Sender: Angie Herbert
Subject: algebra

My daughter is having problems with her algebra homework. She is a year 7 pupil at high school in the UK. She has been given homework on simplifying formulae and she doesn't understand how to do them. Here is an example of one of the questions :


can you help her to understand how to do these and perhaps me too.

puzzled mum
Angela Herbert

Hi Angela,

Simplifing this expression (some teachers may use the expression "collecting like terms") involves gathering all the s's, all the t's and all the c's. There are 9 s's and a further 5 s's so altogether 9+5=14 s's. Likewise there are 7 t's from which you remove 3 t's leaving you with 7-3=4 t's. To say it properly

9s + 7t + 5c + 5s - 3t
= 9s + 5s + 7t - 3t + 5c
= (9 + 5)s + (7 - 3)t + 5c
= 14s + 4t + 5c


Here is another approach.

  1. Give meaning to the variables (for instance s: steaks, t: tomatoes, c: carrots
  2. Rewrite the equation in this meaningful way:
    9 steaks + 7 tomatoes + 5 carrots + 5 steaks - 3 tomatoes
  3. Rewrite the above in a simpler way:
    14 steaks + ...
  4. Remove the meaning of the variables (put back s for steaks, t for tomatoes and c for carrots).
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