Basic Mathematics for College Students

c.We read as “seven minustwenty-three.” Thus, the number to be

subtracted is 23. Subtracting 23 is the same as adding its opposite,.

Add...

Use the rule for adding two

integers with different signs.

... the opposite
Check:  16  23  7 The result checks.

7  23  7 ( 23 ) 16

 23

7  23

158 Chapter 2 The Integers

EXAMPLE (^2) a.Subtract from. b.Subtract from.
StrategyWe will translate each phrase to mathematical symbols and then
perform the subtraction. We must be careful when translating the instruction to
subtract one number fromanother number.
WHYThe order of the numbers in each word phrase must be reversed when we
translate it to mathematical symbols.
Solution
a.Since is the number to be subtracted, we reverse the order in which
and appear in the sentence when translating to symbols.
 8 (12) Write 12 within parentheses.
To find this difference, we write the subtraction as addition of the opposite:
Add...
Use the rule for adding two
integers with different signs.

... the opposite
b.Since is the number to be subtracted, we reverse the order in which and
appear in the sentence when translating to symbols.

 12 (8) Write 8 within parentheses.

To find this difference, we write the subtraction as addition of the opposite:

Add...

Use the rule for adding two

integers with different signs.

... the opposite

 12 ( 8 ) 12  8  4

Subtract 8 from  12

 12

 8  8

 8 ( 12 ) 8  12  4

Subtract 12 from  8

 8

 12  12

 12  8  8  12

Self Check 2

a.Subtract from.

b.Subtract from.

Now TryProblem 33

 7  10

 10  7

The Language of Mathematics When we change a number to its opposite,

we say we have changed(or reversed) its sign.

Caution! When applying the subtraction rule,do not changethe first number.

 6  4  6 (4) 3 (5) 3  5