1. Fraction XI Adding Mixed Numbers With Unlike Denominators
By Monica Yuskaitis

2. Some multiples of 3 & 4 12, 24, 36, 48, Common Multiple
A number that is a multiple of two or more numbers.
Some multiples of 3 & 4
12, 24, 36, 48,

3. Least Common Multiple
The smallest common multiple of a set of two or more numbers.
4 = 4, 8, 12, 16, 20, 24, 28
5 = 5, 10, 15, 20, 25, 30

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

5. Shortcut for Finding the Least Common Denominator or Least Common Multiple
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

6. 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

7. 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

8. 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

9. To Add Mixed Fractions With Unlike Denominators
This number is also called
the least common denominator. 1 3 4
= 4, 8, 12, 16, 20, 24 1 1 +
= 10, 20, 30, 40, 50 10

10. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.
Ask yourself what
you multiply 4 by
to get 20. 1 3 4 20
x 5 = 1 1 + 10 20

11. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.
That’s right 5. Since
you are looking for
the equivalent fraction
you know the top
number must also be
multiplied by 5. 1
x 5 = 3 4 20
x 5 = 1 1 + 10 20

12. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. 1 5
x 5 =
To find the top number
just multiply 1 x 5 to
get your equivalent
fraction. 3 4 20
x 5 = 1 1 + 10 20

13. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator. 1 5
x 5 =
Now ask what you
multiply the 10 by
to get 20. 3 4 20
x 5 = 1 1 + 10 20
x 2 =

14. To Add Mixed Fractions With Unlike Denominators
Find the equivalent fractions for 1/4 & 1/10 with 20 as the denominator.
That’s right 2. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 2. 1 5
x 5 = 3 4 20
x 5 = 1 2
x 2 = 1 + 10 20
x 2 =

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

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

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

18. Add These Mixed Numbers
Now find the
equivalent
fractions for
1/3 & 1/6. 1 10 3 6
x 2 = 1 3 + 6
x 1 = 6
Ask what do you multiply 3 by to get 6
and what do you multiply 6 by to get 6.

19. 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
x 2 = 10 3 6
x 2 = 1
x 1 = 3 + 6
x 1 = 6

20. Add These Mixed Numbers1 2
Now multiply
across.
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 + 6
x 1 = 6

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

22. Add These Mixed Numbers1 2
Add your
whole
numbers.
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 + 6
x 1 = 6 3 13 6

23. Simplify Your Answer 3 ÷ 3 1 13 13 = 6 ÷ 3 2

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

25. 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
x 5 = 15

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

27. Add These Mixed Numbers
Multiply
across. 4 12
x 3 = 11 5 15
x 3 = 1 5
x 5 = 2 + 3
x 5 = 15

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

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

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

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

32. Your Final Answer Is 14 2/15 2 1 4 12
x 3 = 11 1 15 5 15
x 3 =
15) 17 1 5
x 5 = 2 15 + 3
x 5 = 15 2 2 17 14 15 15

33. Add These Mixed Numbers11 1 5 20
x 4 = 24 1 24 6 24
x 4 =
24) 35 5 15
x 3 = 3 24 + 8
x 3 = 24 11 11 35 28 24 24