6.5 IN-DEPTH PATH simplifying expressions

Theory

This paragraph about simplifying expressions is almost the same as previous paragraph about calculating with letters. The only difference is that this paragraph zooms in on subtracting like terms and simplify mixed expressions with addition and subtraction. 

highlight the like terms with the same colour. Do not forget to highlight the plus and minus symbols with the correct colour.

Test yourself 

You really need to understand the theory about simplifying expressions with subtracting and adding like terms. You can test yourself by doing this exercise. 

Simplify

7a + 8 - 7a + 2 - 10 + 9a - 3b + a - 8b 

"Mathemagic"

Extra learning objectives

At the end of this paragraph you are able to...

...explain what "mathemagic" is. 

...use math to solve a magic-trick. 

...design a "mathemagic" trick and explain it.

...show your "mathemagic"trick in an original way. 

...make the connection between mathemagic and 6.5 Simplifying expressions

What is "mathemagic"? 

Mathemagic is a magic trick where math is involved. Most of the time algebra is involved, in algebra letters take the place of numbers. 

Mathemagics example

Materials:

You will need your calculator and your phone number for this magical math trick. 

Steps: 

  1. Write your phone number on a piece of paper
  2. Enter the first four digits of your phone number in your calculator (WITHOUT area code) 
  3. Multiply the first four digits by 80 and push the equal sign. 
  4. Add 1 and push the equal sign. 
  5. Multiply your answer by 250 and push the equal sign. 
  6. Add the last 4 digits of your phone number and push the equal sign. 
  7. Add the last 4 digits of your phone number again, and push the equal sign. 
  8. Subtract 250. 
  9. Divide your answer by 2. 
  10. Your phone number magically appeared in the display of your calculator. 

Example:

  1. With area code: 0612345678, Without area code: 12345678
  2. Enter: 1234
  3. 1234 . 80 = 98720
  4. 98720 + 1 = 98721
  5. 98721 . 250 = 24680250
  6. 24680250 + 5678 = 24685928
  7. 24685928 + 5678 = 24691606
  8. 24691606 - 250 = 24691356
  9. 24691356 : 2 = 12345678
  10. 12345678 is your phone number without area code. 

Figure it out yourself :

Try to find the mathematical formula behind this magical trick. 

Think about algebra and do the math with letters. 

    TIPS: 

* Give the first 4 digits of your phone number the letter x 

* Give the last 4 digits of your phone number the letter y

Exercises

Exercise 1: 

Simplify

a) 5x + 4y - x - 7y 

b) -3v - - 6p + 3 + 4p 

c) -12ac + ac + 3a + 2c 

Exercise 2: 

Look at the mathemagical video below and discover the math behind it.