The table lists words and phrases that indicate subtraction in problem solving.
42 CHAPTER 1 The Real Number System
Word, Phrase, Numerical Expression
or Sentence Example and Simplification
Difference between The difference between 3 and 8 simplifies to
, or 5
Subtracted from* 12 subtracted from 18 , or 6
From , subtract. From12, subtract8. simplifies to
, or 4
Less 6 less 5 , or 1
Less than* 6 less than 5 simplifies to
, or
Decreased by 9 decreased by 4 simplifies to
, or 13
Minus 8 minus 5 , or 3
*Be careful with order when translating.8 - 59 + 4- 9 - 1 - 42
5 + 1 - 62 - 15 - 66 - 512 + 1 - 82Á Á 12 - 818 - 12- 3 + 8
- 3 - 1 - 82
CAUTION When subtracting two numbers, be careful to write them in the correct
order, because, in general,
For example, Think carefully before interpreting an expression
involving subtraction.
5 - 3 Z 3 - 5.
xyyx.
Translating Words and Phrases (Subtraction)Write a numerical expression for each phrase, and simplify the expression.
(a)The difference between 8 and 5
When “difference between” is used, write the numbers in the order given.*
simplifies to , or
(b) 4 subtracted fromthe sum of 8 and
First, add 8 and. Next, subtract 4 from this sum.
simplifies to or 1.
(c) 4 less than
Here, 4 must be taken from 6, so write 6 first.
- 6 - 4 simplifies to - 6 + 1 - 42 , or -10.
- -
- 6
38 + 1 - 324 - 4 5 - 4,
- 3
- 3
- 8 - 5 - 8 + 1 - 52 - 13.
-
NOW TRY EXAMPLE 9
EXERCISE 9
Write a numerical expression
for each phrase, and simplify
the expression.
(a)The difference between 5
and , decreased by 4
(b)7 less than - 2
- 8
NOW TRY ANSWERS
- (a) ; 9
(b)- 2 - 7 ; - 9
35 - 1 - 824 - 4 *In some cases, people interpret “the difference between” (at least for two positive numbers) to represent the
larger minus the smaller. However, we will not do so in this book.Be careful
with order.Notice that “4 less than 6” differs from “4 is less than 6.” The second of these is
symbolized (which is a false statement).
(d)8, decreased by 5 less than 12
First, write “5 less than 12” as Next, subtract from 8.
8 - 112 - 52 simplifies to 8 - 7, or 1. NOW TRY
12 - 5. 12 - 5
4 6- 6
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