It is important to be able to distinguish between the termsof an expression and
the factorsof a term.
8.1 The Language of Algebra 641EXAMPLE (^2) Is used as a factoror a termin each expression?
a. b.
StrategyWe will begin by determining whether is involved in an addition or a
multiplication.
WHYAddition symbols separate expressions into terms.A factoris a number
being multiplied.
Solution
a.Since is added to 6, is a term of.
b.Since mis multiplied by 8,mis a factor of 8 m.
m m m 6
m
m 6 8 m
m
Self Check 2
Is used as a factoror a termin
each expression?
a.
b.
Now TryProblems 27 and 29
5 ab
27 b
b
Translate Word Phrases to Algebraic Expressions.
The tables below show how key phrases can be translated into algebraic expressions.
Caution! Be careful when translating subtraction. Order is important. For
example, when a translation involves the phrase less than,note how the terms
are reversed.
18 less than
18
Caution! Be careful when translating division. As with subtraction, order is
important. For example, divided by is notwritten.
d
s
s d
w
w
3
Addition
the sum of and 8
4 plus
16 added to
4 more than
20 greater than
increased by
exceeds by 35y y 35
T r Tr
F F 20
t t 4
m m 16
c 4 c
a a 8
Subtraction
the difference of 23 and
550 minus
18 less than
7 decreased by
reduced by
12 subtracted from
5 less ƒ 5 ƒ
L L 12
M x Mx
j 7 j
w w 18
h 550 h
P 23 P
Multiplication
the product of 4 and
20 times
twice
double the amount
triple the profit
three-fourths of
3
4
m m
P 3 P
a 2 a
r 2 r
B 20 B
x 4 x
Division
the quotient of and 19
divided by
the ratio of to
split into 4 equal parts
k
4
k
c
d
c d
s
d
s d
R
19
R