Grouping Symbols

Grouping Symbols

1. The Language of Math
Punctuation

2. Punctuation
•Punctuation is used in English and other
languages to give meaning to what is written.
•Periods and question marks end sentences,
commas are used for lists and to separate
phrases, and there are colons and
semicolons and so on.
•When you have learned the “parts of
speech” you will learn to diagram a
sentence, that is, break it into its parts.

3. Punctuation
•Punctuation is used in Mathematics to give
meaning to an expression.
•The punctuation marks are called grouping
symbols. They are:
o( ) parentheses
o[ ] brackets
o{ } braces
o division bar

4. Punctuation
•For example, the meaning of the
expression:
is just that it is a fancy way of writing the
number 1. It is another name for one.
•Reducing a complex expression to a single
number is called evaluating the expression.
7 2 (5 2)
6 (1/2 1/3)
- × -
× -

5. Parentheses ( )
•These always come in left/right pairs and
are used to do the same thing.
•They tell you to calculate what’s inside the
parentheses before doing anything else.
3 (1 2) 3 ( 1) 3 1 4
3 (1 2) 3 ( 1) 3
- - = - - = + =
× - = × - =-

6. The brackets and braces are used instead of
parentheses in complicated expressions to
make it easier to read.
It is difficult to see which left parenthesis
goes with which right parenthesis in
Using brackets and braces makes it easy to
read:

Brackets [ ] & Braces { }
1 (1 (1 (1 2)))- - - -
1 {1 [1 (1 2)]}- - - -

7. Division Bar
•
•
•In other words, evaluate the numerator
and the denominator of a fraction
separately.
2
2 3.
3
¸ is another way of writing
2 3 5
(2 3) (5 1) 5 4
5 1 4
+
= + ¸ - = ¸ =
-
So .

8. •You should pronounce as
“the quantity ” …short pause… “minus ”
•You should pronounce as
“the quantity divided by the quantity “

Math Speak
2 3
4 1
+
+
(2 3) 7+ -
2 3+ 7
2 3+ 4 1+

9. Evaluate the quantity in the parentheses
first…
(3 4) 2
[2 3] 5
{1 2
12 2 14
5 5 25
1 3 2
5
(2 3) (4 2)
} 3
2 3

4 2 2
+ =
´ =
- + =
+ ¸
´ +
-
=
+ ´ =
- + =
+
==
-
Examples

10. Evaluate the quantity in the parentheses
first…
(3 4) 2 12 2
[2 3] 5 5 5
{1 2} 3 1 3
2 3
(2 3) (4 2)
4 2
14
25
2
5
2
´ + = + =
+ ´ = ´ =
- + =- + =
+
= + ¸ - =
-
Examples

11. (3 4) 2 12 2 14
[2 3] 5 5 5 25
{1 2} 3 1 3 2
2 3 5
(2 3) (4 2)
4 2 2
´ + = + =
+ ´ = ´ =
- + =- + =
+
= + ¸ - =
-
Nothing to it!!
Examples

12. Work it out!
8 (5 3)8 8 0- + = - =

13. Work it out!
8 (5 3) 08 8- + = - =

14. Work it out!
8 (5 3) 8 8 0- + = - =

15. Work it out!
8 (5 3)8 2 6- - = - =

16. Work it out!
8 (5 3) 68 2- - = - =

17. Work it out!
8 (5 3) 8 2 6- - = - =

18. Work it out!
(3 ( 5)) (5 3)( 2) 2 0+ - + - - + ==

19. Work it out!
(3 ( 5)) (5 3) ( 2) 20+ - + - = - + =

20. Work it out!
(3 ( 5)) (5 3) ( 2) 2 0+ - + - = - + =

21. Work it out!
2 (5 3)2 2 4´ - = ´ =

22. Work it out!
2 (5 3) 42 2´ - = ´ =

23. Work it out!
2 (5 3) 2 2 4´ - = ´ =

24. Work it out!
10 35) 7(2 3´ - = - =

25. Work it out!
(2 5) 3 10 3 7´ - = - =

26. Work it out!
(2 5) 3 10 3 7´ - = - =