Comparing And Ordering Rational Numbers Worksheets - Fill Online ... - Free Printable

It looks like you've uploaded a worksheet titled "Practice 5-1: Comparing and Ordering Rational Numbers" from the *Pre-Algebra* textbook (Chapter 5, Lesson 5-1). The worksheet includes problems involving comparing rational numbers using inequality symbols (<, >, =), simplifying expressions, and word problems.

Since I can't see the actual image directly, I will solve the problems based on the text you've provided. Let's go through each problem step by step.

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Problems 1–14: Compare using <, >, or =

We need to compare two rational numbers and fill in the correct symbol.

#### 1. $ \frac{1}{2} \quad ? \quad \frac{3}{4} $

Convert to common denominator:
- $ \frac{1}{2} = \frac{2}{4} $
- $ \frac{2}{4} < \frac{3}{4} $

✔ Answer: $ \frac{1}{2} < \frac{3}{4} $

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#### 2. $ \frac{2}{3} \quad ? \quad \frac{1}{6} $

Common denominator: 6
- $ \frac{2}{3} = \frac{4}{6} $
- $ \frac{4}{6} > \frac{1}{6} $

✔ Answer: $ \frac{2}{3} > \frac{1}{6} $

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#### 3. $ -\frac{1}{2} \quad ? \quad -\frac{1}{4} $

Negative numbers: the one closer to zero is greater.
- $ -\frac{1}{4} > -\frac{1}{2} $

So $ -\frac{1}{2} < -\frac{1}{4} $

✔ Answer: $ -\frac{1}{2} < -\frac{1}{4} $

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#### 4. $ \frac{5}{8} \quad ? \quad \frac{7}{12} $

Find LCD of 8 and 12 → 24
- $ \frac{5}{8} = \frac{15}{24} $
- $ \frac{7}{12} = \frac{14}{24} $
- $ \frac{15}{24} > \frac{14}{24} $

✔ Answer: $ \frac{5}{8} > \frac{7}{12} $

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#### 5. $ \frac{3}{5} \quad ? \quad \frac{4}{9} $

LCD of 5 and 9 → 45
- $ \frac{3}{5} = \frac{27}{45} $
- $ \frac{4}{9} = \frac{20}{45} $
- $ \frac{27}{45} > \frac{20}{45} $

✔ Answer: $ \frac{3}{5} > \frac{4}{9} $

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#### 6. $ \frac{1}{3} \quad ? \quad \frac{2}{5} $

LCD of 3 and 5 → 15
- $ \frac{1}{3} = \frac{5}{15} $
- $ \frac{2}{5} = \frac{6}{15} $
- $ \frac{5}{15} < \frac{6}{15} $

✔ Answer: $ \frac{1}{3} < \frac{2}{5} $

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#### 7. $ \frac{2}{3} \quad ? \quad \frac{3}{5} $

LCD of 3 and 5 → 15
- $ \frac{2}{3} = \frac{10}{15} $
- $ \frac{3}{5} = \frac{9}{15} $
- $ \frac{10}{15} > \frac{9}{15} $

✔ Answer: $ \frac{2}{3} > \frac{3}{5} $

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#### 8. $ \frac{1}{4} \quad ? \quad \frac{1}{5} $

Same numerator → larger denominator means smaller value
- $ \frac{1}{4} > \frac{1}{5} $

✔ Answer: $ \frac{1}{4} > \frac{1}{5} $

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#### 9. $ \frac{3}{4} \quad ? \quad -\frac{1}{4} $

Positive vs negative → positive is greater
- $ \frac{3}{4} > -\frac{1}{4} $

✔ Answer: $ \frac{3}{4} > -\frac{1}{4} $

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#### 10. $ \frac{1}{2} \quad ? \quad \frac{1}{3} $

$ \frac{1}{2} = 0.5 $, $ \frac{1}{3} \approx 0.333 $ → $ \frac{1}{2} > \frac{1}{3} $

✔ Answer: $ \frac{1}{2} > \frac{1}{3} $

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#### 11. $ \frac{1}{6} \quad ? \quad \frac{1}{8} $

Smaller denominator → larger fraction
- $ \frac{1}{6} > \frac{1}{8} $

✔ Answer: $ \frac{1}{6} > \frac{1}{8} $

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#### 12. $ \frac{1}{2} \quad ? \quad \frac{3}{4} $

As before: $ \frac{1}{2} = \frac{2}{4} < \frac{3}{4} $

✔ Answer: $ \frac{1}{2} < \frac{3}{4} $

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#### 13. $ \frac{1}{3} \quad ? \quad \frac{1}{4} $

$ \frac{1}{3} > \frac{1}{4} $

✔ Answer: $ \frac{1}{3} > \frac{1}{4} $

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#### 14. $ -\frac{1}{3} \quad ? \quad -\frac{1}{2} $

Compare negatives: $ -\frac{1}{3} > -\frac{1}{2} $ (since -0.333 > -0.5)

So $ -\frac{1}{3} > -\frac{1}{2} $

✔ Answer: $ -\frac{1}{3} > -\frac{1}{2} $

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Problems 15–21: Order from least to greatest

#### 15. $ 2, 2.1 $

Clearly: $ 2 < 2.1 $

✔ Answer: 2, 2.1

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#### 16. $ \frac{1}{2}, \frac{3}{4}, \frac{5}{8} $

Convert to decimals:
- $ \frac{1}{2} = 0.5 $
- $ \frac{5}{8} = 0.625 $
- $ \frac{3}{4} = 0.75 $

Order: $ 0.5 < 0.625 < 0.75 $

So: $ \frac{1}{2}, \frac{5}{8}, \frac{3}{4} $

✔ Answer: $ \frac{1}{2}, \frac{5}{8}, \frac{3}{4} $

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#### 17. $ 3.4, 3.5 $

$ 3.4 < 3.5 $

✔ Answer: 3.4, 3.5

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#### 18. $ 20 \div 7, 4.2 \div 7 $

First compute:
- $ 20 \div 7 \approx 2.857 $
- $ 4.2 \div 7 = 0.6 $

So: $ 0.6 < 2.857 $

Order: $ 4.2 \div 7, 20 \div 7 $

✔ Answer: $ 4.2 \div 7, 20 \div 7 $

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#### 19. $ 9, 7, 9, 3 $

Numbers: 9, 7, 9, 3

Ordered: 3, 7, 9, 9

✔ Answer: 3, 7, 9, 9

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#### 20. $ 9, 12, 16 $

Already increasing: 9, 12, 16

✔ Answer: 9, 12, 16

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#### 21. $ 1, 2, 3 $

Already in order

✔ Answer: 1, 2, 3

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Word Problems

#### 22. A quality control inspector checks every forty-eighth egg for cracks and every fifty-third egg for weight. What is the number of the first egg that she checks for both qualities?

We need the Least Common Multiple (LCM) of 48 and 53.

Check if they are coprime:
- 48 = $ 2^4 \times 3 $
- 53 is a prime number

No common factors → LCM = $ 48 \times 53 $

Calculate:
- $ 48 \times 50 = 2400 $
- $ 48 \times 3 = 144 $
- Total: $ 2400 + 144 = 2544 $

✔ Answer: 2544

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#### 23. A stack sold $ \frac{3}{4} $ inch of wood and $ \frac{1}{2} $ inch next. Did the value of the stock go up or down? Explain.

We need to compare $ \frac{3}{4} $ and $ \frac{1}{2} $

- $ \frac{3}{4} = 0.75 $
- $ \frac{1}{2} = 0.5 $

So $ \frac{3}{4} > \frac{1}{2} $

The stock went down because the second sale was smaller than the first.

✔ Answer: The value went down because $ \frac{1}{2} < \frac{3}{4} $.

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#### 24. Marina needs $ \frac{1}{2} $ yard of ribbon for a wall hanging. She wants to make 5 such hangings. Does she have enough ribbon? Explain.

She needs: $ 5 \times \frac{1}{2} = \frac{5}{2} = 2.5 $ yards

But the problem doesn't say how much ribbon she has. Wait — perhaps it’s implied?

Wait — actually, the original problem says:

> "Marina needs $ \frac{1}{2} $ yard of ribbon for a wall hanging... She wants to make 5 such hangings. Does she have enough ribbon?"

But no amount is given. Perhaps this is a typo or missing info?

Wait — looking back at your image description, maybe it's incomplete. But let's assume the question is asking whether she has enough — but without knowing how much she has, we can’t answer.

Wait — perhaps the ribbon amount is stated elsewhere? Since it's not here, maybe it's assumed she has some amount?

Alternatively, maybe it's just asking for total needed.

But the question says: "Does she have enough?" — so unless there's more context, we can't determine.

But perhaps in the image, it says something like “She has 2 yards” or similar.

Since it's not provided, let's suppose it's missing.

But maybe it's implied: perhaps the student is supposed to calculate total needed and conclude.

But without her current ribbon amount, we cannot say.

Wait — maybe it's a trick: perhaps she only has $ \frac{1}{2} $ yard?

But that would be insufficient.

Alternatively, maybe the problem is simply to compute total needed.

But the question is: “Does she have enough?” — so unless we know how much she has, we can’t answer.

Possibility: maybe the problem says she has 2 yards, which is common.

Let’s assume she has 2 yards.

Then:
- Needs: $ 5 \times \frac{1}{2} = 2.5 $ yards
- Has: 2 yards

So no, she does not have enough.

But since the amount isn't specified in your text, I’ll note:

⚠️ Problem 24 is incomplete as written. We need to know how much ribbon Marina has.

Assuming she has 2 yards, then:

- Needs: 2.5 yards → Not enough

✔ Answer: No, she does not have enough ribbon. She needs 2.5 yards but only has 2.

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#### 25. Order from least to greatest: $ \frac{1}{2}, \frac{1}{3}, \frac{1}{4} $

Convert:
- $ \frac{1}{2} = 0.5 $
- $ \frac{1}{3} \approx 0.333 $
- $ \frac{1}{4} = 0.25 $

So: $ \frac{1}{4} < \frac{1}{3} < \frac{1}{2} $

✔ Answer: $ \frac{1}{4}, \frac{1}{3}, \frac{1}{2} $

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#### 26. $ \frac{1}{2}, \frac{1}{4}, \frac{1}{8} $

These are decreasing fractions.

$ \frac{1}{8} = 0.125 $, $ \frac{1}{4} = 0.25 $, $ \frac{1}{2} = 0.5 $

So: $ \frac{1}{8} < \frac{1}{4} < \frac{1}{2} $

✔ Answer: $ \frac{1}{8}, \frac{1}{4}, \frac{1}{2} $

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#### 27. $ \frac{1}{2}, \frac{1}{3}, \frac{1}{6} $

Convert:
- $ \frac{1}{2} = 0.5 $
- $ \frac{1}{3} \approx 0.333 $
- $ \frac{1}{6} \approx 0.1667 $

Order: $ \frac{1}{6} < \frac{1}{3} < \frac{1}{2} $

✔ Answer: $ \frac{1}{6}, \frac{1}{3}, \frac{1}{2} $

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{1}{2} < \frac{3}{4} $ |
| 2 | $ \frac{2}{3} > \frac{1}{6} $ |
| 3 | $ -\frac{1}{2} < -\frac{1}{4} $ |
| 4 | $ \frac{5}{8} > \frac{7}{12} $ |
| 5 | $ \frac{3}{5} > \frac{4}{9} $ |
| 6 | $ \frac{1}{3} < \frac{2}{5} $ |
| 7 | $ \frac{2}{3} > \frac{3}{5} $ |
| 8 | $ \frac{1}{4} > \frac{1}{5} $ |
| 9 | $ \frac{3}{4} > -\frac{1}{4} $ |
| 10 | $ \frac{1}{2} > \frac{1}{3} $ |
| 11 | $ \frac{1}{6} > \frac{1}{8} $ |
| 12 | $ \frac{1}{2} < \frac{3}{4} $ |
| 13 | $ \frac{1}{3} > \frac{1}{4} $ |
| 14 | $ -\frac{1}{3} > -\frac{1}{2} $ |
| 15 | 2, 2.1 |
| 16 | $ \frac{1}{2}, \frac{5}{8}, \frac{3}{4} $ |
| 17 | 3.4, 3.5 |
| 18 | $ 4.2 \div 7, 20 \div 7 $ |
| 19 | 3, 7, 9, 9 |
| 20 | 9, 12, 16 |
| 21 | 1, 2, 3 |
| 22 | 2544 |
| 23 | The value went down because $ \frac{1}{2} < \frac{3}{4} $ |
| 24 | Incomplete – assuming she has 2 yards: No, not enough (needs 2.5) |
| 25 | $ \frac{1}{4}, \frac{1}{3}, \frac{1}{2} $ |
| 26 | $ \frac{1}{8}, \frac{1}{4}, \frac{1}{2} $ |
| 27 | $ \frac{1}{6}, \frac{1}{3}, \frac{1}{2} $ |

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If you can clarify Problem 24 with the amount of ribbon Marina has, I can adjust the answer accordingly.

Let me know if you'd like these answers formatted neatly for printing or submission!