Comparing Rational Numbers Worksheet | Fun and Engaging 6th Grade ... - Free Printable

Let’s work through each section step by step.

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Section A: Using a number line

1) We are given integers:
-2, 4, -7, 1, 3, -4, 8, -6, -1, 2, -3

We need to place them on the number line centered at 0.
Remember: Negative numbers go left of 0, positive numbers go right.

Sorted order from smallest to largest:
-7, -6, -4, -3, -2, -1, 0 (already marked), 1, 2, 3, 4, 8

So on the number line (assuming equal spacing and enough marks):

Left side (negative):
-7, -6, -4, -3, -2, -1
Right side (positive):
1, 2, 3, 4, 8

(You’d draw dots or write numbers in correct positions — but since we’re not drawing here, just knowing their order is enough for part 2.)

2) Now compare pairs using < or >.

Recall: The open side of the symbol faces the larger number. Like an alligator mouth eating the bigger number!

Let’s do each pair:

First column:
- -2 vs 4 → -2 is less than 4 → -2 < 4
- -7 vs 1 → -7 is less than 1 → -7 < 1
- 3 vs -4 → 3 is greater than -4 → 3 > -4

Second column:
- 8 vs -6 → 8 is greater → 8 > -6
- -1 vs 2 → -1 is less → -1 < 2
- 4 vs -3 → 4 is greater → 4 > -3

Third column:
- -8 vs -4 → Both negative; -8 is farther left → smaller → -8 < -4
- -6 vs -7 → -6 is to the right of -7 → so -6 is greater → -6 > -7
- -3 vs -1 → -3 is left of -1 → smaller → -3 < -1

✔ All checked.

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Section B: Compare integers without number line

Same idea — remember negatives get smaller as they go more negative.

First row:
- -10 vs -7 → -10 is smaller → -10 < -7
- -7 vs -17 → -7 is bigger → -7 > -17
- -169 vs -254 → -169 is closer to zero → bigger → -169 > -254

Second row:
- -10 vs 7 → negative vs positive → -10 < 7
- -170 vs 17 → same → -170 < 17
- -583 vs -599 → -583 is bigger (less negative) → -583 > -599

Third row:
- -10 vs -17 → -10 is bigger → -10 > -17
- 215 vs -649 → positive vs negative → 215 > -649
- -338 vs -180 → -338 is more negative → smaller → -338 < -180

✔ All verified.

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Section C: Compare decimals

Same rules apply — especially with negatives.

First column:
- 2.5 vs 1.5 → 2.5 is bigger → 2.5 > 1.5
- -4.2 vs 3.6 → negative vs positive → -4.2 < 3.6
- -3.5 vs -1.1 → both negative; -3.5 is farther left → smaller → -3.5 < -1.1

Second column:
- -4.9 vs -5.3 → -4.9 is closer to zero → bigger → -4.9 > -5.3
- -2.1 vs -2.4 → -2.1 is to the right → bigger → -2.1 > -2.4
- -8.9 vs -8.8 → -8.9 is more negative → smaller → -8.9 < -8.8

✔ All correct.

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Final Answer:
Section A2:
-2 < 4, -7 < 1, 3 > -4
8 > -6, -1 < 2, 4 > -3
-8 < -4, -6 > -7, -3 < -1

Section B:
-10 < -7, -7 > -17, -169 > -254
-10 < 7, -170 < 17, -583 > -599
-10 > -17, 215 > -649, -338 < -180

Section C:
2.5 > 1.5, -4.2 < 3.6, -3.5 < -1.1
-4.9 > -5.3, -2.1 > -2.4, -8.9 < -8.8