Adding and Subtracting Rational Numbers
CC Math I Standards
I. SPECIAL CLASSIFICATION of RATIONAL NUMBERS
IMPROPER FRACTION: a fraction where the numerator (top) is greater than or equal to the denominator (bottom number).
MIXED FRACTION: the combination (MIX) of a whole number with a fraction.
Examples: Determine each rational as IMPROPER or MIXED or NEITHER.
(1) [pic] = _________________________
(2) [pic]= _________________________
(3) [pic]= ________________________
(4) [pic]= _________________________
(5) [pic]= _________________________
(6) [pic]= _________________________
II. CONVERT a MIXED FRACTION to IMPROPER FRACTION
“Bottom times Whole plus Top”
Step 1: MULTIPLY the Denominator of the Fraction and the Whole Number
Step 2: ADD that product and the Numerator of the Fraction
Step 3: IMPROPER Fraction is the sum over the original denominator with the original sign (positive or negative)
Example 1: Convert 12 ¾ to an improper fraction
Example 2: Convert[pic] to an improper fraction.
PRACTICE: Convert each of the mixed fractions to an improper fraction
(1) [pic]
(2) [pic]
(3) [pic]
(4) [pic]
(5) [pic]
(6) [pic]
III. ADDING and SUBTRACTING MIXED FRACTIONS
Step 1: Make an IMPROPER Fraction
Step 2: Find a common denominator
Step 3: Add or subtract numerators
EXAMPLES:
(1) [pic]
(2) [pic]
(3) [pic]
(4) [pic]
(5) [pic]
(6) [pic]
(7) [pic]
(8) [pic]
IV. MULTIPLYING RATIONAL NUMBERS
Step 1: Make all fractions IMPROPER
Step 2: NEW Numerator = Product of all numerators
Step 3: NEW Denominator = Product of all denominators
Step 4: Reduce Fraction and Check positive and negative signs
(1) [pic]
(2) [pic]
(3) [pic]
(4) [pic]
(5) [pic]
(6) [pic]
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