alt="math"/> yields 6.
In general, subtraction and division are not commutative. The special cases occur when you choose the numbers carefully. For example, if a and b are the same number, then the subtraction appears to be commutative because switching the order doesn’t change the answer. In the case of division, if a and b are opposites, then you get –1 no matter which order you divide them in. By the way, this is why, in mathematics, big deals are made about proofs. A few special cases of something may work, but a real rule or theorem has to work all the time.
You can use this rule to your advantage when doing math computations. Sometimes, changing the order in addition or multiplication situations can make the work much easier.
A. You don’t really want to multiply fractions unless it’s necessary. Notice that the first and last factors are multiplicative inverses of one another:
Just switch the order of the last two numbers:
Q.
A. The second and last terms are reversed, and then the first two terms are grouped.
17
18
19
20
21
Relating Inverses and Identities
In mathematics, inverses and identities are closely related. The definition of an inverse includes references to an identity. And when describing the identity of an operation, you call up the inverses.
Investigating Inverses
In mathematics, the inverse of a number is tied to a specific operation.
The additive inverse of the number 5 is –5; the additive inverse of the number
The multiplicative inverse of the number 5 is
A. The additive inverse is 14, because
Q. Find the additive and multiplicative inverses of the number
A. The additive inverse is
22 11
23
24
25 –1
26 4.5
27
Identifying Identities
The term identity in mathematics is most frequently used in terms of a specific operation. When using addition, the additive identity is the number 0. You can think of it as allowing another number to keep its identity when 0 is added. If you add
When adding a number
