Transcript Algebraic Expressions

ALGEBRAIC
EXPRESSIONS
Translate English to Math
Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1):
The student will be able to use properties of rational and
irrational numbers to write, simplify, and interpret expressions
based on contextual situations.
4
3
In addition to
level 3.0 and
above and
beyond what
was taught in
class, the
student may:
·
Make
connection with
other concepts
in math
·
Make
connection with
other content
areas.
The student will be
able to use properties
of rational and
irrational numbers
to write, simplify, and
interpret expressions
on contextual
situations.
- justify the sums and
products of rational
and irrational numbers
-interpret expressions
within the context of a
problem
2
1
0
The student will
With help
Even with
be able to use
from the
help, the
properties of
teacher, the student has
rational and
student has no success
irrational
partial
with real
numbers to write success with
number
and
real number expressions.
simplify expressi expressions.
ons based on
contextual
situations.
-identify parts of
an
expression as
related to the
context and to
each part
Parts of an Algebraic Expression
• Algebraic expressions
terms
3n + 5
Coefficient:
The number
next a
variable.
Constant:
The number
without a
variable.
do not contain equal
signs.
• Terms: Values that
are added or
subtracted. 3n + 5 has
two terms.
• Factors: Values that
are multiplied. The
term 3n has two
factors: 3 and n.
Translate English to Math
(translate between verbal statements and algebraic expressions)
• In order to translate from the language of English to the
language of Math, you need to understand the words that
are commonly used to represent mathematical
operations.
Add
Add
Sum
Increased by
More than
exceeds
Total
Plus
In all
Gain
Deposit
Subtract
Subtract
Difference
Decreased by
Fewer
Less than
Minus
Take away
Withdraw
Reduced by
Multiply
Multiply
Product
Of
Times
Double
Triple
Twice
Divide
Divide
Quotient
Per
Divided equally
Split into
Fraction
Ratio of
Tips:
• The phrase “less than” reverses the order of what you
read.
• For example: “5 less than n” translates to “n – 5”
• Watch for commas. They can help you decide how to
group terms.
• For example: “8 times, a number increased by 12” translates to
8(n + 12)
NOT
8n + 12
Practice: Translate the following into
algebraic expressions.
1. Five increased by four times a
2.
3.
4.
5.
6.
number.
Eight less than twice a number.
Three times a number,
increased by 9.
The product of 4, and a number
decreased by 7.
The number of feet in x yards.
A number repeated as a factor
3 times.
1.
5 + 4n
2.
2n – 8
3.
3n + 9
4.
4(n – 7)
5.
3x
6.
n • n • n = n3
Complicated Expressions
• Translate the following expression into
English:
• 5x – (2 – 4y)
• “The difference between 5 times a number
and the quantity 4 times another number
less than 2”
• It’s much easier to just leave the expression in math symbols. 
• Look at the words “a number” and “another
number.” These help you identify that there
are multiple variables in the expression.
5x – (2 – 4y)
• How many terms are in
this expression?
• It is tempting to say 3.
• There are only 2
terms.
• -(2 – 4y) is one term.
Because of the
parenthesis, it groups
it as one term.
• The “-” sign in front of
the parenthesis,
represents “-1” which
could be multiplied by
everything in the
parenthesis.
P(1 + r)n
• How many variables are in the above expression?
• 3
• How many terms are in the above expression?
• 1
• How many factors are in the above expression?
• 2
• One factor is “P”
• The other factor is “(1 + r)n”
Practice:
How many terms are in each expression?
1. 9y
1. 1
2. 7 – 4n
2. 2
3. 18 + 3(6 - 4x) + 2
3. 3
4. x2 + 4x + 3
4. 3
5. ½ bh
5. 1
6. 2lw + 2lh + 2hw
6. 3
7. (9 – 2w) - 29
7. 2
Practice:
1.
2.
3.
4.
5.
6.
7.
How many factors are in each expression?
9y
7 – 4n
18 + 3(6 - 4x) + 2
x2 + 4x + 3
½ bh
2lw + 2lh + 2hw
29 - (9 – 2w)
1.
2.
3.
4.
5.
6.
7.
2 (9 & y)
2 (4 & n)
2 (3 & [6-4x])
4 (x & x) & (4 & x)
3 (½ & b & h)
3 factors in each
term for a total of 9
2 ([9-2w] & -1)