Solving Expressions with Given Values
Bell Ringer #4
•
Solve the expressions
•
5x + (7 + y – 2) when x = 4 and y = 2
•
9
2
/ 3 + (5 * 7)
•
ab / c + d2 when a = 5, b = 6, c = 10, and d = 7
Real Numbers
Mr. Haupt 9/13/16
C.C.2.1.8.E.1
Real Numbers
•
Real numbers are any numbers you could possible think of.
•
Fractions, Negatives, Decimals (even ones that never end) are
all real numbers.
•
Among all real numbers there are two major groups, and
three smaller groups.
•
Rational
•
Natural
•
Whole
•
Integers
•
Irrational
•
So what number could not be a real number?
Imaginary Numbers
Imaginary Numbers
•
Imaginary numbers are numbers that do not exist, but
because it may sometimes be necessary to use their values,
we have identified them.
•
They are really easy to spot.
•
Anytime you see a negative number inside the square root
function.
•
We can separate the negative one out. So the square root of -
25 becomes the square root of 25 times the square root of -1.
•
We use the letter “i” for the square root of -1.
•
Why can’t you take the square root of a negative number?
Back to Real Numbers
•
Real numbers can also be separated into two main categories,
and three subcategories.
•
Rational
•
Natural
•
Whole
•
Integers
•
Irrational
•
Rational numbers do not have to be one of the three
subcategories, but they could belong to one, two, or even all
three of them.
Rational Numbers
•
A rational number is any number that is whole, is a
decimal that stops, or is a decimal that repeats forever.
•
Examples of rational numbers
•
10.25
•
-17
•
½
•
-8.33333333...
•
0
•
58
Natural Numbers
•
One of the subcategories a rational number may
also belong to is natural numbers.
•
A natural number is any WHOLE number from 1
to infinite on a number line.
•
Examples:
•
1, 8, 92, 198
Whole Numbers
•
The next subcategory is whole numbers.
•
Includes WHOLE numbers that go from 0 to
infinite on a number line.
•
Examples are the same as natural numbers,
but now we added the zero.
Integers
•
The last subcategory is integers.
•
Integers include all WHOLE numbers from
negative infinite to positive infinite.
Irrational
•
Irrational numbers are any numbers that
have decimals that go on forever without
repeating.
Inequalities
•
Inequalities are used to compare the value of two numbers or
expressions using the signs >, <, or =
When using < or > the big open end of the arrow always faces
the larger value, while the narrow side always points to the
smaller value.
If the values are the same, then use the equal sign.
Later on we will be using “less than or equal to” and “greater
than or equal to.”
<
and
>
.
Absolute Value
•
Absolute value is used to describe how many units away from
zero a number is.
•
The absolute value is always positive. Since we are only
concerned with how far from zero it is, we can ignore any
negative signs within the absolute value brackets.
•
Negatives outside the absolute value brackets still have to be
used.
Opposites
•
Two different numbers with the same absolute value are
opposites.
•
Opposites are basically the positive and negative of a number.
•
-3 is the opposite of 3
•
8 is the opposite of -8
the concept of solving expressions by substituting given values for variables. Understand the distinction between real and imaginary numbers, rational and irrational numbers, as well as natural, whole, and integer numbers.
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Presentation Transcript
Bell Ringer #4 Solve the expressions 5x + (7 + y 2) when x = 4 and y = 2 92/ 3 + (5 * 7) ab / c + d2 when a = 5, b = 6, c = 10, and d = 7
Real Numbers Mr. Haupt 9/13/16 C.C.2.1.8.E.1
Real Numbers Real numbers are any numbers you could possible think of. Fractions, Negatives, Decimals (even ones that never end) are all real numbers. Among all real numbers there are two major groups, and three smaller groups. Rational Natural Whole Integers Irrational So what number could not be a real number?
Imaginary Numbers Imaginary numbers are numbers that do not exist, but because it may sometimes be necessary to use their values, we have identified them. They are really easy to spot. Anytime you see a negative number inside the square root function. We can separate the negative one out. So the square root of - 25 becomes the square root of 25 times the square root of -1. We use the letter i for the square root of -1. Why can t you take the square root of a negative number?
Back to Real Numbers Real numbers can also be separated into two main categories, and three subcategories. Rational Natural Whole Integers Irrational Rational numbers do not have to be one of the three subcategories, but they could belong to one, two, or even all three of them.
Rational Numbers A rational number is any number that is whole, is a decimal that stops, or is a decimal that repeats forever. Examples of rational numbers 10.25 -17 -8.33333333... 0 58
Natural Numbers One of the subcategories a rational number may also belong to is natural numbers. A natural number is any WHOLE number from 1 to infinite on a number line. Examples: 1, 8, 92, 198
Whole Numbers The next subcategory is whole numbers. Includes WHOLE numbers that go from 0 to infinite on a number line. Examples are the same as natural numbers, but now we added the zero.
Integers The last subcategory is integers. Integers include all WHOLE numbers from negative infinite to positive infinite.
Irrational Irrational numbers are any numbers that have decimals that go on forever without repeating.
Inequalities Inequalities are used to compare the value of two numbers or expressions using the signs >, <, or = When using < or > the big open end of the arrow always faces the larger value, while the narrow side always points to the smaller value. If the values are the same, then use the equal sign. Later on we will be using less than or equal to and greater than or equal to. < and >.
Absolute Value Absolute value is used to describe how many units away from zero a number is. The absolute value is always positive. Since we are only concerned with how far from zero it is, we can ignore any negative signs within the absolute value brackets. Negatives outside the absolute value brackets still have to be used.
Opposites Two different numbers with the same absolute value are opposites. Opposites are basically the positive and negative of a number. -3 is the opposite of 3 8 is the opposite of -8
