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, ordering them, and applying real-world scenarios.

Since I can't view images directly, I’ll solve the problems based on the text you provided. Let's go through each problem step by step and explain the solution.

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

We need to compare two rational numbers in each case.

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

Find a common denominator:
LCM of 4 and 3 is 12
$ \frac{3}{4} = \frac{9}{12},\quad \frac{2}{3} = \frac{8}{12} $
So, $ \frac{9}{12} > \frac{8}{12} $ → >

✔ Answer: $ \frac{3}{4} > \frac{2}{3} $

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#### 2. $ \frac{5}{6} \quad \boxed{?} \quad \frac{7}{8} $

LCM of 6 and 8 is 24
$ \frac{5}{6} = \frac{20}{24},\quad \frac{7}{8} = \frac{21}{24} $
$ \frac{20}{24} < \frac{21}{24} $ → <

✔ Answer: $ \frac{5}{6} < \frac{7}{8} $

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

Negative numbers: 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{1}{2} \quad \boxed{?} \quad \frac{3}{5} $

LCM of 2 and 5 is 10
$ \frac{1}{2} = \frac{5}{10},\quad \frac{3}{5} = \frac{6}{10} $
$ \frac{5}{10} < \frac{6}{10} $ → <

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

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

LCM of 3 and 4 is 12
$ \frac{1}{3} = \frac{4}{12},\quad \frac{1}{4} = \frac{3}{12} $
$ \frac{4}{12} > \frac{3}{12} $ → >

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

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

LCM of 5 and 7 is 35
$ \frac{2}{5} = \frac{14}{35},\quad \frac{3}{7} = \frac{15}{35} $
$ \frac{14}{35} < \frac{15}{35} $ → <

✔ Answer: $ \frac{2}{5} < \frac{3}{7} $

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#### 7. $ \frac{3}{8} \quad \boxed{?} \quad \frac{1}{2} $

$ \frac{1}{2} = \frac{4}{8} $, so $ \frac{3}{8} < \frac{4}{8} $ → <

✔ Answer: $ \frac{3}{8} < \frac{1}{2} $

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

LCM of 4 and 3 is 12
$ \frac{1}{4} = \frac{3}{12},\quad \frac{1}{3} = \frac{4}{12} $ → $ \frac{3}{12} < \frac{4}{12} $ → <

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

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

LCM of 3 and 4 is 12
$ \frac{2}{3} = \frac{8}{12},\quad \frac{3}{4} = \frac{9}{12} $ → $ \frac{8}{12} < \frac{9}{12} $ → <

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

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#### 10. $ \frac{1}{6} \quad \boxed{?} \quad \frac{1}{5} $

LCM of 6 and 5 is 30
$ \frac{1}{6} = \frac{5}{30},\quad \frac{1}{5} = \frac{6}{30} $ → $ \frac{5}{30} < \frac{6}{30} $ → <

✔ Answer: $ \frac{1}{6} < \frac{1}{5} $

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#### 11. $ \frac{3}{4} \quad \boxed{?} \quad \frac{5}{6} $

LCM of 4 and 6 is 12
$ \frac{3}{4} = \frac{9}{12},\quad \frac{5}{6} = \frac{10}{12} $ → $ \frac{9}{12} < \frac{10}{12} $ → <

✔ Answer: $ \frac{3}{4} < \frac{5}{6} $

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#### 12. $ \frac{7}{8} \quad \boxed{?} \quad \frac{3}{4} $

$ \frac{3}{4} = \frac{6}{8} $, so $ \frac{7}{8} > \frac{6}{8} $ → >

✔ Answer: $ \frac{7}{8} > \frac{3}{4} $

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

$ \frac{1}{2} = \frac{3}{6},\quad \frac{1}{3} = \frac{2}{6} $ → $ \frac{3}{6} > \frac{2}{6} $ → >

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

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

LCM of 3 and 5 is 15
$ \frac{2}{3} = \frac{10}{15},\quad \frac{3}{5} = \frac{9}{15} $ → $ \frac{10}{15} > \frac{9}{15} $ → >

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

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Problems 15–19: Order from least to greatest

#### 15. $ \frac{2}{3}, \frac{1}{2}, \frac{3}{4} $

Convert all to twelfths:
- $ \frac{2}{3} = \frac{8}{12} $
- $ \frac{1}{2} = \frac{6}{12} $
- $ \frac{3}{4} = \frac{9}{12} $

Order: $ \frac{6}{12}, \frac{8}{12}, \frac{9}{12} $ → $ \frac{1}{2}, \frac{2}{3}, \frac{3}{4} $

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

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#### 16. $ \frac{5}{6}, \frac{1}{3}, \frac{2}{3} $

Convert to sixths:
- $ \frac{5}{6} $
- $ \frac{1}{3} = \frac{2}{6} $
- $ \frac{2}{3} = \frac{4}{6} $

Order: $ \frac{2}{6}, \frac{4}{6}, \frac{5}{6} $ → $ \frac{1}{3}, \frac{2}{3}, \frac{5}{6} $

✔ Answer: $ \frac{1}{3}, \frac{2}{3}, \frac{5}{6} $

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

LCM of 4, 5, 8 = 40
- $ \frac{1}{4} = \frac{10}{40} $
- $ \frac{2}{5} = \frac{16}{40} $
- $ \frac{3}{8} = \frac{15}{40} $

Order: $ \frac{10}{40}, \frac{15}{40}, \frac{16}{40} $ → $ \frac{1}{4}, \frac{3}{8}, \frac{2}{5} $

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

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

Convert to eighths:
- $ \frac{1}{2} = \frac{4}{8} $
- $ \frac{3}{4} = \frac{6}{8} $
- $ \frac{1}{8} $

Order: $ \frac{1}{8}, \frac{4}{8}, \frac{6}{8} $ → $ \frac{1}{8}, \frac{1}{2}, \frac{3}{4} $

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

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#### 19. $ \frac{1}{3}, \frac{1}{4}, \frac{1}{2} $

LCM of 3, 4, 2 = 12
- $ \frac{1}{3} = \frac{4}{12} $
- $ \frac{1}{4} = \frac{3}{12} $
- $ \frac{1}{2} = \frac{6}{12} $

Order: $ \frac{3}{12}, \frac{4}{12}, \frac{6}{12} $ → $ \frac{1}{4}, \frac{1}{3}, \frac{1}{2} $

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

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Problems 20–21: Convert decimals to fractions and compare

#### 20. $ 20y^2 + 2y^2 $

This is an algebraic expression, not a comparison.

But likely typo — probably meant: Compare $ 20y^2 $ and $ 2y^2 $?

But since it's listed under "compare", maybe it's asking to simplify:

$ 20y^2 + 2y^2 = 22y^2 $

But if it's about comparing values, unless $ y $ is given, we can't say which is bigger.

Wait — looking at context, this seems out of place. Likely a formatting error.

Let’s skip for now.

#### 21. $ 9, 12, 16 $

These are whole numbers.

Order from least to greatest: $ 9, 12, 16 $

✔ Answer: $ 9, 12, 16 $

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Problem 22: Quality Control Inspector

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

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

- 48 = $ 2^4 \times 3 $
- 53 is prime

So LCM = $ 48 \times 53 = 2544 $

✔ Answer: 2544

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Problem 23: Stock Value Change

> A stock sold for $ \frac{3}{4} $ one day and $ \frac{1}{2} $ the next. Did the value of the stock go up or down? Explain.

Compare $ \frac{3}{4} $ and $ \frac{1}{2} $

$ \frac{1}{2} = \frac{2}{4} $, so $ \frac{3}{4} > \frac{2}{4} $

So the price went down from $ \frac{3}{4} $ to $ \frac{1}{2} $

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

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Problem 24: Martha's Cookies

> Martha needs $ \frac{1}{2} $ yard of ribbon for a wall hanging. She wants to make 3 such hangings. Does she have enough ribbon? Explain.

She needs $ 3 \times \frac{1}{2} = \frac{3}{2} = 1.5 $ yards

But she has only $ \frac{3}{4} $ yard

Compare: $ \frac{3}{4} = 0.75 $, $ 1.5 > 0.75 $

So no, she does not have enough.

✔ Answer: No, she needs $ 1.5 $ yards but only has $ 0.75 $ yards.

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Problems 25–27: Order from least to greatest

#### 25. $ \frac{1}{2}, \frac{1}{3}, \frac{1}{4} $

LCM of 2,3,4 = 12
- $ \frac{1}{2} = \frac{6}{12} $
- $ \frac{1}{3} = \frac{4}{12} $
- $ \frac{1}{4} = \frac{3}{12} $

Order: $ \frac{3}{12}, \frac{4}{12}, \frac{6}{12} $ → $ \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}{5}, \frac{1}{4}, \frac{1}{3} $

LCM of 5,4,3 = 60
- $ \frac{1}{5} = \frac{12}{60} $
- $ \frac{1}{4} = \frac{15}{60} $
- $ \frac{1}{3} = \frac{20}{60} $

Order: $ \frac{12}{60}, \frac{15}{60}, \frac{20}{60} $ → $ \frac{1}{5}, \frac{1}{4}, \frac{1}{3} $

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

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#### 27. $ \frac{1}{3}, \frac{1}{2}, \frac{1}{4} $

Same as #25: convert to twelfths
- $ \frac{1}{3} = \frac{4}{12} $
- $ \frac{1}{2} = \frac{6}{12} $
- $ \frac{1}{4} = \frac{3}{12} $

Order: $ \frac{3}{12}, \frac{4}{12}, \frac{6}{12} $ → $ \frac{1}{4}, \frac{1}{3}, \frac{1}{2} $

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

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ > $ |
| 2 | $ < $ |
| 3 | $ < $ |
| 4 | $ < $ |
| 5 | $ > $ |
| 6 | $ < $ |
| 7 | $ < $ |
| 8 | $ < $ |
| 9 | $ < $ |
| 10 | $ < $ |
| 11 | $ < $ |
| 12 | $ > $ |
| 13 | $ > $ |
| 14 | $ > $ |
| 15 | $ \frac{1}{2}, \frac{2}{3}, \frac{3}{4} $ |
| 16 | $ \frac{1}{3}, \frac{2}{3}, \frac{5}{6} $ |
| 17 | $ \frac{1}{4}, \frac{3}{8}, \frac{2}{5} $ |
| 18 | $ \frac{1}{8}, \frac{1}{2}, \frac{3}{4} $ |
| 19 | $ \frac{1}{4}, \frac{1}{3}, \frac{1}{2} $ |
| 20 | (Likely typo; possibly $ 22y^2 $) |
| 21 | $ 9, 12, 16 $ |
| 22 | 2544 |
| 23 | Down — $ \frac{1}{2} < \frac{3}{4} $ |
| 24 | No — needs $ 1.5 $ yards, has only $ 0.75 $ |
| 25 | $ \frac{1}{4}, \frac{1}{3}, \frac{1}{2} $ |
| 26 | $ \frac{1}{5}, \frac{1}{4}, \frac{1}{3} $ |
| 27 | $ \frac{1}{4}, \frac{1}{3}, \frac{1}{2} $ |

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