The Language of Mathematics

• The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves
• Mathematics as a language uses symbols to express a formula or to represent a constant
• Mathematics language has syntax to make the expression well-formed and to make the characters and symbols clear and valid without violating the rules
• Mathematical symbols include:

  • Add (+)
  • Divide (÷)
  • Multiply (×)
  • Divide (/)
  • Equals (=)
  • Not equal to (≠)
  • Equivalent (≈)
  • Plus (+)
  • Minus (-)
  • Less than (<)
  • Less than or equal to (≤)
  • Greater than (>)
  • Greater than or equal to (≥)
  • Plus or minus (±)
  • Infinity (∞)
  • Therefore (∴)
• English statement to Mathematical Statement:

  • The difference of eight and three is five: 8 - 3 = 5
  • The sum of six and four, diminished by seven is three: 6 + 4 - 7 = 3
  • Twice the difference of ten and eight is four: 2(10 - 8) = 4
  • The sum of five times a number and one-fifth is eleven: 5x + 1/5 = 11
  • The product of twice a number and six is eight plus a number: 2x * 6 = 8 + x
• Mathematical statement to English Statement:

  • 14x - 2 = 5: The difference between one-fourth of a number and two is five
  • 3x - 6 = 2x: Three times a number diminished by six is twice the number
  • 5 + 2x = 11: The sum of five and twice a number is eleven
  • 3x = -21: Three times a number is the negative of twenty-one
  • 4x - 12 = 2(x - 5): The difference between four times a number and twelve is twice the difference of a number and five