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

2. Subtracting Mixed Numbers
To subtract mixed numbers, you must make sure the fractions have the same denominator, that’s the same bottom number. Find the lowest common multiple of the two denominators. That is the number you will use for the denominator in both fractions.

3. 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

4. To Subtract Mixed Numbers With Unlike Denominators
Find the multiples of each denominator. 1 3 4
= 4, 8, 12, 16, 20, 24 1 1 - 10
= 10, 20, 30, 40, 50

5. To Subtract Mixed Numbers 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 Subtract Mixed Numbers 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 Subtract Mixed Numbers 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

8. To Subtract Mixed Numberss 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

9. To Subtract Mixed Numbers 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

10. To Subtract Mixed Numberss 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

11. To Subtract Mixed Numbers 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 =

12. To Subtract Mixed Numbers 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 =

13. To Subtract Mixed Numbers With Unlike Denominators
Now just subtract the numerators. 1 5
x 5 = 3 4 20
x 5 = 1 2
x 2 =
Remember! We never subtract the denominators. 1 - 10 20
x 2 = 3 20

14. To Subtract Mixed Numbers With Unlike Denominators
Now subtract the whole numbers. 1 5
x 5 = 3 4 20
x 5 = 1 2
x 2 = 1 - 10 20
x 2 = 3 2 20

15. Subtract These Mixed Numbers
Use the short
cut to find the
Least Common
Denominator
(LCD). 1 10 3 6 1 3 - 6 6

16. Subtract 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.

17. Subtract 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

18. Subtract These Mixed Numbers1 2
Now multiply
across.
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 - 6
x 1 = 6

19. Subtract These Mixed Numbers1 2
Subtract your
new
numerators.
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 - 6
x 1 = 6 1 6

20. Subtract These Mixed Numbers1 2
Subtract your
whole
numbers.
x 2 = 10 3 6
x 2 = 1 1
x 1 = 3 - 6
x 1 = 6 1 7 6

21. Subtract These Mixed Numbers1 2
Your answer is:
x 2 = 10 3 6
x 2 = 1 1
x 1 = 1 3 - 6
x 1 = 6 7 6