Transcript Lesson 1 – 3 Algebraic Expressions

1. List the numbers from least to
greatest, and graph on a number line.
9
− 7
1. 2
4
2. What type of numbers are the
following?
a. 36
b.
6
5
c. 37
d. –9
1. − 7
1. 2
9
4
− 7 ≈ −2.6457 …
2. a. 36 = 6
b.
6
5
R, Q, Z, W, N
R, Q
c. 37 ≈ 6.0827… R, I
d. –9
R, Q, Z
Algebra II
 To
evaluate algebraic expressions
 To
simplify algebraic expressions
Addition
Subtraction
 Plus
 Minus
 Together
 Take
 Sum
 Added
to
 Total of
 Combined
 Both
 Difference
away
 Fewer than
 Less than
 Decreased by
 Change
Multiplication
Division
 Multiplied
 Divided
 Product
 Times
 Of
 Twice
of
by
(x 2)
by
 Quotient of
1. Seven fewer than a number t
t–7
2. Twice the sum of a and b.
2(a + b)
3. The quotient of the sum of 2
and a number b, and 3
2+𝑏
3
4. The sum of the product of a
number k and 4, and a number m
4k + m
5. You start with $20 and save $6
each week.
20 + 6x
x = # of weeks
6. You have $150, but are
spending $2 each day.
150 – 2x
x = # of days
 Evaluate
– substitute a number for
each variable in an algebraic
expression and simplify using the
order of operations. Solve.
 Order
of Operations
◦ Parentheses
◦ Exponents
◦ Multiply/Divide (left to right)
◦ Add/Subtract (left to right)
7. 7(a + 4) + 3b – 8 for a = –4 , b = 5
= 7(–4 + 4) + 3(5) – 8
= 7(0) + (3)5 – 8
= 0 + 15 – 8
= 15 – 8
=7
8.
𝑥
2
=
=
=
=
=
+𝑦
2
1
+
2
1
+
2
1 2
2 2
2
+
4
3
4
1 2
2
1
4
1
+
4
1
4
for x = 1 , y =
1
2
9.
2(𝑥 2 −𝑦 2 )
3
2((6)2 −(−3)2 )
=
3
2(36−9)
=
3
2(27)
=
3
54
=
3
=18
for x = 6 , y = −3
 Term
– An expression that is a
number, a variable, or the product
of a number and one ore more
variables
5, –10xy, 7w
 Coefficient
term
- numerical factor of a
 Constant
term – a term with no
variables
5, –7
 Like
terms – have same variables
raised to the same powers
9x2 –12x2
7x 3x
Simplify expressions by combining
like terms.
10.
7𝑥 2 + 3𝑦 2 + 2𝑦 2 -4𝑥 2
=3𝑥 2 + 5𝑦 2
11.
–(3k + m) + 2(k – 4m)
= –3k – m + 2k – 8m
= – k – 9m
12.
𝑥3
𝑥
𝑥3
𝑥
- +
+
2
3
5
2
𝑥3
𝑥3
𝑥
𝑥
= + − +
2
5
3
2
𝑥3 5
𝑥3 2
=
+
−
2 5
5 2
5𝑥 3
2𝑥 3
2𝑥
=
+
− +
10
10
6
7𝑥 3
𝑥
=
+
10
6
𝑥 2
3 2
3𝑥
6
+
𝑥 3
2 3
 Write
an algebraic expression to
model the situation
 The junior class will be selling
roses as a class project. What is
the class’s income after it pays
the florist a flat fee of $200 and
sells x roses for $2 each?
 Explain how you came up with the
algebraic expression.