Question

find the quotient. annex zeros as needed so that you dont have a remainder. \\(4\enclose{longdiv}{15.38}\\) be sure to include the decimal point in your answer!

Explanation:

Step1: Divide 15 by 4

4 goes into 15 three times (3×4 = 12). Subtract 12 from 15, we get 3. Bring down the 3 to make 33.

Step2: Divide 33 by 4

4 goes into 33 eight times (8×4 = 32). Subtract 32 from 33, we get 1. Bring down the 8 to make 18.

Step3: Divide 18 by 4

4 goes into 18 four times (4×4 = 16). Subtract 16 from 18, we get 2. Annex a zero to make 20.

Step4: Divide 20 by 4

4 goes into 20 five times (5×4 = 20). Subtract 20 from 20, we get 0.
Now, combine the results: 3 (from 15÷4) + 0.8 (from 33÷4) + 0.04 (from 18÷4) + 0.005 (from 20÷4) = 3.845? Wait, no, let's do the long division properly.

Wait, the number is 15.38. Let's write it as 15.380 (annexing a zero to make it easier to divide without remainder).

15.380 ÷ 4:

- 4 into 15: 3, remainder 3. Write 3 above the tens place.
- Bring down 3 (from 15.380) to make 33. 4 into 33: 8, remainder 1. Write 8 above the tenths place.
- Bring down 8 (from 15.380) to make 18. 4 into 18: 4, remainder 2. Write 4 above the hundredths place.
- Bring down 0 (annexed) to make 20. 4 into 20: 5, remainder 0. Write 5 above the thousandths place.

So putting it together: 3.845? Wait, no, wait 15.38 ÷ 4:

Wait, 4 × 3.845 = 15.38? Let's check: 4×3 = 12, 4×0.8 = 3.2, 4×0.04 = 0.16, 4×0.005 = 0.02. Wait, 12 + 3.2 = 15.2, 15.2 + 0.16 = 15.36, 15.36 + 0.02 = 15.38. Yes! Wait, no, 4×3.845 = 15.38? Wait 3.845 × 4: 3×4=12, 0.8×4=3.2, 0.04×4=0.16, 0.005×4=0.02. 12+3.2=15.2, 15.2+0.16=15.36, 15.36+0.02=15.38. Yes. But wait, when we annex a zero, we have 15.380. So the division is:

15.380 ÷ 4:

- 15 ÷ 4 = 3, remainder 3.
- 33 ÷ 4 = 8, remainder 1.
- 18 ÷ 4 = 4, remainder 2.
- 20 ÷ 4 = 5, remainder 0.

So the quotient is 3.845? Wait, no, wait 15.38 ÷ 4:

Wait, 4 × 3.84 = 15.36, which is less than 15.38. 4 × 3.845 = 15.38. So the correct quotient is 3.845? Wait, but let's do the long division step by step:

3.845
________
4 | 15.380
12
---
3 3
3 2
---
1 8
1 6
---
2 0
2 0
---
0

Yes, so the quotient is 3.845? Wait, but the problem says "annex zeros as needed so that you don't have a remainder". So 15.38 has a remainder when divided by 4, so we annex a zero to make it 15.380, then divide. So the result is 3.845? Wait, no, wait 15.38 ÷ 4:

Wait, 15.38 ÷ 4:

15 ÷ 4 = 3, remainder 3.

3.3 ÷ 4 = 0.8, remainder 0.1 (because 0.8×4=3.2, 3.3-3.2=0.1)

0.18 ÷ 4 = 0.04, remainder 0.02 (because 0.04×4=0.16, 0.18-0.16=0.02)

0.020 ÷ 4 = 0.005, remainder 0.

So adding them up: 3 + 0.8 + 0.04 + 0.005 = 3.845. Wait, but maybe I made a mistake. Let's check 4 × 3.845 = 15.38. Yes, 4×3=12, 4×0.8=3.2, 4×0.04=0.16, 4×0.005=0.02. 12+3.2=15.2, 15.2+0.16=15.36, 15.36+0.02=15.38. Correct.

Wait, but maybe the problem expects us to annex a zero to 15.38 to make it 15.380, then divide by 4. So the quotient is 3.845? Wait, no, let's do the division again:

15.38 ÷ 4:

- 4 into 15: 3, 3×4=12, 15-12=3.
- Bring down 3 (from 15.38) to make 33. 4 into 33: 8, 8×4=32, 33-32=1.
- Bring down 8 (from 15.38) to make 18. 4 into 18: 4, 4×4=16, 18-16=2.
- Annex a zero to make 20. 4 into 20: 5, 5×4=20, 20-20=0.

So the decimal places: 3 (units), 8 (tenths), 4 (hundredths), 5 (thousandths). So 3.845. Wait, but maybe the problem has a typo or I miscalculated. Wait, 15.38 ÷ 4: 15 ÷ 4 = 3.75? No, 4×3.75=15. Wait, no, 15.38 ÷ 4:

Wait, 4×3.8 = 15.2, 15.38 - 15.2 = 0.18. 0.18 ÷ 4 = 0.045. So 3.8 + 0.045 = 3.845. Yes, that's correct. So the quotient is 3.845. Wait, but let's check with a calculator: 15.38 ÷ 4 = 3.845. Yes, that's correct.

Wait, but maybe the problem expects us to annex a zero to 15.38 to make it 15.380, then divide by 4, which gives 3.845. So the answer is 3.845? Wait, no, maybe I made a mistake in the steps. Let's do the long division properly:

3.845
________
4 | 15.380
12
---
3 3
3 2
---
1 8
1 6
---
2 0
2 0
---
0

Yes, that's correct. So the quotient is 3.845.

Answer:

3.845