Let’s go through each part step by step to order the rational numbers from smallest to largest.
We’ll convert all numbers to decimals or compare them directly if they’re easy (like integers or simple fractions). Remember:
- Negative numbers are smaller than positive numbers.
- Absolute value |x| means “distance from zero” — so it’s always non-negative. For example, |-4| = 4, and |-0.5| = 0.5.
- Fractions like ½ = 0.5, ¾ = 0.75, etc.
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A) Numbers: 3, -2, |-4|, 1½
→ |-4| = 4
→ 1½ = 1.5
So we have: 3, -2, 4, 1.5
Order: -2, 1.5, 3, 4 → which is:
-2, 1½, 3, |-4|
✔ Matches given answer.
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B) Numbers: ¾, |-1|, 3, -2¼
→ |-1| = 1
→ -2¼ = -2.25
→ ¾ = 0.75
So: 0.75, 1, 3, -2.25
Order: -2.25, 0.75, 1, 3 →
-2¼, ¾, |-1|, 3
✔ Matches given answer.
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C) Numbers: 1.5, |2½|, -½, -1
→ |2½| = 2.5
→ -½ = -0.5
So: 1.5, 2.5, -0.5, -1
Order: -1, -0.5, 1.5, 2.5 →
-1, -½, 1.5, |2½|
✔ Matches given answer.
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D) Numbers: |-4|, 2½, -4.3, 0.8
→ |-4| = 4
→ 2½ = 2.5
So: 4, 2.5, -4.3, 0.8
Order: -4.3, 0.8, 2.5, 4 →
-4.3, 0.8, 2½, |-4|
✔ Matches given answer.
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E) Numbers: ¼, 0.8, |-1|, -1½, 1.3
→ ¼ = 0.25
→ |-1| = 1
→ -1½ = -1.5
So: 0.25, 0.8, 1, -1.5, 1.3
Order: -1.5, 0.25, 0.8, 1, 1.3 →
-1½, ¼, 0.8, |-1|, 1.3
✔ Matches given answer.
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F) Numbers: -2, |-0.5|, -1⅓, ¾, -2.5
→ |-0.5| = 0.5
→ -1⅓ ≈ -1.333...
→ ¾ = 0.75
→ -2.5 is already decimal
So: -2, 0.5, -1.333..., 0.75, -2.5
Order: -2.5, -2, -1.333..., 0.5, 0.75 →
-2.5, -2, -1⅓, |-0.5|, ¾
✔ Matches given answer.
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G) Numbers: 0.3, ½, |0.9|, -1½, -¾
→ ½ = 0.5
→ |0.9| = 0.9
→ -1½ = -1.5
→ -¾ = -0.75
So: 0.3, 0.5, 0.9, -1.5, -0.75
Order: -1.5, -0.75, 0.3, 0.5, 0.9 →
-1½, -¾, 0.3, ½, |0.9|
✔ Matches given answer.
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All answers provided in the sheet are correct.
Final Answer:
The ordered lists from smallest to largest are as shown in the answer key for parts A through G. All solutions are verified correct.
Parent Tip: Review the logic above to help your child master the concept of ordering rational numbers worksheet with answers.
