Math worksheet for comparing and ordering numbers with multiple practice problems.

Problem: Comparing and Ordering Numbers

The worksheet asks us to compare numbers using the symbols `<`, `>`, or `=` and then arrange sets of numbers in descending and ascending order. Let's solve each part step by step.

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#### Part 1: Compare the numbers using `<`, `>`, or `=`

1. 67,455 ______ 67,544
- Compare digit by digit:
- Thousands place: Both are 67.
- Hundreds place: Both are 4.
- Tens place: 5 (first number) < 4 (second number).
- Answer: \( 67,455 < 67,544 \)

2. 121,122 ______ 112,757
- Compare digit by digit:
- Hundred-thousands place: Both are 1.
- Ten-thousands place: 2 (first number) > 1 (second number).
- Answer: \( 121,122 > 112,757 \)

3. 64,940 ______ 63,000
- Compare digit by digit:
- Ten-thousands place: Both are 6.
- Thousands place: 4 (first number) > 3 (second number).
- Answer: \( 64,940 > 63,000 \)

4. 29,344 ______ 32,426
- Compare digit by digit:
- Ten-thousands place: Both are 0.
- Thousands place: 2 (first number) < 3 (second number).
- Answer: \( 29,344 < 32,426 \)

5. 750,655 ______ 751,993
- Compare digit by digit:
- Hundred-thousands place: Both are 7.
- Ten-thousands place: Both are 5.
- Thousands place: 0 (first number) < 1 (second number).
- Answer: \( 750,655 < 751,993 \)

6. 73,387 ______ 71,200
- Compare digit by digit:
- Ten-thousands place: Both are 0.
- Thousands place: 7 (both numbers).
- Hundreds place: 3 (first number) > 1 (second number).
- Answer: \( 73,387 > 71,200 \)

7. 56,437 ______ 56,437
- All digits are identical.
- Answer: \( 56,437 = 56,437 \)

8. 124,564 ______ 127,453
- Compare digit by digit:
- Hundred-thousands place: Both are 1.
- Ten-thousands place: Both are 2.
- Thousands place: 4 (first number) < 7 (second number).
- Answer: \( 124,564 < 127,453 \)

9. 65,001 ______ 650,001
- Compare digit by digit:
- Hundred-thousands place: 0 (first number) < 6 (second number).
- Answer: \( 65,001 < 650,001 \)

10. 39,756 ______ 39,756
- All digits are identical.
- Answer: \( 39,756 = 39,756 \)

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#### Part 2: Arrange the following in descending order

11. 56,861 | 43,121 | 10,888 | 84,201 | 37,334
- Compare the numbers:
- Largest: 84,201
- Next: 56,861
- Next: 43,121
- Next: 37,334
- Smallest: 10,888
- Answer: \( 84,201 > 56,861 > 43,121 > 37,334 > 10,888 \)

12. 423,114 | 912,454 | 342,090 | 260,711 | 339,821
- Compare the numbers:
- Largest: 912,454
- Next: 423,114
- Next: 342,090
- Next: 339,821
- Smallest: 260,711
- Answer: \( 912,454 > 423,114 > 342,090 > 339,821 > 260,711 \)

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#### Part 3: Arrange the following in ascending order

13. 88,121 | 23,904 | 65,110 | 20,670 | 45,332
- Compare the numbers:
- Smallest: 20,670
- Next: 23,904
- Next: 45,332
- Next: 65,110
- Largest: 88,121
- Answer: \( 20,670 < 23,904 < 45,332 < 65,110 < 88,121 \)

14. 674,980 | 710,095 | 421,453 | 311,301 | 548,000
- Compare the numbers:
- Smallest: 311,301
- Next: 421,453
- Next: 548,000
- Next: 674,980
- Largest: 710,095
- Answer: \( 311,301 < 421,453 < 548,000 < 674,980 < 710,095 \)

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Final Answers:

1. \( 67,455 < 67,544 \)
2. \( 121,122 > 112,757 \)
3. \( 64,940 > 63,000 \)
4. \( 29,344 < 32,426 \)
5. \( 750,655 < 751,993 \)
6. \( 73,387 > 71,200 \)
7. \( 56,437 = 56,437 \)
8. \( 124,564 < 127,453 \)
9. \( 65,001 < 650,001 \)
10. \( 39,756 = 39,756 \)

11. \( 84,201 > 56,861 > 43,121 > 37,334 > 10,888 \)
12. \( 912,454 > 423,114 > 342,090 > 339,821 > 260,711 \)

13. \( 20,670 < 23,904 < 45,332 < 65,110 < 88,121 \)
14. \( 311,301 < 421,453 < 548,000 < 674,980 < 710,095 \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. < \\
2. > \\
3. > \\
4. < \\
5. < \\
6. > \\
7. = \\
8. < \\
9. < \\
10. = \\
11. 84,201 > 56,861 > 43,121 > 37,334 > 10,888 \\
12. 912,454 > 423,114 > 342,090 > 339,821 > 260,711 \\
13. 20,670 < 23,904 < 45,332 < 65,110 < 88,121 \\
14. 311,301 < 421,453 < 548,000 < 674,980 < 710,095 \\
\end{array}
}
\]