Powerpoint 33 math vocab

MA.A.1.3.1 Associates Verbal Names With Written Names
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Negative numbers

What are negative numbers?
a. All numbers less than or equal to zero
b. All numbers less then negative 1 (i.e., -1).
c. All numbers equal to or less than negative 1 (i.e., -1).
d. All numbers that students don’t want to learn.
e. All numbers less than zero (i.e., 0).

What are negative numbers?
Negative numbers are numbers that are less than zero.
Examples: -3
-0.472
-1/2
-984.32794078
-46 3/8
-Ö83

integers

What is an integer?
a. An integer is a whole number.
b. An integer is a negative whole number.
c. An integer is a positive whole number, zero,
or a negative whole number.
d. An integer is a number that can be written as
a ratio of two numbers.

What is an integer?
An integer is a whole number that can be written as a positive whole
number, zero, or a negative whole number.
The numbers . . . , -4, -3, -2, -1, 0, 1, 2, 3, 4, . . . consisting of the
negative whole numbers, zero, and the positive whole numbers are
called integers. -3 and 31 are both examples of integers. They
contain no decimals or fractional components.

coordinate

Which of the following is a coordinate?
a. 4 and 6
b. (-1.2, -4.5)
c. 23.45
d. c and d

What is a coordinate?
A coordinate is a pair of values that represent a point on a
coordinate plane, also known as an ordered pair, (x,y).
The coordinate plane is also known as the Cartesian Coordinate
System. It is made up of a horizontal and a vertical number line
that intersect at right angles, called the x-axis and y-axis
respectively.

inequality

What is an inequality?
An inequality is a math statement or expression formed by placing
a less than or greater than sign between two expressions.
For example, 1 < 2
or
3x + 3 > 6 - y

absolute value

What is absolute value?
Absolute value is the distance of a number from zero on the
number line. It is written as |n|, where n is a real number.
For example, |-4| = 4 or |x| = x and |-x| = x

Write the expression for:
The absolute value of -1?
A.) -|1|
B.) |-1|
C.) -|-1|
D.) none of the above

The absolute value of 45?
A.) |45|
B.) -|45|
C.) |-45|
D.) -|-45|

The absolute value of -32.7?
A.) -|32.7|
B.) |-32.7|
C.) -|-32.7|
D.) none of the above

The absolute value of -x2?
A.) -|- x2|
B.) -| x2|
C.) |- x2|
D.) | x2|

The absolute value of -(x + 3)?
A.) |-(X + 3)|
B.) -|(X + 3)|
C.) |X + 3|
D.) -|-(X + 3)|

Evaluate:
|-1| =

Evaluate:
|45| =

Evaluate:
The absolute value of -32.7?

Evaluate:
The absolute value of -x2?
A.) x2
B.) - x2

Evaluate:
The absolute value of -(x + 3)?
A.) -(x + 3)
B.) (x + 3)
C.) -x + 3
D.) -x - 3

bases

What is a base?
A base is a number that is to be multiplied in an exponential power
expression.

exponents

What is an exponent?
An exponent is a number that appears as a superscript next
to a number called a base. It tells you how many times
the base needs to be multiplied.
The entire number is called a power or exponential power.
For example, 24 = 2 · 2 · 2 · 2 = 16; 4 is the exponent
a8 = a · a · a · a · a · a · a · a; 8 is the exponent

Evaluate:
24 = ____

Evaluate:
73 = ____

Exponential power

What is an exponential power?
An exponential power is a term that includes a base and an
exponent. It is the number that is to be multiplied times itself the
total number of times expressed by the exponent. It is many times
called just a power.
6327
29
x3
(ac)12

Scientific notation

What is scientific notation?
Scientific notation is a way of writing very big or very small
numbers so they are easier to manipulate arithmetically.
When you first see a number written in scientific notation, it might
look hard to read. But it really isn’t once you understand why it is
written like it is and practice writing numbers that way.
Scientific notation involves two parts:
• The base number
• The power of ten

Write 6,543,210 in scientific notation?
1. Move the decimal point from the right of the zero
(6543210.) to the right of the left-most digit, between the 6
and 5 (6.543210)
2. Count the number of place values the decimal has been
moved to the left. (In this case, it has moved to the left six
places.)
3. This number is now the exponent that will be used as
the power of 10, so it is written as 106.
The answer then becomes 6.543210 x 106.
Drop any insignificant zeros on the end of the decimal.

Write 43,671 in scientific notation?

Square root

What is a square root?
A square root is the number that is multiplied by itself to
get the number that is being evaluated.
For example, √16 = 4 because 4 · 4 = 16

Evaluate:
= ____

Perfect square

What is a perfect square?
A perfect square is a number that is the square of an integer.
For example, 16 is a perfect square because 4 · 4 = 16

Do you know the perfect squares between 1 and 144?
Every student should know the perfect squares
up through 144. They aren’t that hard.
Let’s see if you can name them.
12 = _______

Good, now let’s try:
22 = _______

Next:
32 = _______

Try this one:
42 = _______

How about?
52 = _______

Keep going . . .
62 = _______

You’re more than half way!
72 = _______

This one is easy:
82 = _______

This is the last single digit one:
92 = _______

Everybody knows this one.
102 = _______

This one is a bit tough for some:
112 = _______

And last but not least:
122 = _______
Great! Now let’s see how knowing this
can help with square roots.

Radical sign

What is a radical sign?
A radical sign is the sign used to identify the
Operation of taking the square root of a number.
Here are the square roots shown with the radical
sign for the perfect squares through 144:
144 = ±12
121 = ±11
100 = ±10
81 = ± 9
64 = ± 8
49 = ± 7
36 = ± 6
25 = ± 5
16 = ± 4
9 = ± 3
4 = ± 2
1 = ±1

Principal square root

What is a principal square root?
A principal square root is the positive
value of a square root of a number.
For example, the principal √16 = 4.

Ratio

What is a ratio?
A ratio is a mathematical comparison of two numbers
to each other that have the same dimensional units
(so units are not required).
The two numbers can be separated by either a colon (:)
or placed on both sides of a fraction line.
e.g. 4:5 is a ratio; 3 is also a ratio of 3 to 8.
8

Calculate a ratio.
A math class has a total of 23 students. 10 are boys.
Write the ratio of boys to girls in this class as a fraction?
[Note: Since we are comparing students to students,
there is no need to include dimensions.]

Rewriting a ratio.
Write the answer to the previous problem using the colon
instead of the fractional form for a ratio.

Rate

What is a rate?
A rate is a measurement that compares two scalar dimensions,
normally, but not always, between quantity and time, to each
other. It is a ratio that says how long it takes to do something,
or how two dimensions relate to each other in the physical world.
It compares two different kinds of units, or two different things
measured in different portions of the same units.
Examples of rate units are:
miles per hour
feet per minute
kilometers per day
dollars per week
liters per second
gallons per month
ounces per pound (notice different portions of the same units here)
Rates are usually in dimensions of
length (distance) in the numerator
and time in the denominator, but
not always

When converting between rate units we use a tool called
“Dimensional Analysis.”
Dimensional analysis allows us to convert from one
rate unit to another.
For example, if we want to convert the number of inches
per day that a snail moves to compare it to the speed of a
man walking, we would use dimensional analysis to convert
inches per day to miles per hour. Since certain units can be
equated, for instance, 12 inches = 1 foot, we can relate
them into a rate unit like this:
12 inches
1 foot

Percent

What is percent?
A percent is a number representing the
ratio between a quantity and 100.
“Per cent” means “divided by 100”
Thus, a number’s percentage is the relationship
between the part associated with the number versus
the whole quantity, represented by 100.
It is equivalent to a fraction with 100 in the denominator.
It is written as a number followed by the symbol “%.”

Write 21 / 70 as a percent?
21 / 70 is the same as 21 divided by 70.
21 / 70 = .3 = 3/10 (10/10) = 30 / 100 = 30%

Write 4 / 5 as a percent?
a. 80%
b. 75%
c. 70%
d. 60%

Percent proportion

What is percent proportion?
A percent proportion is a relationship between
two fractions that us often used to solve percent
problems. It looks like this:
part = ?
whole 100

Solving percent proportion problems:
Using the “percent proportion” equation:
part = ?
whole 100
The fraction of part-to-whole is expressed in this equation:
What percent of 200 is 60?
60 is the part; 200 is the whole.
So the equation becomes:
Solving: 60:200=?:100
(The product of the means = the product of the extremes.)
6000 = 200?; ? = 6000/200 = 30

Part

What is a part?
A part is a piece of the whole in a math problem.
For example, What is 20% of 600?
“What” represents the part, 600 is the whole.
So the percent proportion problem is:
part:600=20:100
(part)100=12000
part = 12000 = 120
100

Powerpoint 33 math vocab

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