Algebra Concepts
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SUM
sum – the answer to an addition problem
Ex. 4 + 5 = 9…The sum is 9.
DIFFERENCE
difference – the answer to a subtraction problem
Ex. 8 – 2 = 6…The difference is 6.
PRODUCT
product – the answer to a multiplication problem
Ex. 3 × 4 = 12…The product is 12.
QUOTIENT
quotient – the answer to a division problem
Ex. 18 ÷ 6 = 3…The quotient is 3.
ESTIMATE
estimate (noun/verb) – an answer that is close to the real answer; to quickly perform an
approximation
Ex. 28.7 + 42.25 ≈ 30 + 40 = 70…The estimate is 70.
COMPATIBLE NUMBERS
compatible numbers – numbers that can be divided evenly; useful in estimating quotients
Ex. 27.2 ÷ 4.14 ≈ 28 ÷ 4 = 7…28 and 4 are compatible #s.
PROPER FRACTION
proper fraction – a fraction that represents a positive number that has a value less than 1 (denominator is larger than numerator)
IMPROPER FRACTION
improper fraction – a fraction that represents a positive number that has a value more than 1 (numerator is larger than denominator) is an improper fraction.
EQUIVALENT FRACTION
equivalent fraction – a fraction that has the same value as a given fraction are equivalent fractions.
SIMPLEST FORM
simplest form (of a fraction) – an equivalent fraction for which the only common factor of the
numerator and denominator is 1
MIXED NUMBER
mixed number – the sum of a whole number and a fraction
RECIPROCAL
reciprocal – a number that can be multiplied by another number to make 1 (numerator and denominator are switched)
PERCENT
percent – a ratio that compares a number to 100
SEQUENCE
sequence – a set of numbers that follow a pattern
Ex. 4, 6, 8, 10, 12…is a sequence of numbers.
ARITHMETIC SEQUENCE
arithmetic sequence – a sequence where each term is found by adding or subtracting the exact same
number to the previous term
Ex. 4, 6, 8, 10, 12…is an arithmetic sequence (add 2)
GEOMTRIC SEQUENCE
geometric sequence – a sequence where each term is found by multiplying or dividing by the exact
same number to the previous term
Ex. 2, 6, 18, 54, 162…is a geometric sequence (multiply 3)
GROUPING SYMBOLS
Ex. (parenthesis), [brackets], {braces}, long division bar
ORDER OF OPERATIONS
order of operations – the procedure to follow when simplifying a numerical expression
1 – Grouping symbols
2 – Exponents
3 – Multiplication and Division (from left to right)
4 – Addition and Subtraction (from left to right)
NUMERICAL EXPRESSION
numerical expression – a mathematical phrase that contains numbers and operation symbols
Ex. 14 + 8 ÷ 4 – 21
VARIABLE EXPRESSION
variable expression – a mathematical phrase that contains variables, numbers, and operation
symbols
Ex. 45 – (x + 3y)
EVALUATE
evaluate – to replace variables with numbers and then simplify an expression
Ex. To evaluate 4x + 10 when x = 3, replace “x” with 3 and simplify: 4(3) + 10 = 12 + 10 = 22
ABSOLUTE VALUE
absolute value – the distance a number is from zero on the number line
Ex. |-3| = 3; “The absolute value of -3 is 3.”
OPPOSITES
opposites – pairs of numbers that have the same absolute value
Ex. 4 and -4 are opposites because they are 4 units from 0.
INTEGERS
integers – the set of numbers that includes whole numbers and their opposites
X-AXIS – the horizontal number line that, together with the y-axis, establishes the coordinate plane
Y-AXIS – the vertical number line that, together with the x-axis, establishes the coordinate plane
COORDINATE PLANE
coordinate plane – plane formed by two number lines (the horizontal x-axis and the vertical y-axis)
intersecting at their zero points
QUADRANT
quadrant – one of four sections on the coordinate plane formed by the intersection of the x-axis and the y-axis
ORDERED PAIR
ordered pair – a pair of numbers that gives the location of a point in the coordinate plane. Also referred to as the “coordinates” of a point
Ex. The ordered pair (3, 2) describes the location that is found by moving 3 units to the right of zero on the x-axis and then 2 units up from the x-axis.
ORIGIN
origin – the intersection of the x-axis and the y-axis on the coordinate plane
Ex. The origin is described by the ordered pair (0,0).
X-COORDINATE
x-coordinate – the number that indicates the position of a point to the left or right of the y-axis
Ex. The 4 in (4,3) is the x-coordinate, and tells you to move 4 places to the right of the y-axis
Y-COORDINATE
y-coordinate – the number that indicates the position of a point above or below the x-axis
Ex. The 3 in (4,3) is the y-coordinate, and tells you to move 3 places above the x-axis
EQUATION
equation – a mathematical sentence that uses an equals (=) sign to indicate that the side to the left of the equals sign has the same value as the side to the right of the equals sign
Ex. The equation x + 4 = 10 has a solution of x = 6.
INVERSE OPERATION
inverse operations – operations that undo each other Ex. Addition and subtraction are inverse operations.
Multiplication and division are also inverse operations.
INEQUALITY
inequality – a mathematical sentence that uses a symbol (<, >, ≤, ≥, ≠) to indicate that the left and right
sides of the sentence hold values that are different
Ex. The inequality x > 8 has an infinite number of solutions.
PERIMETER
perimeter – the distance around the outside of a figure
Ex. The perimeter of a rectangle whose length is 18 feet and width is 5 feet is: 18+5+18+5 = 46 feet.
CIRCUMFERENCE
circumference – the distance around a circle
Ex. The circumference of a circle whose radius is 4 inches is:
2π(4) = 8π inches or approximately 25.12 inches.
AREA
area – the number of square units inside a 2-dimensional figure
Ex. The area of a rectangle whose length is 18 feet and width is 5 feet is: 18×5 = 90 square feet.
VOLUME
volume – the number of cubic units inside a 3-dimensional figure
Ex. The volume of a rectangular prism whose length is 10 feet, width is 4 feet, and height is 2 feet is: 10×4×2 = 80 cubic feet.
RADIUS
radius – a line segment that runs from the center of the circle to somewhere on the circle
CHORD
chord – a line segment that runs from somewhere on the circle to another place on the circle
DIAMETER
diameter – a chord that passes through the center of the circle
CENTRAL TENDENCY
central tendency – an attempt to find the “average” or “central value” of a given set of data.
Ex. In statistics, there are three main measures of central tendency: MEAN, MEDIAN, MODE
MEAN
mean – the sum of the data items divided by the number of data items
Ex. The mean of (16, 10, 13, 11, 10) is 60/5 = 12.
MEDIAN
median – the middle data item found after sorting the data items in ascending order; could be the mean of two middle numbers if the data set has an even number of items
Ex. The median of (10, 10, 11, 13, 16) is 11.
MODE
mode – the data item that occurs most often; there could be no mode, one mode, or multiple modes
Ex. The mode of (10, 10, 11, 13, 16) is 10.
RANGE
range – the difference between the highest and the lowest data item
Ex. The range of (10, 10, 11, 13, 16) is 16 – 10 = 6.
OUTLIER
outlier – a data item that is much higher or much lower than all the other data items
Ex. The outlier of (2, 3, 5, 5, 6, 7, 10, 45) is 45.
RATIO
ratio – a comparison of two quantities by division
Ex. The ratio of students to staff members at a given school is 16:1 (also 16 to 1…or 16/1).
RATE
rate – a ratio that compares quantities measured in different units
Ex. The student’s typing rate was 200 words per 6 minutes.
UNIT RATE
unit rate – a rate that has a denominator of 1
Ex. The unit rate describing his speed was 14 meters per second.
PROPORTION
proportion – a statement (equation) showing two ratios to be equal
CONGRUENT FIGURES
congruent figures – figures that have the same size AND same shape
SIMILAR FIGURES
similar figures – figures that have the same shape BUT different size. The corresponding sides of
similar figures are proportional in length.
SCALE DRAWING
scale drawing – an enlarged or reduced drawing that is similar to an actual object or place
SCALE
scale – the ratio of the model distance to the actual distance
Ex. The scale on the map is 1 in. to 25 mi.
OUTCOMES
outcomes – possible results of action
EVENT
event – an outcome or a group of outcomes
COMPLEMENT
of an event complement (of an event) – the opposite of the event
PROBABILITY
probability – a ratio that explains the likelihood of an event
THEORETICAL PROBABILITY
theoretical probability – the ratio of the number of favorable outcomes to the number of possible
outcomes (based on what is expected to occur).
EXPERIMENTAL PROBABILITY
experimental probability – the ratio of the number of times an event occurs to the number of times
an experiment is done (based on real experimental data).
DISTRIBUTIVE PROPERTY
distributive property – a way to simplify an expression that contains a single term being multiplied
by a group of terms.
***For any numbers a, b, and c, a(b + c) = ab + ac
Ex. 5(2x + 3) = 10x + 15
TERM
term – a number, a variable, or product of a number and a variable(s)
Ex. There are 3 terms in the expression: 4x + y + 2
CONSTANT
Constant – a term with no variable part (i.e. a number)
COEFFICIENT
Coefficient – a number that multiplies a variable
Ex. For the term 8x, the 8 is the coefficient.
LIKE TERMS
like terms – terms with the same variable part (including exponent)…like terms can be combined using
the distributive property in reverse
Ex. 4x + 6x = (4 + 6)x = 10x
DISCOUNT
discount – the amount by which a price is decreased
Ex. If shoes marked at $56 have a discount of $10, the new price is now $46.
MARKUP
Markup – the amount by which a price is increased
Ex. If the jacket was purchased at $25 from the manufacturer, and a $50 markup is applied, the new price is $75.