Post on 31-Dec-2015
The Language of Math
The Language of Math
Punctuation
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.
Punctuation
• Punctuation is used in Mathematics to give meaning to an expression.
• The punctuation marks are called grouping symbols. They are:o ( ) parentheseso [ ] bracketso { } braceso division bar
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)
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
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)]}
Division Bar
•
•
• In other words, evaluate the numerator and the denominator of a fraction separately.
22 3.
3 is another way of writing
2 3 5(2 3) (5 1) 5 4
5 1 4
So .
• You should pronounce as “the quantity ” …short pause… “minus ”
• You should pronounce as
“the quantity divided by the quantity “
Math Speak
2 34 1
(2 3) 7 2 3 7
2 3 4 1
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
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
(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
Work it out!
8 (5 3) 8 8 0
Work it out!
8 (5 3) 08 8
Work it out!
8 (5 3) 8 8 0
Work it out!
8 (5 3) 8 2 6
Work it out!
8 (5 3) 68 2
Work it out!
8 (5 3) 8 2 6
Work it out!
(3 ( 5)) (5 3) ( 2) 2 0
Work it out!
(3 ( 5)) (5 3) ( 2) 2 0
Work it out!
(3 ( 5)) (5 3) ( 2) 2 0
Work it out!
2 (5 3) 2 2 4
Work it out!
2 (5 3) 42 2
Work it out!
2 (5 3) 2 2 4
Work it out!
10 35) 7(2 3
Work it out!
(2 5) 3 10 3 7
Work it out!
(2 5) 3 10 3 7