Download Chapter 2—Operations with Rational Numbers

Chapter 2—Operations with Rational Numbers
Writing rational
numbers in as
decimals—going
from fraction to
decimal

Write the rational
a
number as a fraction
b



if necessary
May need to rewrite a
mixed # as an improper
fraction
Use long division to find
the quotient of a ÷ b
If the remainder
repeats, the rational
number is a repeating
decimal
e.g.

2
15
If the remainder is 0,
the rational number is a
terminating decimal e.g.
-5
1
5
Notes and Examples:
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Remember, when adding and subtracting rational #’s:
 As fractions, must have a common denominator
 As decimals, must line up decimals
 The integer rules for add and subtracting apply to all rational numbers
Set of Real Numbers
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Chapter 2—Operations with Rational Numbers
Simplifying a
rational number
(in fraction form)



Identify the greatest
common factor between
the numerator and
denominator
Divide both the
numerator and
denominator by that
GCF—greatest common
factor
You may hear the words
“reduce” or “lowest
terms”—they both mean
simplest form!
Notes and Examples:
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Remember, when adding and subtracting rational #’s:
2 1
 Solutions must be in simplest form—e.g. =
4 2
 A fraction in simplest form is called “relatively prime”—1 is the GCF
Chapter 2—Operations with Rational Numbers
Notes and Examples:
Comparing and
Ordering Rational
Numbers


Good idea to rewrite all
rational numbers in one
form (either all fractions
or all decimals)
Decimals tend to be
easier to work with—
think of money!
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Remember, when comparing and ordering rational numbers:
 All real #’s –rational and irrational, have a place on the number line
 The number line is the same # line we used to compare and order
integers
Chapter 2—Operations with Rational Numbers
Adding Rational
Numbers
Decimals
Notes and Examples:
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Fractions
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Remember, when adding and subtracting rational #’s:
 Integer rules for adding and subtracting apply to all rational numbers
 Subtract the lesser absolute value from the greater absolute value
Chapter 2—Operations with Rational Numbers
Subtracting
Rational Numbers
Decimals
Notes and Examples:
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Fractions
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Remember, when adding and subtracting rational #’s:
 Integer rules for adding and subtracting apply to all rational numbers
 “Keep-Change-Change” when subtracting two rational #’s
 Subtract the lesser absolute value from the greater absolute value
Chapter 2—Operations with Rational Numbers
Multiplying
Rational Numbers
Decimals
Notes and Examples:
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Fractions
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Remember, when multiplying and dividing rational #’s:
 Integer rules for multiplying and dividing apply to all rational numbers
 “Count the number of negatives—only  when in pairs”
 Try to simplify before you multiply—solution should be in simplest form
Chapter 2—Operations with Rational Numbers
Dividing
Rational Numbers
Decimals
Notes and Examples:
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Fractions
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Remember, when multiplying and dividing rational #’s:
 Integer rules for multiplying and dividing apply to all rational numbers
 “Happy or Grouchy?”
 When dividing, you are really multiplying by the reciprocal of the divisor
Other Notes and Information:
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