6th Grade Math Review Quiz on Decimal Patterns and Estimating Quotients

It looks like you've uploaded a math worksheet titled "Review Quiz, Lesson 6.1: Patterns For Dividing With Decimals" and "Review Quiz, Lesson 6.2: Estimate Decimal Quotients", but I can't see the actual image or its content. However, based on your description and the visible text in your message, I can help solve the problems listed.

Let me walk through both sections of the quiz step by step, solving each problem and explaining the reasoning.

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Part 1: Review Quiz, Lesson 6.1 – Patterns for Dividing With Decimals

Instructions: Divide each quotient by using patterns and mental math to divide.

We'll use the pattern that dividing by powers of 10 moves the decimal point to the left.

#### Problem Set A:
1. 136.5 ÷ 10 = ?
- Move decimal one place left → 13.65

2. 136.5 ÷ 100 = ?
- Move decimal two places left → 1.365

3. 136.5 ÷ 1000 = ?
- Move decimal three places left → 0.1365

4. 136.5 ÷ 10000 = ?
- Move decimal four places left → 0.01365

#### Problem Set B:
5. 85.25 ÷ 100 = ?
- Move decimal two places left → 0.8525

6. 85.25 ÷ 1000 = ?
- Move decimal three places left → 0.08525

7. 85.25 ÷ 10 = ?
- Move decimal one place left → 8.525

8. 85.25 ÷ 10000 = ?
- Move decimal four places left → 0.008525

#### Problem Set C:
9. 28966 ÷ 10 = ?
- Move decimal one place left → 2896.6

10. 28966 ÷ 100 = ?
- Move decimal two places left → 289.66

11. 28966 ÷ 1000 = ?
- Move decimal three places left → 28.966

12. 28966 ÷ 10000 = ?
- Move decimal four places left → 2.8966

13. 28966 ÷ 100000 = ?
- Move decimal five places left → 0.28966

14. 28966 ÷ 1000000 = ?
- Move decimal six places left → 0.028966

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#### Question 7:
> Any number to the power of 0 gives you an answer of ________.

✔ Answer: 1

Any non-zero number raised to the power of 0 is 1.

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#### Question 8:
> When dividing by a power of ten, we always move the decimal to the ________.

✔ Answer: left

Because dividing by 10, 100, 1000, etc., makes the number smaller.

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Part 2: Review Quiz, Lesson 6.2 – Estimate Decimal Quotients

Instructions: Use estimation to find the quotient.

We’ll round the numbers to make division easier.

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1. 45.73 ÷ 6.92 ≈ ?

- Round 45.73 → 46
- Round 6.92 → 7
- 46 ÷ 7 ≈ 6.57 → Estimate: 7

But let’s do it simply:
46 ÷ 7 ≈ 6.6 → Rounded estimate: 7

✔ Estimate: 7

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2. 711.17 ÷ 79.2 ≈ ?

- Round 711.17 → 710
- Round 79.2 → 80
- 710 ÷ 80 = 71 ÷ 8 = 8.875 → Estimate: 9

✔ Estimate: 9

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3. 556.4 ÷ 14.9 ≈ ?

- Round 556.4 → 560
- Round 14.9 → 15
- 560 ÷ 15 = 37.33... → Estimate: 37

✔ Estimate: 37

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4. 13.31 ÷ 7.57 ≈ ?

- Round 13.31 → 13
- Round 7.57 → 8
- 13 ÷ 8 = 1.625 → Estimate: 1.6

✔ Estimate: 1.6

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5. 82.89 ÷ 7.6 ≈ ?

- Round 82.89 → 83
- Round 7.6 → 8
- 83 ÷ 8 = 10.375 → Estimate: 10

✔ Estimate: 10

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6. 996.11 ÷ 7.82 ≈ ?

- Round 996.11 → 1000
- Round 7.82 → 8
- 1000 ÷ 8 = 125

✔ Estimate: 125

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✔ Final Answers:

#### Lesson 6.1 – Patterns for Dividing with Decimals

1. 13.65
2. 1.365
3. 0.1365
4. 0.01365
5. 0.8525
6. 0.08525
7. 8.525
8. 0.008525
9. 2896.6
10. 289.66
11. 28.966
12. 2.8966
13. 0.28966
14. 0.028966

Q7: 1
Q8: left

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#### Lesson 6.2 – Estimate Decimal Quotients

1. 7
2. 9
3. 37
4. 1.6
5. 10
6. 125

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