8th Grade Common Core Math Worksheets - Free Printable

Let’s go through each problem one by one and solve them carefully.

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1. Use > or < to write a true sentence: 11 ___ 71

We know that 11 is less than 71.
So, we use <.

→ 11 < 71

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2. Compare: 105 ○ 406

105 is much smaller than 406.
So, 105 < 406 → put < in the circle.

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3. Which of the following is a true statement?

[A] 618 > 189 → True (618 is bigger)
[B] 981 < 967 → False (981 is bigger)
[C] 139 > 603 → False (139 is smaller)
[D] 808 < 486 → False (808 is bigger)

Only [A] is true.

→ Answer: [A]

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4. If you put the numbers 246, 248, 256, and 253 in order from smallest to largest, which number would be fourth?

Order them:

Smallest: 246
Then: 248
Then: 253
Largest (fourth): 256

→ Answer: [B] 256

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5. Order the numbers 519, 951, and 159 from least to greatest.

Least: 159
Middle: 519
Greatest: 951

So: 159, 519, 951

→ Answer: [B] 159, 519, 951

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6. Order the numbers 169, 961, and 619 from least to greatest.

Least: 169
Middle: 619
Greatest: 961

→ Answer: 169, 619, 961

*(Note: This question doesn’t have multiple choice — so just list them.)*

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7. Compare: 13,363 ○ 46,943

13 thousand vs 46 thousand → 13,363 is smaller.

→ Put < in the circle.

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8. Compare: -7 ○ -1

On the number line, -7 is to the left of -1 → so it’s smaller.

-7 < -1

→ Put < in the circle.

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9. Compare: -5 ○ -6

-5 is to the right of -6 on the number line → so -5 is greater.

-5 > -6

Options:
[A] not given
[B] >
[C] =
[D] <

→ Answer: [B] >

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10. Name a point between –3 and –4 on a number line.

Any number between -3 and -4 works. For example: -3.5

You could also say -3.1, -3.9, etc. But -3.5 is easy and clear.

→ Answer: -3.5 (or any decimal between -3 and -4)

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11. (a) Arrange these numbers in order from greatest to least: 0, 3, -3, 1/3

First, convert all to decimals if needed:

3 = 3.0
1/3 ≈ 0.333
0 = 0
-3 = -3.0

From greatest to least:
3, then 1/3, then 0, then -3

→ Answer: 3, 1/3, 0, -3

(b) List the numbers in part (a) that are not integers.

Integers: whole numbers (positive, negative, zero). So:

3 → integer
1/3 → NOT integer (it’s a fraction)
0 → integer
-3 → integer

Only 1/3 is not an integer.

→ Answer: 1/3

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12. If 23/8, 11/2, 9/6, and 15/7 are placed in order from least to greatest, which would be first?

Convert each to decimal:

23/8 = 2.875
11/2 = 5.5
9/6 = 1.5
15/7 ≈ 2.142...

Now order from least to greatest:

1.5 (9/6), then ~2.142 (15/7), then 2.875 (23/8), then 5.5 (11/2)

First (smallest) is 9/6

→ Answer: [A] 9/6

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13. Insert =, <, or > to make a true statement: -1/2 [?] -2/3

Convert to decimals:

-1/2 = -0.5
-2/3 ≈ -0.666...

On number line: -0.5 is to the RIGHT of -0.666 → so -0.5 is GREATER.

So: -1/2 > -2/3

→ Answer: >

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14. Which of the following is *not* a true statement?

[A] 32.18 = 32.1800000 → TRUE (adding zeros at end doesn’t change value)
[B] 24.30009 < 24.31 → TRUE (24.30009 is less than 24.31000)
[C] 32.7400 > 32.74 → FALSE! They are equal. Adding zeros after decimal doesn’t change value.
[D] 29.337 > 29.327 → TRUE (337 > 327 in thousandths place)

So [C] is NOT true.

→ Answer: [C]

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15. √355 and 6π — Which number is smaller? Show how you arrived at your answer.

Step 1: Estimate √355

We know:

18² = 324
19² = 361

So √355 is between 18 and 19.

Try 18.8² = ?

18.8 × 18.8 = (18 + 0.8)² = 18² + 2×18×0.8 + 0.8² = 324 + 28.8 + 0.64 = 353.44

Close! Try 18.85²:

18.85 × 18.85 ≈ let’s compute:

= (18.8 + 0.05)² = 18.8² + 2×18.8×0.05 + 0.05² = 353.44 + 1.88 + 0.0025 = 355.3225 → too big

So √355 ≈ 18.84 (since 18.84² = ? Let’s check roughly: 18.84 × 18.84)

Actually, better to use calculator-style estimate: since 18.8² = 353.44, and 355 - 353.44 = 1.56

Increment: derivative approx: d(x²)/dx = 2x → dx = dy/(2x) = 1.56 / (2×18.8) ≈ 1.56 / 37.6 ≈ 0.0415

So √355 ≈ 18.8 + 0.0415 ≈ 18.8415

Now 6π: π ≈ 3.1416 → 6 × 3.1416 = 18.8496

Compare:

√355 ≈ 18.8415
6π ≈ 18.8496

So √355 is slightly smaller.

→ Answer: √355 is smaller

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16. Use the three digits 2, 8, and 6 once each to make an even number less than 600.

Even number → must end with 2, 6, or 8.

Less than 600 → hundreds digit must be 2 or 6? Wait — if hundreds digit is 6, then number is 6xx → which is ≥ 600 → not allowed.

So hundreds digit must be 2.

Then remaining digits: 8 and 6.

We need even number → last digit must be even → both 8 and 6 are even, so either can be last.

Possible numbers:

Start with 2:

- 268 → ends with 8 → even → and 268 < 600 → OK
- 286 → ends with 6 → even → 286 < 600 → OK

Both work. We can pick either.

→ Answer: 268 (or 286)

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Final Answers compiled:

1. <
2. <
3. [A]
4. [B]
5. [B]
6. 169, 619, 961
7. <
8. <
9. [B]
10. -3.5 (example)
11(a). 3, 1/3, 0, -3
11(b). 1/3
12. [A]
13. >
14. [C]
15. √355 is smaller
16. 268 (or 286)

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Final Answer:
1. <
2. <
3. [A]
4. [B]
5. [B]
6. 169, 619, 961
7. <
8. <
9. [B]
10. -3.5
11(a). 3, 1/3, 0, -3
11(b). 1/3
12. [A]
13. >
14. [C]
15. √355 is smaller
16. 268