Ch 2'3 Adding and Subtracting Fractions

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Ch 2.3 Adding and Subtracting Fractions
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To add or subtract fractions they must have the
same (common) denominator. Add or subtract the
numerators over the common denominator and reduce
if possible.
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If the fractions have different denominators,
then a common denominator must be found, all
fractions changed to an equivalent fraction using
that denominator, then do the addition or
subtraction.
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To find a common denominator, count by multiples
of the largest denominator until a number is
obtained that is divisible by the other
denominator(s).
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Example

• Count by 12s until a number divisible by 4 is
  obtained.
• Since 12 is divisible by 4, 12 is the least
  common denominator (LCD)
• Change each fraction to an equivalent fraction
  having 12 as the denominator, add and reduce if
  possible.

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Example

• Count by 16s until a number divisible by 4,6,and
  12 is obtained. Since 12 is divisible by 4 and 6,
  only check for the 12.
• 16,32,48
• Since 48 is divisible by 12, 48 is the least
  common denominator (LCD)
• Change each fraction to an equivalent fraction
  having 48 as the denominator, add and reduce if
  possible.

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To add mixed numbers

• Find the LCD of the fractions
• Add the whole number parts
• Add the fraction parts
• Reduce the result if possible

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To subtract mixed numbers follow a similar
approach but if the fraction being subtracted is
larger than the one it is being subtracted from,
then you must borrow from the whole number.
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Add
2 A b/c 3 7 A b/c 12
1_1/4
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Add
7 A b/c 3 A b/c 4 5 A b/c 11 A b/c 12
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A blueprint calls for a piece of bar stock
in. long. If a tolerance of in. is
allowed, what is the longest and shortest
acceptable measures for the piece?
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A rod in. long has been cut as shown in
the illustration. Assume the waste in each cut is
in. What is the length of the remaining
piece?