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2. Fraction Addition & Subtraction (w/ different denominators)
Copyright © 1999 Lynda Greene

3. 3 2 4 5 + Find the Least Common Denominator (LCD)
1) Find the multiples of each denominator
2) Pick the smallest number
both lists have in common
LCD = 20
4, 8, 12, 16, 20, 24, ...
5, 10, 15, 20, 25, 30, ...
Copyright © 1999 Lynda Greene

4. Now that we can find the LCD, we are able to add
& subtract fractions with different denominators 15 3 2 4 5 + 20 = x5
1) Find the LCD (20)
2) Rewrite each fraction with the LCD on the bottom.
Ask yourself: 4 x ? = 20
Multiply the top and bottom
by this number
3) Now figure out
(for each fraction)
what number
changes the old
bottom number into the new LCD 8 x4
Ask yourself: 5 x ? = 20
Multiply the top and bottom
by this number
Copyright © 1999 Lynda Greene

5. 15 8 + 20 20 15 + 8 20 23 = 20 Now that the two fractions
have a Common
Denominator we can:
Add the tops
Keep the bottom
Reduce if possible + 20 20
15 + 8 20 23 = 20
This fraction can’t be reduced
Copyright © 1999 Lynda Greene

6. + 8 8 + LCD = 8 Another Example: 1) Find the LCD
multiples of 4: 4, 8, 12, 16, 20, 24,
multiples of 8: 8, 16, 24, 32,
8 8 +
2) Re-write the fractions with
the LCD on the bottom
Copyright © 1999 Lynda Greene

7. + 3 10 8 8 + = x2 3) The first fraction: the bottom number didn’t
change, so leave
the top the same.
4) The second fraction:
We changed a 4
into an 8,
so 4 x ? = 8 (2) x2
5) Multiply the top and bottom of the second fraction by 2 3 10 +
8 8
ADD THE TOPS
KEEP THE BOTTOMS
6) Now that the denominators
(bottoms) are
the same, we
can add the tops.
ALWAYS REDUCE
IF POSSIBLE =
Copyright © 1999 Lynda Greene

8. More than two fractions:x1 x3 x2 + +
LCD = 6
Rewrite all three fractions with a 6 on the bottom
multiples of 2: 2, 4, 6, 8, 10, 12,...
multiples of 3: 3, 6, 9, 12, 15,...
multiples of 6: 6, 12, 18, 24, 30,...
Multiply the tops by the correct numbers + 15 2 7
Fraction 1: 2 x ? = 6 (3)
Fraction 2: 3 x ? = 6 (2)
Fraction 3: 6 x ? = 6 (1)
Copyright © 1999 Lynda Greene

9. Now that the three fractions have a Common Denominator we can:
* Add (or subtract) the tops
* Keep the bottom
* Reduce if possible + 15 2 7 6
ADD/SUBTRACT THE TOPS
KEEP THE BOTTOM 6 6
 6
REDUCE 6 24 = = 3 1
Copyright © 1999 Lynda Greene

10. We need a common denominator Find the LCM’s:
4,8, 12, 20,…
3, 6, 9, 12, 15, …
4 and 3 have “12” in common
Create 2 fractions with
This denominator

11. 27 28 Now multiply each fraction (top and bottom) by the number
that will make them into 12’s. 27 28
Now that they have the same denominators, we can subtract the tops(numerators).
This can’t be reduced

12. Addition & Subtraction Practice: Press enter to see answers
Copyright © 1999 Lynda Greene