Download Target Sheet Ch. 2

Chapter 2 Target Sheet
Properties of Real Numbers
Targets:
1.
I can find the absolute values of numbers (2.1)
2.
I can analyze a conditional statement (2.1)
3.
4.
I can add real numbers (2.2)
I can give an example for each property of addition for real numbers (2.2)
5.
I can subtract real numbers (2.3)
6.
I can evaluate a variable expression (2.3)
7.
I can multiply real numbers (2.4)
8.
I can give an example for each property of multiplication for real numbers (2.4)
9.
I can use the properties of multiplication to justify a product (2.4)
10. I can apply the distributive property to create equivalent expressions (2.5)
11. I can identify the parts of an expression (2.5)
12. I can simplify an expression (2.5)
13. I can find the multiplicative inverses of numbers (2.6)
14. I can divide real numbers (2.6)
15. I can simplify an expression involving division (2.6)
16. I can find square roots (2.7)
17. I can classify numbers (2.7)
18. I can give an example of each of the properties of equality (2.8)
Vocabulary:
Whole numbers
Integers
Rational numbers
Real numbers
Irrational numbers
Terminating decimal
Repeating decimal
Opposites
Absolute value
Mean
Equivalent expressions
Conditional statement
Hypothesis
Conclusion
Counterexample
Additive identity
Additive inverse
Multiplicative identity
Multiplicative inverse (Reciprocal)
Coefficient
Like terms
Constant term
Conjecture
Perfect square
Principal square root (positive)
Negative square root
Radicand (radical)
Processes:
Subtraction Rule: Never subtract… change to an addition problem by adding the opposite
Addition Rule: When “adding” two numbers remember: same sign add absolute values
different signs subtract absolute values
Addition Rule: When “adding” more than two numbers remember to:
1. group same sign numbers in grouping symbols first
2. add the positive group to get a positive sum
3. add the negative group to get a negative sum
3. subtract absolute values found from the two sums and use the addition sign rules
Multiplication Rule: Multiply absolute values of all terms then apply multiplication sign rule
Division Rule: Never divide…change to a multiplication problem by taking the multiplicative inverse of the second
term, then multiply and apply multiplication sign rule
Sign Rules:
Subtracting two real numbers…change to addition problem, then use addition sign rule
Adding two real numbers… use the sign of the largest absolute value
Multiplication of two or more real numbers…count the negative signs:
zero or even number makes product positive
odd number makes product negative
Division of two real numbers… count the negative signs:
zero makes quotient positive
one makes quotient negative
Absolute value of any real number except zero: The distance from zero on a number line…
absolute value is always positive
Absolute value of zero: is zero
4-step Problem-solving Plan – See Problem Solving handout
No Way I’m Remembering It!

Natural numbers include only positive counting numbers
1, 2, 3, …

Whole numbers include all natural numbers plus zero
0, 1, 2, 3, …

Integers include all whole numbers plus negative counting numbers
…, -3, -2, -1, 0, 1, 2, 3, …

Rational numbers include all integers, plus any number that can be written as a fraction (ratio)
…, -3, -2, -1, 0, 1, 2, 3, …
0.5, -3.78, 0.3, ½, -3/4, √4

Irrational numbers do not include any rational numbers; Irrational numbers cannot be written as a fraction (ratio)
√5, -√2, π
Properties:
Commutative
Associative
Identity
Inverse
Property of Zero
Property of –1
Distributive
When changing the order does not
change the sum or product
When changing the groupings does
not change the sum or product
The sum of a number and zero is
the number; the product of a
number and one is that number
The sum of a number and its
opposite is zero; the product of a
number and its multiplicative
inverse (reciprocal) is one
The product of a number and 0 is 0
The product of a number and –1 is
the opposite of the number
a+b=b+a
ab = ba
(a + b) + c = a + (b + c)
(a • b)c = a(b • c)
a+0= a
a•1 = a
5+2=2+5
7(10) = 10(7)
(2 + 3) + 5 = 2 + (3 + 5)
(5 • 4) 10 = 5 (4 • 10)
7+0=7
7(1) = 7
a + -a = 0
a • 1/a = 1
2 + -2 = 0
2 • ½=1
a•0 = 0
a • -1 = -a
Creates an equivalent
expression of real numbers
rewritten for easier mental math
a(b + c) = ab + ac
a(b – c) = ab – ac
-3 • 0 = 0
4 • -1 = -4
-2 • -1 = 2
5(b + 4) = 5b + 20
2(b – 4) = 2b – 8
a=a
If
a = b,
then b = a
3=3
If
1+4=5
Then 5 = 1 + 4
If
a = b and b = c,
then a = c
If
2+3=1+4
And 1 + 4 = 5
Then 2 + 3 = 5
If
a = b,
then a + c = b + c
If
2(4) = 8(1)
Then 2(4) + 5 = 8(1) + 5
If
a = b,
then a – c = b – c
If
3(4) = 6(2)
Then 3(4) – 7 = 6(2) – 7
If
a = b,
then ac = bc
If
2+4=6
Then 5(2 + 4) = 5(6)
If
If
Properties of Equality:
Reflexive
Symmetric
Transitive
Addition
Subtraction
Multiplication
Division
c≠0
A quantity is equal to itself.
If one quantity equals a second,
then the second quantity equals
the first.
If one quantity equals a second
and the second quantity equals
the third, then the first quantity
equals the third.
If the same quantity is added to
two equal quantities, then the
resulting quantities are equal.
If the same quantity is
subtracted from two equal
quantities, then the resulting
quantities are equal.
If the same quantity is
multiplied to two equal
quantities, then the resulting
quantities are equal.
If two equal quantities are
divided by the same quantity,
then the resulting quantities are
equal.
a = b,
then a = b
c c
3(4) = 12
Then 3(4) = 12
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