Day 1
Evaluatin g A lge braic
Expression
Objec tive: To use the Order of
Opera tions to evaluate
arithmetic and
algeb raic expressions.
Order of O pera tions (O 3 )
is an agreemen t tha t results
in everyone doing the pro b lem
the same wa y tha t results in
one answer
Driving ca rs
on the ri ght
side of the road
is such an
agreemen t
Order of O pera tions
Compute fro m LEFT to RIGH T
1. GROUP ING
2. EXPONENTIA LS
3. MULTIPLY / DIVIDE
4. ADD / SUBRA CT
Ex
4 + 2 x 5 =
The re a re no gro upin g symbols
The re a re no exponen tials
Start with multiplying
= 4 + 10
=
14
Day 1
Ex. Compute
5 + 36
÷ 6 x 2 + 3
3
Using O , these a re no signs of
grouping - no exponentials.
Start with Mult / Divide, whichever
comes 1
=
=
=
st
5 + 36 ÷ 6 x 2 + 3
5 + 6
x 2 + 3
5 +
12
+ 3
20
a/b = a – 1 /b
N. B.
Notice in the O 3 , mult and
division are on the sa me
line: so we do whic hever
comes 1 s t .
The reason they are on the same
line is beca use division is defined
in terms of multiplica tion
a
÷ b = a x 1/b
8
÷ 4 = 8 x 1/4
Day 2
Evaluatin g A lge braic
Expression
Ex
Compute
5 + 2(5 + 3)
÷ 2 x 4
Using O 3 ; Gro uping is 1 st
=
=
=
=
=
Ex
5
5
5
5
5
+ 2 (5 + 3) ÷ 2
+ 2 • 8 ÷ 2 x
+
16 ÷ 2 x
+
8
x
+
32
37
Complete
32 • 4
3
x 4
4
4
4
÷ 12 + 4
Using O , E xponentia ls is 1
=
=
=
=
=
3 2 • 4 ÷ 12 + 4
9 • 4 ÷ 12 + 4
3 6 ÷ 12 + 4
3
+ 4
7
st
To evaluate an a lgebraic
expression, you simply substitute the
numbers for the va riables and use
O
3
Ex.
Evaluate a + bc; if a = 2 ,
b = 3, and c = 5
a + bc
Subs tituting
2 + 3 • 5
Now use O 3
= 2 + 15
= 17
Ex.
=
=
=
Ex.
Evaluate 2l + 2 w,
if l = 8 and w = 5
2l + 2 w
2 • 8 + 2 • 5
16
+ 10
26
1
(B + C) • H, if
2
B = 1 0, C = 8, and H = 5
Evaluate
1
(10 + 8) • 5
2
1
(10 + 8) • 5
2
Gro uping 1
=
1
(18) • 5
2
=
=
9 • 5
45
st
3
N.B.
Knowing O , is important –
being ab le to manipula te
rules is just as i mpo rtan t .
Ex.
Compute
4 x 13 x 25
Using O 3 , we sho uld multi ply fro m
left to right.
=
=
4 x 13 x 25
5 2 x 25
1300
Manipulating the same pro blem
4 x 13 x 25
will make the computation easier –
a lo t easier
4 x 13 x 25
Using the Commutative an d
Associative Prope rties, 1 ca n re write
tha t a rithmetic e xpression as
4 x 13 x 25
(4 x 25) x 13
100
x 13
1 300
=
=
=
Evaluate
3x + 2 y – 5, if x = 5
and y = 3½
=
=
=
3x + 2y – 5
3 • 5 + 2 (3 ½) – 5
15
+
7
– 5
17
Evaluate
6a - 6 + 3 xy , if
2
a
a = 4, b = 10, x = 2, and y=6
=
=
6 • 4 – 10 + 3 • 2 • 6
2
4
1 2 – 11 ½
12 – 1 0 + 36
4
= 1
=
2
12 – 46
4
If a = 2 , b = 3 , c = 5 , d = 1, e = 0,
and f = 6 , eva luate the fo llo wing
algeb raic e xpressions
1)
f – 4
2)
3a + 4f
c
3)
6b + 5a
4)
6
5)
f
+
2
6)
3ab – 5ac
2
2
bc
a
÷ 6
2
+ 2f