6.5 SUPPORTING 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!

flowers, like terms

                        Like terms: "Things" which are the same

When you are using letters, you still have to pay attention to the order of operations. 

order of operations, order of operations pyramid

Examples

Subtracting with numbers only

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

  • -3 + 2 = -1 

-> Imagine you having a debt of three euros. You will get 2 euros pocket money from your parents. How much money do you have? 

money, debt, like terms, math, negative numbers, subtracting
  • 3 - 2 = 1 

-> There are still three euros left in your wallet. You are hungry so you are going to buy a hamburger at McDonald's for 2 euros. How much money is left? 

mcdonalds, math, subtracting, like terms, negative numbers, mathematics
  • -3 -2 = -5 

-> Imagine you having a debt of 3 euros by one of your friends. However, you still need to buy some food so you are borrowing 2 euros more. How much money do you have to pay back?  

friends, debt, money, food, negative numbers, subtracting, math, mathematics
  • 3 - - 2 = 5 

-> You have three euros you lend a friend 2 euros. He is repaying his debt of  2 euros. How much money do you have? 

- - = +, minus minus equals plus, rules, math, mathematics, negative numbers, positive numbers, rule, mathematics

Subtracting with letters

The same as with subtracting numbers, you can subtract letter but only if they are like terms!

  • -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 understand that you have 1 apple. The same is with letters. 

apple, like terms, negative numbers, leave the one out
  • 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. 

Simplify 

  • 2w + 5w - 3b - 7b = 7w - 10b 

Tip: highlight the like terms which belong to each other with the same colour.

  • 5x - 4y - 8x + 3y 

= 5x - 4y - 8x + 3y 

= -3x -1y 

= -3x - y 

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

Exercises

Exercise 1:

simplify

a) 7x + 2x 

b) 8y - 3y 

c) 4a - a 

d) 19q - 6b 

e) 7b + 10b - 3b

f) -8m - 5m - 9m 

g) 2g + 8u - 19g - - 11u 

h) a - b + a + b 

Exercise 2: 

Complete the sum letter pyramid.