6.5 NORMAL PATH simplifying expressions

Theory

This paragraph is almost the same as  6.4 Calculations with letters.  However, in this paragraph we are going to look at and practice with  subtracting like terms. 

Just as you can add like terms, you may also subtract like terms. 

Pay attention: ! You may only subtract and add like term!

                           Those twins look the same --> like terms

Examples

Subtracting like terms

Tip: Make a little story in your head if you have difficulties with adding and subtracting negative numbers. 

  • -3a + 2a = -1a = -a 

-> Don't write the 1 in your answer because this is unnecessary information. Example: You could say I have an apple. Everybody will know that you have 1 apple. The same is with letters. 

  • 3b - 2b = 1b = b

-> Again, don't write the 1 in your answer because this information is unnecessary. Example: You could say I have a banana. Everybody will understand that you have 1 banana. The same is with letters. 

  • -3y -2y = -5y 
  • 3s - - 2s =  3s + 2s = 5s 
  • 6h - 8j = 6h - 8j 

You can not simplify this any further because the h and the j are no like terms.  If you need to simplify non like terms you just need to copy the original exercise or you can give n.a. as answer n.a. is an abbreviations for no answer. 

Mixed additions and subtractions

It is also possible to simplify expressions which have plus and minus symbols in one expression, in other words mixed expressions. 

Tip: highlight the like terms which belong together with the same colour.  

  • 5x - 4y - 8x + 3y 

= -3x -1y 

= -3x - y 

The - and the + symbols belong the the number behind the symbol 

Exercises

Exercise 1:

Simplify 

a) 8y - 3y 

b) 4a - a 

c) 19q - 6b 

d) 7b + 10b - 3b

e) -8m - 5m - 9m 

f) 2g + 8u - 19g - - 11u 

g) a - b + a + b 

h) 2q + 6u - 2q - 6u 

Exercise 2:

Complete the sum letter pyramid.