Transcript Expressions - TeacherWeb

Objective
The student will be able to:
translate verbal expressions into
math expressions and vice versa.
What is the area of a rectangle?
Length times Width
If the length is 3 meters and the width is 2
meters, what is the area?
A=LxW
A = 3 x 2 = 6 meters2
A, L and W are the variables. It is any
letter that represents an unknown number.
VOCABULARY
A numerical expression is a mathematical phrase with only
numbers and operation symbols (+, -, x, ÷).
Example: 8 + 5 - 2
An algebraic expression is a mathematical phrase that
contains a variable and operation symbols.
A variable is a symbol (usually a letter) that stands for a
number.
Algebraic expression: 5y + 2
Evaluating Algebraic
Expressions
• Replace the variable with the value that you
are given.
• Now we have a numerical expression.
• Solve using order of operations.
Example: Evaluate 2b-8 for b=11
2b-8
2(11)-8
22 - 8
14
Substitute the 11 for
the variable.
Multiplying comes
before subtracting.
An algebraic expression
contains:
1) one or more numbers or variables, and
2) one or more arithmetic operations.
Examples:
x-3
3 • 2n
4
1
m
In expressions, there are many
different ways to write multiplication.
1)
2)
3)
4)
5)
ab
a•b
a(b) or (a)b
(a)(b)
axb
We are not going to use the multiplication symbol
any more. Why?
Division, on the other hand, is
written as:
x
1)
3
2) x ÷ 3
Throughout this year, you will hear many
words that mean addition, subtraction,
multiplication, and division. Complete the
table with as many as you know.
Addition Subtraction Multiplication Division
Here are some phrases you may have listed.
The terms with * are ones that are often
used.
Addition
Subtraction
Multiplication
sum*
difference*
product*
quotient*
increase
decrease
times
divided
plus
minus
multiplied
ratio
add
subtract
twice
half
more than
less than
doubled
a third
total
Division
Write an algebraic expression for
1) m increased by 5.
m+5
2) 7 times the product of x and t.
7xt or 7(x)(t) or 7 • x • t
3) 11 less than 4 times a number.
4n - 11
4) two more than 6 times a number.
6n + 2
5) the quotient of a number and 12.
x
12
Which of the following expressions represents
7 times a number decreased by 13?
1.
2.
3.
4.
7x + 13
7x - 13
13 - 7x
13 + 7x
Answer Now
Which one of the following expressions
represents 28 less than three times a number?
1.
2.
3.
4.
28 - 3x
3x - 28
28 + 3x
3x + 28
Answer Now
Write a verbal expression for:
1) 8 + a.
The sum of 8 and a
2) m
r
.
The ratio of m to r
Do you have a different way of writing
these?
Which of the following verbal expressions
represents 2x + 9?
1.
2.
3.
4.
9 increased by twice a number
a number increased by nine
twice a number decreased by 9
9 less than twice a number
Answer Now
Which of the following expressions represents
the sum of 16 and five times a number?
1.
2.
3.
4.
5x - 16
16x + 5
16 + 5x
16 - 5x
Answer Now
When looking at the expression
103, 10 is called the
base
and 3 is called the
exponent or power.
103 means 10 • 10 • 10
103 = 1000
How is it said?
21
Two to the first power
22
Two to the second power or two squared
23
Two to the third power or two cubed
2n7
Two times n to the seventh power
Which of the following verbal expressions
represents x2 + 2x?
1.
2.
3.
4.
the sum of a number squared and
twice a number
the sum of a number and twice the
number
twice a number less than the number
squared
the sum of a number and twice the
number squared
Answer Now
Which of the following expressions
represents four less than the cube of a
number?
3
1. 4 – x
2. 4 – 3x
3. 3x – 4
4. x3 – 4
Answer Now
Evaluate.
21
2
22
2•2=4
23
2•2•2=8
2n7
We can’t evaluate because we don’t
know what n equals to!!
Is 35 the same as 53?
Evaluate each and find out!
35 = 3 • 3 • 3 • 3 • 3 = 243
53 = 5 • 5 • 5 = 125
243 ≠ 125
They are not the same!
Translate each verbal expressions
into an algebraic expression:
(a)the sum of 8 and y
8+y
(b) 4 less than x
x-4
(c) a number decreased by one
n-1
(d) The difference between x and y
x-y
(e) One half of a
½a
(f) Nine less than the total of 9 and
a number
(9 + n)- 9
Write an algebraic expression to describe Jerry’s age. Use the
following information:
Jerry is 4 years younger than his brother Steve.
First, we have to know how old Steve is. We do not have an
age for Steve, soFirst, we have to know how old Steve is. We
do not have an age for Steve, so we will use a variable:
Let s = Steve’s age
Now that we have determined Steve’s age (s), we can use it
to determine Jerry’s age. Jerry is 4 years younger than Steve.
j=s-4
If Steve is 22 years old, then how
old is Jerry?
j=s–4
j = 22 - 4
j = 18
Jerry is 18 years old.