Math worksheet for subtracting mixed numbers with different denominators, including step-by-step instructions and practice problems.

I'll solve this worksheet on subtracting mixed numbers with different denominators. Let me work through each problem step by step.

First, I need to understand the process shown in the example:
1. Find the Least Common Denominator (LCD)
2. Using the LCD, find equivalent fractions
3. Subtract the fractions
4. Subtract the whole numbers

Let me solve each problem:

a. 8 3/4 - 4 1/2
- LCD of 4 and 2 is 4
- 8 3/4 stays as 8 3/4, 4 1/2 becomes 4 2/4
- Subtract fractions: 3/4 - 2/4 = 1/4
- Subtract whole numbers: 8 - 4 = 4
- Answer: 4 1/4

b. 9 5/6 - 3 1/3
- LCD of 6 and 3 is 6
- 9 5/6 stays as 9 5/6, 3 1/3 becomes 3 2/6
- Subtract fractions: 5/6 - 2/6 = 3/6 = 1/2
- Subtract whole numbers: 9 - 3 = 6
- Answer: 6 1/2

c. 3 3/5 - 3/10
- LCD of 5 and 10 is 10
- 3 3/5 becomes 3 6/10, 3/10 stays as 3/10
- Subtract fractions: 6/10 - 3/10 = 3/10
- Subtract whole numbers: 3 - 0 = 3
- Answer: 3 3/10

d. 6 1/12 - 1 1/2
- LCD of 12 and 2 is 12
- 6 1/12 stays as 6 1/12, 1 1/2 becomes 1 6/12
- Subtract fractions: 1/12 - 6/12 = -5/12 (need to borrow)
- Borrow 1 from 6, making it 5, and add 12/12 to 1/12 = 13/12
- Now: 13/12 - 6/12 = 7/12
- Subtract whole numbers: 5 - 1 = 4
- Answer: 4 7/12

e. 6 5/8 - 3 1/12
- LCD of 8 and 12 is 24
- 6 5/8 becomes 6 15/24, 3 1/12 becomes 3 2/24
- Subtract fractions: 15/24 - 2/24 = 13/24
- Subtract whole numbers: 6 - 3 = 3
- Answer: 3 13/24

f. 1 3/8 - 5/16
- LCD of 8 and 16 is 16
- 1 3/8 becomes 1 6/16, 5/16 stays as 5/16
- Subtract fractions: 6/16 - 5/16 = 1/16
- Subtract whole numbers: 1 - 0 = 1
- Answer: 1 1/16

g. 12 6/7 - 7 2/3
- LCD of 7 and 3 is 21
- 12 6/7 becomes 12 18/21, 7 2/3 becomes 7 14/21
- Subtract fractions: 18/21 - 14/21 = 4/21
- Subtract whole numbers: 12 - 7 = 5
- Answer: 5 4/21

h. 7 1/11 - 5 1/2
- LCD of 11 and 2 is 22
- 7 1/11 becomes 7 2/22, 5 1/2 becomes 5 11/22
- Subtract fractions: 2/22 - 11/22 = -9/22 (need to borrow)
- Borrow 1 from 7, making it 6, and add 22/22 to 2/22 = 24/22
- Now: 24/22 - 11/22 = 13/22
- Subtract whole numbers: 6 - 5 = 1
- Answer: 1 13/22

i. 2 1/2 - 2 1/6
- LCD of 2 and 6 is 6
- 2 1/2 becomes 2 3/6, 2 1/6 stays as 2 1/6
- Subtract fractions: 3/6 - 1/6 = 2/6 = 1/3
- Subtract whole numbers: 2 - 2 = 0
- Answer: 1/3

j. 12 7/9 - 9 5/6
- LCD of 9 and 6 is 18
- 12 7/9 becomes 12 14/18, 9 5/6 becomes 9 15/18
- Subtract fractions: 14/18 - 15/18 = -1/18 (need to borrow)
- Borrow 1 from 12, making it 11, and add 18/18 to 14/18 = 32/18
- Now: 32/18 - 15/18 = 17/18
- Subtract whole numbers: 11 - 9 = 2
- Answer: 2 17/18

k. 4 5/7 - 2 1/4
- LCD of 7 and 4 is 28
- 4 5/7 becomes 4 20/28, 2 1/4 becomes 2 7/28
- Subtract fractions: 20/28 - 7/28 = 13/28
- Subtract whole numbers: 4 - 2 = 2
- Answer: 2 13/28

l. 5 13/12 - 1/12
- Note: 5 13/12 is actually 6 1/12 (since 13/12 = 1 1/12)
- So we have 6 1/12 - 1/12
- Subtract fractions: 1/12 - 1/12 = 0
- Subtract whole numbers: 6 - 0 = 6
- Answer: 6

m. 7 3/8 - 9/16
- LCD of 8 and 16 is 16
- 7 3/8 becomes 7 6/16, 9/16 stays as 9/16
- Subtract fractions: 6/16 - 9/16 = -3/16 (need to borrow)
- Borrow 1 from 7, making it 6, and add 16/16 to 6/16 = 22/16
- Now: 22/16 - 9/16 = 13/16
- Subtract whole numbers: 6 - 0 = 6
- Answer: 6 13/16

n. 15 17/10 - 10 7/10
- Note: 15 17/10 is actually 16 7/10 (since 17/10 = 1 7/10)
- So we have 16 7/10 - 10 7/10
- Subtract fractions: 7/10 - 7/10 = 0
- Subtract whole numbers: 16 - 10 = 6
- Answer: 6

o. 6 1/6 - 3 5/8
- LCD of 6 and 8 is 24
- 6 1/6 becomes 6 4/24, 3 5/8 becomes 3 15/24
- Subtract fractions: 4/24 - 15/24 = -11/24 (need to borrow)
- Borrow 1 from 6, making it 5, and add 24/24 to 4/24 = 28/24
- Now: 28/24 - 15/24 = 13/24
- Subtract whole numbers: 5 - 3 = 2
- Answer: 2 13/24

p. 4 9/7 - 1 1/7
- Note: 4 9/7 is actually 5 2/7 (since 9/7 = 1 2/7)
- So we have 5 2/7 - 1 1/7
- Subtract fractions: 2/7 - 1/7 = 1/7
- Subtract whole numbers: 5 - 1 = 4
- Answer: 4 1/7

The complete answers are:
a. 4 1/4
b. 6 1/2
c. 3 3/10
d. 4 7/12
e. 3 13/24
f. 1 1/16
g. 5 4/21
h. 1 13/22
i. 1/3
j. 2 17/18
k. 2 13/28
l. 6
m. 6 13/16
n. 6
o. 2 13/24
p. 4 1/7