \div x isn't incorrect, fractions are typically used for algebraic expressions.