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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