(c) Two-thirds ofthe sum of 5 and 3
simplifies to or
(d) 15 %of the difference between 14 and 2
0.15 314 - 1 - 224 simplifies to 0.15 3164 , or 2.4.
-
-
16
3
.
2
3
3 - 84 ,
2
3
3 - 5 + 1 - 324
- -
SECTION 1.6 Multiplying and Dividing Real Numbers 55
NOW TRY
EXERCISE 7
Write a numerical expression
for each phrase, and simplify
the expression.
(a)Twice the sum of
and 7
(b)40% of the difference
between 45 and 15
- 10
NOW TRY ANSWERS
- (a) ;
(b)0.40 145 - 152 ; 12
21 - 10 + 72 - 6Remember that
15%=0.15.(e) Doublethe product of 3 and 4
simplifies to or 24. NOW TRY
In algebra, quotients are usually represented with a fraction bar. The symbol
is seldom used. The table gives some phrases associated with division.
2 # 13 # 42 21122 ,
Numerical Expression
Phrase Example and Simplification
Quotient of The quotient of 24 and 3 or
Divided by 16 divided by 4 , or 4
Ratio of The ratio of2 to 3^23- 16
- 4
- 324 , - 8
When translating a phrase involving division, we write the first number named as
the numerator and the second as the denominator.
Interpreting Words and Phrases Involving DivisionWrite a numerical expression for each phrase, and simplify the expression.
(a)The quotient of14 and the sum of 9 and 2
simplifies to or -2.
14
- 7
,
14
- 9 + 2
-
NOW TRY EXAMPLE 8
EXERCISE 8
Write a numerical expression
for the phrase, and simplify
the expression.
The quotient of 21 and the
sum of 10 and - 7“Quotient”
indicates division.(b)The product of 5 and 6, divided bythe difference between 7 and 8
simplifies to or 2. NOW TRY
OBJECTIVE 8 Translate simple sentences into equations.
Translating Sentences into EquationsWrite each sentence as an equation, using xas the variable. Then find the solution
from the list of integers between 12 and 12, inclusive.
(a)Three timesa number is 18.
The word times The word is
indicates multiplication. translates as.or
The integer between 12 and 12, inclusive, that makes this statement true is ,
since 31 - 62 =-18.The solution of the equation is 6.-
- - 6
3 #x= -18, 3 x=- 18 3 #x= 3 x
=-
-
EXAMPLE 9
- 30
- 15
,
51 - 62
- 7 - 8
- -
- 10 +^211 - 72 ; 7