FRACTIONS
ADDING, SUBTRACTING, MULTIPLYING, DIVIDING
The Academic Support Center @ Daytona State College (Math, Page 1 of 20)
Fractions
The Academic Support Center @ Daytona State College (Math, Page 2 of 20)
Reducing
• Find a number that will divide evenly
into the numerator and denominator.
• Divide both top and bottom by that
number, and check to see if you can
still reduce further.
The Academic Support Center @ Daytona State College (Math, Page 3 of 20)
The Academic Support Center @ Daytona State College (Math, Page 4 of 20)
Improper Fraction/Mixed Number
• To convert from an improper fraction to a mixed
number, divide the numerator by the denominator.
• The answer is the whole number and the
remainder is the numerator of the fraction. The
denominator stays the same.
The Academic Support Center @ Daytona State College (Math, Page 5 of 20)
The Academic Support Center @ Daytona State College (Math, Page 6 of 20)
Improper Fraction/Mixed Number
• To convert from mixed number to improper
fraction, multiply the whole number by the
denominator and add the numerator. This will be
the new numerator and the denominator stays the
same.
The Academic Support Center @ Daytona State College (Math, Page 7 of 20)
The Academic Support Center @ Daytona State College (Math, Page 8 of 20)
Adding & Subtracting
• Must have a common denominator.
• Add or subtract only the numerator.
• Reduce your answer.
The Academic Support Center @ Daytona State College (Math, Page 9 of 20)
The Academic Support Center @ Daytona State College (Math, Page 10 of 20)
Adding and Subtracting
Least Common Denominator
• Multiply the bottom of the
fraction by the number
needed to get the common
denominator.
• Then multiply the top by
the same number.
• Do the same for the second
fraction.
The Academic Support Center @ Daytona State College (Math, Page 11 of 20)
Adding and Subtracting
Least Common Denominator
Either answer, improper fraction or
mixed number, is mathematically correct.
The context of the problem may tell you
which form you want to use.
The Academic Support Center @ Daytona State College (Math, Page 12 of 20)
The Academic Support Center @ Daytona State College (Math, Page 13 of 20)
Adding Mixed Numbers
• You must still find the common denominator before
adding or subtracting.
• Convert any improper fraction to a mixed number and
combine with the whole number.
The Academic Support Center @ Daytona State College (Math, Page 14 of 20)
The Academic Support Center @ Daytona State College (Math, Page 15 of 20)
Subtracting Mixed Numbers
• Taking a larger fraction from a smaller fraction: convert
to improper fractions.
• Find common denominator and subtract numerators.
• Reduce if possible.
The Academic Support Center @ Daytona State College (Math, Page 16 of 20)
Multiplication
• Convert to improper fractions first.
• Reduce/cross cancel.
• Multiply straight across.
The Academic Support Center @ Daytona State College (Math, Page 17 of 20)
The Academic Support Center @ Daytona State College (Math, Page 18 of 20)
Division
• Again, convert to improper fractions first, if
needed.
• Invert the second fraction (the inverted fraction is
known as the reciprocal).
• Cross cancel if possible and multiply as usual.
The Academic Support Center @ Daytona State College (Math, Page 19 of 20)
The Academic Support Center @ Daytona State College (Math, Page 20 of 20)