2.6.3 Forming Expressions & Equations

How do I form an expression?

• An expression is an algebraic statement without an equals sign e.g. or 
• Sometimes we need to form expressions to help us express unknown values
• If a value is unknown you can represent it by a letter such as
• You can turn common phrases into expressions
  • Here you can represent the "something" by any letter
    
    

    2 less than "something"
    Double the amount of "something"
    5 lots of "something"
    3 more than "something"
    Half the amount of "something"

• You might need to use brackets to show the correct order
  • "something" add 1 then multiplied by 3
    • which simplifies to 
  • "something" multiplied by 3 then add 1
    • which simplifies to 
• To make the expression as easy as possible choose the smallest value to be represented by a letter
  • If Adam is 10 years younger than Barry then Barry is 10 years older than Adam
    • Represent Adam's age as  then Barry's age is 
    • This is easier than calling Barrys age and Adams age
  • If Adam's age is half of Barry's age then rewrite as...
    • Again it's easier to look at it as Barry's age is double Adam's age
    • So if Adam's age is  then Barry's age is 
    • Rather than using  for Barry's age and  for Adams's age

How do I form an equation?

• An equation is simply an expression with an equals sign that can then be solved
• You will first need to form an expression and make it equal to a value or another expression
• It is useful to know alternative words for basic operations:
  • For addition: sum, total, more than, increase, etc
  • For subtraction: difference, less than, decrease, etc
  • For multiplication: product, lots of, times as many, etc
  • For division: shared, split, grouped, etc
• Using the first example above 
  • If Adam is 10 years younger than Barry and the sum of their ages is 25 you can find out how old each one is
    • Represent Adam's age as  then Barry's age is 
    • We can solve the equation  or 
• Sometimes you might have two unrelated unknown values and have to use the given information to form two simultaneous equations