Math worksheet for comparing mixed numbers, featuring 20 problems where students must choose the correct symbol to compare pairs of mixed numbers.

I will solve this worksheet by comparing each pair of mixed numbers and placing the correct symbol (>, <, or =) in the box between them. I'll go through each problem step-by-step.

The general strategy for comparing mixed numbers is:
1. Compare the whole number parts first.
2. If the whole numbers are equal, then compare the fractional parts.

Let's begin.

Problem 1: 2 3/5 vs. 4 2/3
- Whole numbers: 2 vs. 4. Since 2 < 4, we don't need to compare the fractions.
- Answer: 2 3/5 < 4 2/3

Problem 2: 3 1/2 vs. 2 1/6
- Whole numbers: 3 vs. 2. Since 3 > 2, we don't need to compare the fractions.
- Answer: 3 1/2 > 2 1/6

Problem 3: 4 1/2 vs. 1 2/3
- Whole numbers: 4 vs. 1. Since 4 > 1, we don't need to compare the fractions.
- Answer: 4 1/2 > 1 2/3

Problem 4: 3 1/3 vs. 2 2/4
- Whole numbers: 3 vs. 2. Since 3 > 2, we don't need to compare the fractions.
- Answer: 3 1/3 > 2 2/4

Problem 5: 3 1/5 vs. 6 2/5
- Whole numbers: 3 vs. 6. Since 3 < 6, we don't need to compare the fractions.
- Answer: 3 1/5 < 6 2/5

Problem 6: 3 6/2 vs. 4 3/5
- First, simplify 3 6/2. 6/2 = 3, so 3 6/2 = 3 + 3 = 6.
- Now compare 6 vs. 4 3/5. The whole number 6 is greater than 4.
- Answer: 3 6/2 > 4 3/5

Problem 7: 2 3/5 vs. 6 1/8
- Whole numbers: 2 vs. 6. Since 2 < 6, we don't need to compare the fractions.
- Answer: 2 3/5 < 6 1/8

Problem 8: 5 2/2 vs. 3 5/2
- Simplify both fractions.
- 5 2/2 = 5 + 1 = 6.
- 3 5/2 = 3 + 2 1/2 = 5 1/2.
- Now compare 6 vs. 5 1/2. Since 6 > 5 1/2.
- Answer: 5 2/2 > 3 5/2

Problem 9: 6 4/3 vs. 5 1/6
- Simplify 6 4/3. 4/3 = 1 1/3, so 6 4/3 = 6 + 1 1/3 = 7 1/3.
- Now compare 7 1/3 vs. 5 1/6. The whole number 7 is greater than 5.
- Answer: 6 4/3 > 5 1/6

Problem 10: 3 1/3 vs. 3 6/8
- Whole numbers are equal (both are 3), so we compare the fractions: 1/3 vs. 6/8.
- Find a common denominator. The LCM of 3 and 8 is 24.
- 1/3 = 8/24
- 6/8 = 18/24
- Since 8/24 < 18/24, 1/3 < 6/8.
- Answer: 3 1/3 < 3 6/8

Problem 11: 3 2/3 vs. 2 4/6
- Whole numbers: 3 vs. 2. Since 3 > 2, we don't need to compare the fractions.
- Answer: 3 2/3 > 2 4/6

Problem 12: 6 5/3 vs. 4 7/5
- Simplify both.
- 6 5/3 = 6 + 1 2/3 = 7 2/3.
- 4 7/5 = 4 + 1 2/5 = 5 2/5.
- Compare 7 2/3 vs. 5 2/5. The whole number 7 is greater than 5.
- Answer: 6 5/3 > 4 7/5

Problem 13: 9 2/6 vs. 6 6/3
- Simplify both.
- 9 2/6 = 9 1/3.
- 6 6/3 = 6 + 2 = 8.
- Compare 9 1/3 vs. 8. The whole number 9 is greater than 8.
- Answer: 9 2/6 > 6 6/3

Problem 14: 5 4/3 vs. 5 6/3
- Whole numbers are equal (both are 5), so we compare the fractions: 4/3 vs. 6/3.
- 4/3 = 1 1/3 and 6/3 = 2.
- Since 1 1/3 < 2, 4/3 < 6/3.
- Answer: 5 4/3 < 5 6/3

Problem 15: 3 2/6 vs. 2 5/7
- Whole numbers: 3 vs. 2. Since 3 > 2, we don't need to compare the fractions.
- Answer: 3 2/6 > 2 5/7

Problem 16: 6 6/6 vs. 7 5/6
- Simplify 6 6/6. 6/6 = 1, so 6 6/6 = 7.
- Now compare 7 vs. 7 5/6. Since 7 < 7 5/6.
- Answer: 6 6/6 < 7 5/6

Problem 17: 7 3/5 vs. 1 2/4
- Whole numbers: 7 vs. 1. Since 7 > 1, we don't need to compare the fractions.
- Answer: 7 3/5 > 1 2/4

Problem 18: 4 5/2 vs. 7 2/3
- Simplify 4 5/2. 5/2 = 2 1/2, so 4 5/2 = 6 1/2.
- Compare 6 1/2 vs. 7 2/3. The whole number 6 is less than 7.
- Answer: 4 5/2 < 7 2/3

Problem 19: 3 4/5 vs. 7 2/5
- Whole numbers: 3 vs. 7. Since 3 < 7, we don't need to compare the fractions.
- Answer: 3 4/5 < 7 2/5

Problem 20: 4 7/3 vs. 3 1/6
- Simplify 4 7/3. 7/3 = 2 1/3, so 4 7/3 = 6 1/3.
- Compare 6 1/3 vs. 3 1/6. The whole number 6 is greater than 3.
- Answer: 4 7/3 > 3 1/6

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Here is the completed worksheet with all the correct symbols filled in:

1) 2 3/5 < 4 2/3
2) 3 1/2 > 2 1/6
3) 4 1/2 > 1 2/3
4) 3 1/3 > 2 2/4
5) 3 1/5 < 6 2/5
6) 3 6/2 > 4 3/5
7) 2 3/5 < 6 1/8
8) 5 2/2 > 3 5/2
9) 6 4/3 > 5 1/6
10) 3 1/3 < 3 6/8
11) 3 2/3 > 2 4/6
12) 6 5/3 > 4 7/5
13) 9 2/6 > 6 6/3
14) 5 4/3 < 5 6/3
15) 3 2/6 > 2 5/7
16) 6 6/6 < 7 5/6
17) 7 3/5 > 1 2/4
18) 4 5/2 < 7 2/3
19) 3 4/5 < 7 2/5
20) 4 7/3 > 3 1/6