Notes 1.5 Algebra Equations
Inverse Operations
Let’s look at the words inverse and operation using a dictionary and a math
glossary definition.
Dictionary
Inverse
an element x* in a set S
related to a designated
element x in S such that
x* · x = x · x* = I, where ·
is a binary operation
defined in S and I is the
identity element.
Operation a process or action, such
as addition, substitution,
transposition or
differentiation,
performed in a specific
sequence and in
accordance with specific
rules
Glossary
Note: in your glossary the two
words are listed together. The
word operation is a noun and it
is modified by the adjective
inverse.
Write what your book says
here. You can find it on page
613.
Now, let’s make sure that we can write a good description of inverse
operations in our own words. (In math inverse and opposite do not always
mean the same, so be careful to not say “opposite” for now.)
To solve an equation we “undo” it by applying what we know about number
facts and inverse operations.
To undo add we _________________.
To undo subtract we _________________.
To undo multiply we _________________.
To undo divide we _________________.
This means that every multiplication has a division partner and every
subtraction has an addition partner. Write the partner problems for each
example. A partner problem is a simple equation written using the inverse
operation.
3 · 4 = 12
7–4=3
9 + 2 = 11
10 ÷ 2 = 5
52 = 25
Use mental math and inverse operations to solve these equations. Answer
with good algebra form.
a.
8 + x = 15
b. a – 18 = 20
c. 6 =
d. 20 = y ÷ 5