1. Adding Mixed Numbers With Unlike Denominators

2. Mixed Numbers
Mixed numbers are whole numbers and fractions together. 1 3 2

3. Shortcut for finding a common denominator
Check to see if the smaller denominator
divides evenly into the larger denominator.
If it does, use the larger denominator for
your LCD or LCM. 1 3
2 will divide evenly into 8,
so 8 is your LCD or LCM. 2 1 1 + 8

4. To Add Fractions Mixed Numbers With Unlike Denominators
Find the multiples of each denominator. 1 3 4
= 4, 8, 12, 16, 20, 30 1 1 + 10
= 10, 20, 30, 40, 50

5. To Add Mixed Fractions With Unlike Denominators
Compare the lists of multiples. Circle the common multiples between the two lists. 1 3 4
= 4, 8, 12, 16, 20, 24 1 1 +
= 10, 20, 30, 40, 50 10

6. To Add Mixed Fractions With Unlike Denominators
Use the least common
multiple as the denominator. 1 3 4
= 4, 8, 12, 16, 20, 24 1 1 +
= 10, 20, 30, 40, 50 10

7. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions with 20 as the denominator.
What you multiply
4 by to get 20? 1 3 4 20
x 5 = 1 1 + 10 20

8. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions with 20 as the denominator.
Since you are looking for equivalent fractions, multiply the numerator
by 5 as well. 1 3
x 5 = 4 20
x 5 = 1 1 + 10 20

9. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions with 20 as the denominator. 1 5
Multiply Across! 3
x 5 = 4 20
x 5 = 1 1 + 10 20

10. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions with 20 as the denominator. 1 5
x 5 =
What you
multiply the 10 by
to get 20? 3 4 20
x 5 = 1 1 + 10 20
x 2 =

11. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions with 20 as the denominator.
Since you are looking for equivalent fractions, multiply the numerator by 2 as well. 1 5
x 5 = 3 4 20
x 5 = 1 2
x 2 = 1 + 10 20
x 2 =

12. To Add Mixed Fractions With Unlike Denominators
Now just add the numerators. 1 5 3
x 5 = 4 20
x 5 =
Remember! Never add the denominators. 1 2
x 2 = 1 + 10 20
x 2 = 7 20

13. To Add Mixed Fractions With Unlike Denominators
Now add the whole numbers. 1 5 3
x 5 = 4 20
x 5 = 1 2
x 2 = 1 + 10 20
x 2 = 7 4 20

14. Add These Mixed Numbers
Use the short
cut to find the
Least Common
Denominator
(LCD). 1 10 3 6 1 + 3 6 6

15. Add These Mixed Numbers
Now find the
equivalent
fractions. 1 10 3 6
x 2 = 1 + 3 6 6
x 1 =
What do you multiply 3 by to get 6
and what do you multiply 6 by to get 6?

16. Add These Mixed Numbers
Since you are
writing equivalent
fractions, now
multiply the top
numbers by the
same number you
did in the
bottom. 1 2
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 + 6 6
x 1 =

17. Add These Mixed Numbers1 2
Add your
new
numerators.
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 + 6 6
x 1 = 3 6

18. Add These Mixed Numbers
Add your
whole
numbers. 1 2
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 + 6 6
x 1 = 3 ÷ 3 1 13 13 = 6 ÷ 3 2
Simplify!!

19. Add These Mixed Numbers
Find the
least common
multiple for
5 and 3. Write
this number
as your new
denominator. 4 11 5 15 1 2 + 3 15

20. Add These Mixed Numbers
Ask yourself
what you
multiply the
bottom number
by to get 15. 4 11 5 15
x 3 = 1 2 + 3 15
x 5 =

21. Add These Mixed Numbers
Multiply the
top number
by the same
number you
did in the
bottom. 12 4 11
x 3 = 5 15
x 3 = 1 5
x 5 = 2 + 3 15
x 5 =

22. Add These Mixed Numbers
Now add
your new
numerators. 4 12
x 3 = 11 5 15
x 3 = 1 5
x 5 = 2 + 3 15
x 5 = 17 15

23. Change Your Improper Fraction to a Mixed Number2 1 4 12
x 3 = 11 15 5 15
x 3 =
15) 17 1 5
x 5 = 2 15 + 3
x 5 = 15 2 17 15

24. Add Your 1 to Your Whole Numbers2 1 1 4 12
x 3 = 11 15 5 15
x 3 =
15) 17 1 5
x 5 = 2 15 + 3
x 5 = 15 2 17 14 15

25. Put Your Remainder Fraction Next to Your Answer2 1 1 4 12
x 3 = 11 15 5 15
x 3 =
15) 17 1 5
x 5 = 2 15 + 3 15
x 5 = 2 2 17 14 15 15

26. Add These Mixed Numbers1 11 1 5 20 24
x 4 = 24 6 24
x 4 =
24) 35 5 15 3
x 3 = 24 + 8 24
x 3 = 11 11 35 28 24 24