Classification of Numbers Properties of Real Numbers Order of Operations R1 Real Numbers.
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Transcript of Classification of Numbers Properties of Real Numbers Order of Operations R1 Real Numbers.
![Page 1: Classification of Numbers Properties of Real Numbers Order of Operations R1 Real Numbers.](https://reader033.fdocuments.net/reader033/viewer/2022061517/5697bff31a28abf838cbca42/html5/thumbnails/1.jpg)
•Classification of Numbers
•Properties of Real Numbers
•Order of Operations
R1 Real Numbers
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The numbers 3, 4, 5, and 6 are called elements.
S = { 3, 4, 5, 6 }
When we want to treat a collection of similar but
distinct objects as a whole, we use the idea of a set.
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We do not list an element more than once, because the elements of a set are
distinct.
If a set has no elements, it is called the empty set or null
set.
The order in which you list elements in a set is not
relevant.
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Natural Numbers – N1, 2, 3, 4, 5, 6, 7, …Whole Numbers – W0, 1, 2, 3, 4, 5, 6, …Integers – I…, – 2, – 1, 0, 1, 2, …
Classification of Real Numbers
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Rational NumbersAny number that can be written in the form of a fraction.
Irrational NumbersAny number that neither terminates nor repeats.
64, 0.72, 2.914, 36
4 , 2, 8 3
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TruncationDrop all the digits that follow the specified final digit in the decimal.RoundingIdentify the specified final digit in the decimal. If the next digit is 5 or more, add 1 to the final digit. Otherwise leave the number as it appears.
Approximations
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Truncating: 24.748Rounding: 24.749
Approximate 24.7486 to 3 decimal places by both truncating and rounding.
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Convert Natural Numbers, Whole
Numbers, and Integers into fractional form 31. 64 2. 4
3. 14 4. 6
1
325. 16 6. 27
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Convert each mixed number into fractional
form
Multiply the whole number by the denominator and add the numerator all over the
denominator
3 7
1. 8 2. 64 8
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Convert terminating decimals into fractional
form
The number of places you move the decimal point is
equal to the number of zeros in the denominator.
21. 0.42 2. 6.8 3. 4.8 10x
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Convert repeating decimals into fractional
form
Repeating decimals are over 9Nonrepeating decimals are over 0Work from right to left in the denominatorSubtract the nonrepeating digits from the entire decimal for the numerator
1. 0.4 2. 0.74 3. 2.5
4. 0.246 5. 0.246 6. 0.246
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1. Perform all operations within grouping symbols from innermost outward.
2. Perform all operations with exponents from left to right.
3. Perform all multiplication and division from left to right.
4. Perform all addition and subtraction from left to right.
Order of Operations
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1. Find the LCD2. Multiply numerator by factor
of LCD3. Add the numerators together4. Keep the denominator the
same5. Simplify the expression
Adding and Subtracting Rational
Numbers
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Adding and Subtracting Rational
Numbers
5 4 3 4 7
3. 2 4. 6 26 3 4 9 6
5 7 8 5
1. 2. 4 78 12 3 2
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1. Inverse Property for division2. Reduce fractions with common
factors3. Multiply the numerators
together4. Multiply the denominators
together5. Simplify the expression
Multiplying and Dividing Rational
Numbers
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Multiplying and Dividing Rational
Numbers
15 9 14 21
3. 4. 24 28 27 36
16 7 24 9
1. 2. 21 12 20 16
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R2 Algebra Review
•Graphing Inequalities
•Absolute Value
•Evaluating Expressions
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A real number that corresponds to a particular point on the
number line is called a coordinate.The origin corresponds to the
real number zero.The correspondence between points on a line and the real
numbers is called a coordinate system.
Real Number Line
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Graph the following inequalities on the number line.
Graphing Inequalities
or uses and or uses
1. Graph all the numbers x for which x 2
2. Graph all the numbers x for which x 4
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Distance from zero on the number line.
The absolute value of a real number a is denoted by the
symbol |a|.
Absolute Value
4 4 and 9 9
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The distance between two points P and Q is denoted by
d(P,Q) = |b – a|.Let P, Q, and R be points on the number
line with coordinates –7, 4, and –3 .
1. Find the distance between P and Q.2. Find the distance between Q and R..
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Write an equivalent expression without using absolute value
bars.
5. 6 6. 3x 9 , if x 3
3. 5 2 4. 3 5
1. 2 6 2. 19 7
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1.Substitute each value for the variable using a grouping symbol
2.Follow all order of operations
3.Simplify your answer
Evaluating Expressions
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Evaluate each expression, if x = 4, y = –2, and z = 3
3x 2xz 2 3 5 43. 4.
3y 8 y 2z 3 y x 3
31. 3xy 4z 9 2. 2z 3x 4y
3 x 4 y 3x 2y5. 6.
y z 5 5z x 1