4th Grade Multiples Worksheet: Practice finding multiples and solving related word problems.

Let's solve each problem step by step and explain the reasoning.

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1) Find two multiples of 6 between 40 and 50.

Step: List multiples of 6:
- 6, 12, 18, 24, 30, 36, 42, 48, 54, ...

Now find which ones are between 40 and 50:
- 42 and 48

✔ Answer: 42 and 48

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2) Circle the numbers below that are multiples of 30.

List:
50, 140, 200, 120, 210, 130, 270

Check which are divisible by 30:

- 50 ÷ 30 = 1.66... → ✘
- 140 ÷ 30 ≈ 4.66 → ✘
- 200 ÷ 30 ≈ 6.66 → ✘
- 120 ÷ 30 = 4 → ✔
- 210 ÷ 30 = 7 → ✔
- 130 ÷ 30 ≈ 4.33 → ✘
- 270 ÷ 30 = 9 → ✔

✔ Circle: 120, 210, 270

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3) Find two multiples of 8 between 60 and 75.

List multiples of 8:
- 8, 16, 24, 32, 40, 48, 56, 64, 72, 80...

Between 60 and 75:
- 64 and 72

✔ Answer: 64 and 72

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4) Circle the numbers below that are multiples of 40

List:
60, 160, 350, 140, 200, 320, 300, 420

Check divisibility by 40:

- 60 ÷ 40 = 1.5 → ✘
- 160 ÷ 40 = 4 → ✔
- 350 ÷ 40 = 8.75 → ✘
- 140 ÷ 40 = 3.5 → ✘
- 200 ÷ 40 = 5 → ✔
- 320 ÷ 40 = 8 → ✔
- 300 ÷ 40 = 7.5 → ✘
- 420 ÷ 40 = 10.5 → ✘

✔ Circle: 160, 200, 320

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5) Fill in the table:

| Number | Multiple of 30 | Multiple of 70 |
|--------|----------------|----------------|
| 150 | Yes | No |
| 140 | | |
| 200 | | |
| 120 | | |
| 210 | | |
| 350 | | |
| 420 | | |

Now check each:

#### 140:
- 140 ÷ 30 ≈ 4.66 → ✘ (not multiple of 30)
- 140 ÷ 70 = 2 → ✔ (multiple of 70)

→ No, Yes

#### 200:
- 200 ÷ 30 ≈ 6.66 → ✘
- 200 ÷ 70 ≈ 2.85 → ✘

→ No, No

#### 120:
- 120 ÷ 30 = 4 → ✔
- 120 ÷ 70 ≈ 1.71 → ✘

→ Yes, No

#### 210:
- 210 ÷ 30 = 7 → ✔
- 210 ÷ 70 = 3 → ✔

→ Yes, Yes

#### 350:
- 350 ÷ 30 ≈ 11.66 → ✘
- 350 ÷ 70 = 5 → ✔

→ No, Yes

#### 420:
- 420 ÷ 30 = 14 → ✔
- 420 ÷ 70 = 6 → ✔

→ Yes, Yes

✔ Final Table:

| Number | Multiple of 30 | Multiple of 70 |
|--------|----------------|----------------|
| 150 | Yes | No |
| 140 | No | Yes |
| 200 | No | No |
| 120 | Yes | No |
| 210 | Yes | Yes |
| 350 | No | Yes |
| 420 | Yes | Yes |

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6) I am a multiple of 70. I am between 300 and 500. I am 20 more than a multiple of 100. Who am I?

Let’s break it down:

- Multiples of 70 between 300 and 500:
- 70×4 = 280 → too small
- 70×5 = 350 → ✔
- 70×6 = 420 → ✔
- 70×7 = 490 → ✔
- 70×8 = 560 → too big

So possible: 350, 420, 490

Now, “I am 20 more than a multiple of 100”

So:
- 20 more than 300 = 320 → not in list
- 20 more than 400 = 420 → ✔ yes!
- 20 more than 500 = 520 → too big

So only 420 fits.

✔ Answer: 420

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7) I am a multiple of 60. I am between 400 and 600. I am 40 away from a multiple of 100. Who am I?

First: multiples of 60 between 400 and 600:

- 60×7 = 420
- 60×8 = 480
- 60×9 = 540
- 60×10 = 600 → but 600 is not less than 600, so exclude if "between" means exclusive

So: 420, 480, 540

Now, “I am 40 away from a multiple of 100” → meaning:
- The number is either 40 more or 40 less than a multiple of 100.

Check each:

#### 420:
- 420 - 40 = 380 → not multiple of 100
- 420 + 40 = 460 → not multiple of 100
- Closest multiples: 400, 500 → 420 - 400 = 20 ≠ 40 → ✘

#### 480:
- 480 - 40 = 440 → not multiple of 100
- 480 + 40 = 520 → no
- 480 - 400 = 80 → no
- 500 - 480 = 20 → no → ✘

#### 540:
- 540 - 40 = 500 → ✔ (500 is a multiple of 100!)
- 540 + 40 = 580 → not multiple of 100

So 540 is 40 more than 500 → 500 + 40 = 540 → ✔

Also, 540 is a multiple of 60: 60 × 9 = 540 → ✔

And between 400 and 600 → ✔

✔ Answer: 540

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✔ Final Answers:

1) 42 and 48
2) Circle: 120, 210, 270
3) 64 and 72
4) Circle: 160, 200, 320
5) Table filled as above
6) 420
7) 540

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