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Algebra 1 Key Vocabulary Words
Chapter 3
Section 3.1: inverse operations
equivalent equations
reciprocal
solution
Section 3.2: like terms (see Ch 2.5)
input (see Ch 1.6)
output (see Ch 1.6)
solution of an equation (see Ch 1.4)
Section 3.3: distributive property (see Ch 2.5)
Section 3.4: identity
Section 3.5: ratio
proportion
simplest form
Section 3.6: cross product
scale drawing
Section 3.7: percent
Permission for Use Granted by Dr. Kate Kinsella 10/08
Word
Inverse
Operations
3.1
Meaning
DEF:
Two operations that
undo each other.
Examples
Subtraction is the inverse
operation of Addition.
Oral Practice
To solve the equation, x – 5 = 10, we use
the inverse operation of addition.
To solve the equation, x + 7 = 9, To solve the equation, 2x + 5 = 12, we
we use inverse operation of
use the inverse operations of
__________ and _________.
addition.
Writing Practice:
Addition and subtraction are inverse operations.
____________ and ____________ are also inverse operations.
Equivalent
Equations
3.1
DEF:
Equations that have
the same solution(s)
If you perform inverse
operations on both sides of the
equation, you produce
equivalent equations.
2x + 3 = 7 is equivalent to
2x = 4
To produce an equivalent equation to
x + 5 = 12, we will subtract 5 from both
sides of the equation.
To produce an equivalent equation to
3x = 15, we will ________ both sides of
the equation by ____.
Writing Practice:
To produce an equivalent equation to 2x + 6 = 8, we will ________ both sides of the equation by ___.
Permission for Use Granted by Dr. Kate Kinsella 10/08
Word
Reciprocal
3.1
Meaning
DEF:
Two non zero
numbers whose
product is 1
Examples
Oral Practice
The reciprocal of 5_ is
.
because,
5 ∙15=1
because
.
Writing Practice:
_____ and ______ are reciprocals, because
The reciprocal of _____ is ______, because
Identity
3.4
DEF:
An equation that
is true for all values
of the variable.
.
.
The equation 2x – 6 = 2(x – 3)
is an identity because,
2x – 6 = 2x – 6 is true for all
values of x.
The equation 3x + 7 + 2x = 5x + 7 is an
identity because, 5x + 7 = 5x + 7 is true
for all values of x.
The solution of 5x + 7 = 5x + 7 is all
real numbers because it is an identity.
Writing Practice:
The equation ___________________ is an identity because, __________________is true for all values of x.
The solution of __________________is all real numbers because it is an identity.
Permission for Use Granted by Dr. Kate Kinsella 10/08
Word
Ratio
3.5
Meaning
DEF:
The relation between
two quantities
expressed as a
quotient of numbers.
Examples
Oral Practice
There are 5 boys for every 4
girls in PE.
The ratio of
Amy has 3 red marbles and 5 green
marbles. The ratio of
Writing Practice:
There are _________ for every _________. The ratio of _____ = ______ or __:__ or ___ to ___.
Proportion
3.5
DEF:
An equation that
states that two
ratios are equal.
In symbols,
The equation
proportion because
The equation
is a
.
because
is a proportion
.
Writing Practice:
The equation ____= ___ because _____ = _______.
Permission for Use Granted by Dr. Kate Kinsella 10/08
Word
Cross Product
3.6
Meaning
DEF:
The product of the
numerator of one
ratio and the
denominator of the
other ratio.
In symbols, if
.
Examples
The cross product in the
proportion
.
Oral Practice
The cross product in the proportion
is 3(x) = 2(x + 3).
Writing Practice:
The cross product in the proportion _____=_____ is ______ = _______.
Scale Drawing
3.6
DEF:
A two-dimensional
drawing of an object
in which the
dimensions of the
drawing is in
proportion to the
dimensions of the
object.
A school map is a scale
drawing of the school.
The floor plan is a scale drawing of
the interior of the house.
Writing Practice:
The floor plan is a scale drawing of the interior of the house.
The ________ is a scale drawing of the ________________ .
Permission for Use Granted by Dr. Kate Kinsella 10/08
Word
Percent
3.7
Meaning
DEF:
A fraction whose
denominator is 100.
In symbols,
Examples
Oral Practice
5 is 25% of 20 can be written as
.
Writing Practice:
____ is ____% of ____ can be written as ____ = ______(
22
22 is 25% of 88 can be written as
.
).
DEF:
Writing Practice:
Permission for Use Granted by Dr. Kate Kinsella 10/08