Math worksheet for comparing rational numbers, featuring problems involving fractions, decimals, and absolute values.

Let's solve each problem step by step using the rules of comparing rational numbers, including absolute values, fractions, decimals, and operations.

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Part 1: Comparing Rational Numbers (1–30)

We'll use >, <, or = to compare each pair.

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1) $ \frac{2}{3} > \frac{3}{5} $
✔ Already done.
Convert both to decimals:
$ \frac{2}{3} \approx 0.666 $, $ \frac{3}{5} = 0.6 $ → $ 0.666 > 0.6 $

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2) $ -\frac{2}{3} \quad ? \quad -\frac{2}{5} $
Compare negative numbers: the one with the larger absolute value is smaller.
$ |-\frac{2}{3}| = \frac{2}{3} \approx 0.666 $, $ |-\frac{2}{5}| = 0.4 $ → $ -\frac{2}{3} < -\frac{2}{5} $
✔ Answer: <

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3) $ |-2.3| \quad ? \quad -2.8 $
$ |-2.3| = 2.3 $, and $ -2.8 $ is negative.
Positive > negative → $ 2.3 > -2.8 $
✔ Answer: >

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4) $ -0.7 \quad ? \quad -0.65 $
Both negative. Compare absolute values:
$ 0.7 > 0.65 $ → so $ -0.7 < -0.65 $
✔ Answer: <

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5) $ \frac{3}{4} \quad ? \quad |-0.8| $
$ \frac{3}{4} = 0.75 $, $ |-0.8| = 0.8 $ → $ 0.75 < 0.8 $
✔ Answer: <

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6) $ \frac{1}{8} \quad ? \quad \frac{1}{9} $
Same numerator, smaller denominator → larger fraction.
$ \frac{1}{8} > \frac{1}{9} $
✔ Answer: >

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7) $ -1\frac{1}{4} \quad ? \quad -1.75 $
Convert mixed number: $ -1\frac{1}{4} = -1.25 $
Compare: $ -1.25 > -1.75 $ (since less negative)
✔ Answer: >

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8) $ -\frac{5}{2} \quad ? \quad -3 $
$ -\frac{5}{2} = -2.5 $, $ -3 = -3 $ → $ -2.5 > -3 $
✔ Answer: >

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9) $ |-0.6| \quad ? \quad |-0.55| $
$ |-0.6| = 0.6 $, $ |-0.55| = 0.55 $ → $ 0.6 > 0.55 $
✔ Answer: >

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10) $ \frac{3}{4} \quad ? \quad |-\frac{3}{5}| $
$ \frac{3}{4} = 0.75 $, $ |-\frac{3}{5}| = \frac{3}{5} = 0.6 $ → $ 0.75 > 0.6 $
✔ Answer: >

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11) $ -\frac{3}{4} \quad ? \quad -\frac{3}{5} $
Both negative. Absolute values:
$ \frac{3}{4} = 0.75 $, $ \frac{3}{5} = 0.6 $ → $ -\frac{3}{4} < -\frac{3}{5} $
✔ Answer: <

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12) $ |-4\frac{1}{2}| \quad ? \quad \frac{9}{2} $
$ |-4\frac{1}{2}| = 4.5 $, $ \frac{9}{2} = 4.5 $ → equal
✔ Answer: =

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13) $ \frac{7}{4} \quad ? \quad \frac{3}{2} $
$ \frac{7}{4} = 1.75 $, $ \frac{3}{2} = 1.5 $ → $ 1.75 > 1.5 $
✔ Answer: >

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14) $ |0.82| \quad ? \quad -0.9 $
$ |0.82| = 0.82 $, positive vs negative → $ 0.82 > -0.9 $
✔ Answer: >

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15) $ \frac{1}{8} \quad ? \quad 0.375 $
$ \frac{1}{8} = 0.125 $, $ 0.375 $ → $ 0.125 < 0.375 $
✔ Answer: <

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16) $ -0.27 \quad ? \quad -0.5 $
Both negative. $ 0.27 < 0.5 $ → so $ -0.27 > -0.5 $
✔ Answer: >

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17) $ 1\frac{2}{3} \quad ? \quad \frac{8}{2} $
$ 1\frac{2}{3} = \frac{5}{3} \approx 1.666 $, $ \frac{8}{2} = 4 $ → $ 1.666 < 4 $
✔ Answer: <

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18) $ |-2.3| \quad ? \quad |-5/2| $
$ |-2.3| = 2.3 $, $ |-5/2| = 2.5 $ → $ 2.3 < 2.5 $
✔ Answer: <

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19) $ -0.36 \quad ? \quad -0.2 $
Both negative. $ 0.36 > 0.2 $ → $ -0.36 < -0.2 $
✔ Answer: <

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20) $ \frac{1}{4} \quad ? \quad \frac{5}{20} $
$ \frac{5}{20} = \frac{1}{4} $ → equal
✔ Answer: =

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21) $ -\frac{2}{5} \quad ? \quad -\frac{3}{5} $
Both negative. $ \frac{2}{5} < \frac{3}{5} $ → $ -\frac{2}{5} > -\frac{3}{5} $
✔ Answer: >

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22) $ |-5/3| \quad ? \quad |-3/2| $
$ |-5/3| = \frac{5}{3} \approx 1.666 $, $ |-3/2| = 1.5 $ → $ 1.666 > 1.5 $
✔ Answer: >

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23) $ 2\frac{1}{3} \quad ? \quad \frac{7}{3} $
$ 2\frac{1}{3} = \frac{7}{3} $ → equal
✔ Answer: =

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24) $ |-5\frac{1}{4}| \quad ? \quad -5.5 $
$ |-5\frac{1}{4}| = 5.25 $, $ -5.5 $ → positive > negative → $ 5.25 > -5.5 $
✔ Answer: >

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25) $ |0.62| \quad ? \quad |-0.7| $
$ |0.62| = 0.62 $, $ |-0.7| = 0.7 $ → $ 0.62 < 0.7 $
✔ Answer: <

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26) $ -\frac{3}{8} \quad ? \quad -\frac{3}{10} $
Both negative. Compare absolute values:
$ \frac{3}{8} = 0.375 $, $ \frac{3}{10} = 0.3 $ → $ 0.375 > 0.3 $ → $ -\frac{3}{8} < -\frac{3}{10} $
✔ Answer: <

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27) $ |-3\frac{1}{4}| \quad ? \quad \frac{15}{4} $
$ |-3\frac{1}{4}| = 3.25 $, $ \frac{15}{4} = 3.75 $ → $ 3.25 < 3.75 $
✔ Answer: <

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28) $ |-0.9| \quad ? \quad \frac{3}{3} $
$ |-0.9| = 0.9 $, $ \frac{3}{3} = 1 $ → $ 0.9 < 1 $
✔ Answer: <

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29) $ -1\frac{1}{4} \quad ? \quad -1\frac{1}{5} $
$ -1\frac{1}{4} = -1.25 $, $ -1\frac{1}{5} = -1.2 $ → $ -1.25 < -1.2 $
✔ Answer: <

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30) $ |-1\frac{5}{6}| \quad ? \quad \frac{11}{6} $
$ |-1\frac{5}{6}| = 1\frac{5}{6} = \frac{11}{6} $ → equal
✔ Answer: =

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Part 2: Compare these amounts (31–40)

Now evaluate expressions on both sides.

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31) $ 2 - \frac{1}{4} \quad ? \quad \frac{1}{2} \times 3 $
Left: $ 2 - 0.25 = 1.75 $
Right: $ 0.5 \times 3 = 1.5 $ → $ 1.75 > 1.5 $
✔ Answer: >

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32) $ |4 - 12| \quad ? \quad 2^3 $
Left: $ |-8| = 8 $
Right: $ 2^3 = 8 $ → equal
✔ Answer: =

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33) $ |-4| \times |-3| \quad ? \quad |-2 - 9| $
Left: $ 4 \times 3 = 12 $
Right: $ |-11| = 11 $ → $ 12 > 11 $
✔ Answer: >

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34) $ \frac{2}{3} + \frac{2}{3} \quad ? \quad 2 - \frac{1}{4} $
Left: $ \frac{4}{3} \approx 1.333 $
Right: $ 1.75 $ → $ 1.333 < 1.75 $
✔ Answer: <

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35) $ |2 - 3\frac{1}{2}| \quad ? \quad \frac{3}{2} $
$ 2 - 3.5 = -1.5 $, $ |-1.5| = 1.5 $, $ \frac{3}{2} = 1.5 $ → equal
✔ Answer: =

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36) $ \frac{13}{4} \quad ? \quad |1\frac{1}{2} - 5| $
Left: $ \frac{13}{4} = 3.25 $
Right: $ |1.5 - 5| = |-3.5| = 3.5 $ → $ 3.25 < 3.5 $
✔ Answer: <

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37) $ |-0.7| \quad ? \quad \frac{1}{2} + \frac{1}{4} $
Left: $ 0.7 $
Right: $ 0.5 + 0.25 = 0.75 $ → $ 0.7 < 0.75 $
✔ Answer: <

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38) $ 1 - 0.06 \quad ? \quad 0.85 $
Left: $ 0.94 $ → $ 0.94 > 0.85 $
✔ Answer: >

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39) $ 5 \times |-0.4| \quad ? \quad |9 - 11| $
Left: $ 5 \times 0.4 = 2 $
Right: $ |-2| = 2 $ → equal
✔ Answer: =

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40) $ 1 - \frac{3}{6} \quad ? \quad |\frac{1}{2} - 1| $
Left: $ 1 - 0.5 = 0.5 $
Right: $ |-0.5| = 0.5 $ → equal
✔ Answer: =

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✔ Final Answers:

#### Part 1:
1) >
2) <
3) >
4) <
5) <
6) >
7) >
8) >
9) >
10) >
11) <
12) =
13) >
14) >
15) <
16) >
17) <
18) <
19) <
20) =
21) >
22) >
23) =
24) >
25) <
26) <
27) <
28) <
29) <
30) =

#### Part 2:
31) >
32) =
33) >
34) <
35) =
36) <
37) <
38) >
39) =
40) =

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Let me know if you'd like this in a printable format or need explanations for any specific question!