Estimating Quotients worksheet with division problems and examples.

Let's solve each problem on the worksheet "Estimating Quotients" step by step. The goal is to estimate the quotient by using compatible numbers (numbers that are close to the actual dividend and easily divisible by the divisor). We’ll follow the instructions: list three division statements with the same divisor, find which dividend is closest to the original, and then estimate the quotient.

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Problem 1: 15 ÷ 7 = ?

Step 1: List three division statements using the same divisor (7):

- 7 ÷ 7 = 1
- 14 ÷ 7 = 2
- 21 ÷ 7 = 3

Step 2: Which dividend is closest to 15?

- 14 is closer to 15 than 7 or 21.
- So, 14 ÷ 7 = 2 is the best estimate.

✔ Answer: So, 15 ÷ 7 is about 2

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Problem 2: 28 ÷ 5 = ?

Step 1: List three division statements using the same divisor (5):

- 5 ÷ 5 = 1
- 10 ÷ 5 = 2
- 15 ÷ 5 = 3
- 20 ÷ 5 = 4
- 25 ÷ 5 = 5
- 30 ÷ 5 = 6

We need three statements. Let’s pick:

- 20 ÷ 5 = 4
- 25 ÷ 5 = 5
- 30 ÷ 5 = 6

(Alternatively, you could use 15, 20, 25 — but since 28 is near 25 or 30, better to include those.)

But let's pick:
- 20 ÷ 5 = 4
- 25 ÷ 5 = 5
- 30 ÷ 5 = 6

Step 2: Which dividend is closest to 28?

- 25 is 3 away from 28
- 30 is 2 away from 28 → so 30 is closer

Wait! Actually:
- 28 - 25 = 3
- 30 - 28 = 2 → so 30 is closer

So, 30 ÷ 5 = 6

But wait — let’s double-check: 28 is closer to 25? No:

- 28 - 25 = 3
- 30 - 28 = 2 → yes, 30 is closer

But actually, 28 is between 25 and 30, and closer to 25? No:

- 25 → 28 → 30
- Distance: 28 - 25 = 3
- 30 - 28 = 2 → so 30 is closer

So, 30 ÷ 5 = 6 → estimate is 6

But let’s check: 28 ÷ 5 = 5.6 → so rounding to nearest whole number is 6

✔ Answer: So, 28 ÷ 5 is about 6

> Note: Some might argue 25 is closer, but 28 is only 2 away from 30, and 3 away from 25 → so 30 is closer.

Wait — no! 28 - 25 = 3, 30 - 28 = 2 → yes, 30 is closer

But actually, 28 is closer to 25? No — 28 is 3 above 25, 2 below 30 → so 30 is closer

Yes → 30 is closer

So, 30 ÷ 5 = 6 → estimate = 6

✔ Answer: So, 28 ÷ 5 is about 6

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Problem 3: 43 ÷ 8 = ?

Step 1: List three division statements using divisor 8:

- 8 ÷ 8 = 1
- 16 ÷ 8 = 2
- 24 ÷ 8 = 3
- 32 ÷ 8 = 4
- 40 ÷ 8 = 5
- 48 ÷ 8 = 6

Pick three around 43:

- 32 ÷ 8 = 4
- 40 ÷ 8 = 5
- 48 ÷ 8 = 6

Step 2: Which dividend is closest to 43?

- 43 - 40 = 3
- 48 - 43 = 5
- So, 40 is closer

So, 40 ÷ 8 = 5 → estimate = 5

✔ Answer: So, 43 ÷ 8 is about 5

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Problem 4: 56 ÷ 9 = ?

Step 1: List three division statements using divisor 9:

- 9 ÷ 9 = 1
- 18 ÷ 9 = 2
- 27 ÷ 9 = 3
- 36 ÷ 9 = 4
- 45 ÷ 9 = 5
- 54 ÷ 9 = 6
- 63 ÷ 9 = 7

Pick three around 56:

- 45 ÷ 9 = 5
- 54 ÷ 9 = 6
- 63 ÷ 9 = 7

Step 2: Which dividend is closest to 56?

- 56 - 54 = 2
- 63 - 56 = 7
- So, 54 is closest

54 ÷ 9 = 6 → estimate = 6

✔ Answer: So, 56 ÷ 9 is about 6

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✔ Final Answers:

1. 15 ÷ 7 is about 2
2. 28 ÷ 5 is about 6
3. 43 ÷ 8 is about 5
4. 56 ÷ 9 is about 6

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✔ Summary of Work:

| Problem | Estimate |
|--------|---------|
| 1. 15 ÷ 7 | 2 |
| 2. 28 ÷ 5 | 6 |
| 3. 43 ÷ 8 | 5 |
| 4. 56 ÷ 9 | 6 |

These estimates are made by choosing a dividend close to the original that is divisible by the divisor, then dividing.

Let me know if you'd like this explained in simpler terms for a child!