Download UNIT 2: Writing and Interpreting Numerical Expressions

TOPIC 8: Writing and Interpreting Numerical Expressions
 Why do we need a standard method for evaluating expressions?
 When and how do we use the order of operations?
 How can we model real life situations mathematically?
Expression: a mathematical phrase containing numbers, operation symbols,
grouping symbols, and sometimes variables.
Example: 6 + 2 * 9
Evaluate an Expression: to carry out the operations in an expression in the
proper order in order to find the value of it.
Example: 6 + 2 * 9
6 + 18
24
Order of Operations: A procedure for correctly evaluating an expression.
The sequence in which you must carry out the operations is:
1. Parentheses: Simplify the operations inside parentheses
first!
2. Exponents: find the value of the powers in the expression.
3. Multiplication & Division:
OR
All in one step from left to right.
Division & Multiplication:
4. Addition & Subtraction:
OR
All in one step from Left to Right
Subtraction & Addition:
We abbreviate this procedure by using the acronym:
P
Please
E
Excuse
MD
My Dear
AS
Aunt Sally
Funnel Method: The way Mrs. Gerould requires students to show the steps
used to evaluate an expression.
1. Write out an expression
horizontally.
2. Determine which operation
should be carried out first
according to the order of
operations. UNDERLINE IT.
3. Carry out that operation and
rewrite the rest of the
expression exactly the way it
appeared before under the
original expression.
4. Underline the next operation.
5. Continue carrying out one
operation at a time and
rewriting the expression after
each step until you’ve
completed all operations.
6. Circle your final value.
1. 3 + 5 * (5 – 2) + 8
3. 3 + 5 * (5 – 2) + 8
4.
3+5*3+8
5.
6.
3+5*3+8
3 + 15 + 8
18 + 8
2.
26
Grouping Symbols: symbols used to increase the priority of a specific
operation.
(Parentheses)- 3 * (2 + 7)
In this example, they require that the addition is carried out before the
multiplication.
[Brackets]- 54 [3 * (2 + 7)]

Used when there are parentheses inside another set of grouping symbols.
{Braces}- 10 – {54 [3 * (2 + 7)] + 3}

Grouping symbols inside grouping symbols, inside grouping symbols.
Always start carrying out operations within the most inside set of grouping
symbols and work your way out!!!
As you eliminate the parentheses, change the brackets to parentheses and the
braces to brackets.
EXAMPLE (using the funnel method):
10 – {54 [3 * (2 + 7)] + 3}
10 – [54 (3 * 9) + 3]
10 – (54 27 + 3)
10 – (2 + 3)
10 – 5
5



Translating Verbal Phrases into Mathematical Expressions
Translate: to change words from one language to another.
Example:
English -“How are you?”
Spanish – “Como estas?”
The sentences look different, but mean the same thing.
We will be translating from English words to Math symbols.
You must identify the key word(s) in the phrase that indicate
which operation to use.
Examples of Numerical Expressions:
the product of 3 and 5 …………….……………3 • 5
6 more than 2 …………………………………..2 + 6
15 decreased by 7 ……..………………………15 – 7
the quotient of 12 and 3, decreased by 1………12 ÷ 3 – 1
add 8 and 7, then multiply by 3……………….(8 + 7) • 3
**Be sure to add grouping symbols if you are supposed to add or
subtract before you multiply or divide.**
Examples of Algebraic Expressions:
Anytime there is an unknown number in the phrase, use a variable
(letter) in its place.
the product of a number and 3, increased by 5……….3 • n + 5
add 6 and a number, then multiply by 4 ……………..(6 + n) • 4