Adding

1
Adding Subtracting Fractions
2
Adding Fractions

• If we were adding apples,
• 1 apple 1 apple 2 apples
• Same with fractions
• You just add the tops and copy the bottom.

3
Adding Fractions

• Oops!
• What if we cant just copy the bottom because
  the bottoms are different?

4
Adding Fractions

• We need a common denominator.
• Its much easier to understand common
  denominators if you understand what common
  multiples are.

5
Multiples of a Number

• A multiple of a number is a number that you can
  get by multiplying your original number by a
  whole number.
• For example, the multiples of 6 would be
• 6, 12, 18, 24, 30, 36, 42, 48, . . .

6
Common Multiples

• If you had two numbers like 6 and 12, a common
  multiple would be a number that is a multiple of
  each of them.
• Multiples of 6 6, 12, 18, 24, . . .
• Multiples of 12 12, 24, 36, 48, . . .
• 12 and 24 are two of the many common multiples of
  6 and 12.

7
Least Common Multiples

• Even though 6 and 12 have many common multiples,
  we usually work with the smallest, or least
  common multiple.
• Multiples of 6 6, 12, 18, 24, . . .
• Multiples of 12 12, 24, 36, 48, . . .
• 12 is the least common multiple of 6 and 12.

8
Common Denominator

• In order to add or subtract fractions, you need
  to have a common denominator.
• The fractions must have the same number on the
  bottom.

9
Common Denominators

• Finding common denominators is the same as
  finding common multiples.
• The denominator is the number on the bottom of a
  fraction.
• Finding a common denominator for
• is the same as finding the common multiples of 6
  and 12.

10
Least Common Denominator

• Although you can add fractions using any common
  denominator, most people like to work with
  smaller numbers so they use the least common
  denominator.
• Its abbreviated L.C.D.

11
Adding Fractions

• To add these fractions, we must first transform
  them into equivalent fractions that have the same
  number on the bottom.

12
Adding Fractions

• Weve already decided that the least common
  multiple of 6 and 12 is 12.
• Therefore the L.C.D. of our fractions is 12.

13
Adding Fractions

• We only have to change the first fraction so that
  it has a 12 on the bottom.
• We have to be careful not to change the value of
  the fraction when we change what it looks like!

14
Changing Fractions

• An easy way to change a 6 into a 12 is to
  multiply it by 2.
• If we multiply the bottom by 2, we must also
  multiply the top by 2.

15
Changing Fractions

• Why arent we changing the value when we multiply
  by 2 on the top and bottom?

16
Adding Fractions

• Now our problem is easy!

17
ARF!

• We arent finished until we reduce the answer.
• ALWAYS REDUCE FRACTIONS!

18
Subtracting fractions

• Good news!
• Subtracting fractions is just like adding except
  that you subtract the tops and copy the bottom!

19
Remember
To add or subtract you need the bottoms of the
fractions to be the same.
If they arent the same, find a common
denominator. L.C.D. is the least common
denominator. Change the fraction by multiplying
the top and the bottom by the same number. Add or
subtract the tops and copy the bottom.