Algebra Toolkit

Letters standing for numbers

• Algebra uses letters in place of numbers that are unknown or that stand for any value
• A letter used this way is called a variable
• Knowing what a letter represents matters as much as the working, so questions define it before using it

Writing operations

• Addition and subtraction are written with the usual signs
• Multiplication has no sign at all: the letters are simply written together
  • ab means a × b, and 5ab means 5 × a × b
  • A number is written before the letters, so 5a rather than a5
• Division is written as a fraction rather than with a division sign
  • a/b means a ÷ b
• Powers and roots behave exactly as they do with numbers
  • a² means a × a, and 4a² squares first and multiplies by 4 afterwards
• Brackets group in the usual way, so 3(a + b) adds first and multiplies the result by 3
• The order of operations is unchanged, which is what settles how an expression such as ab + c/3 is read