Grade 5 Long Division Worksheet: Missing dividend or divisor ... - Free Printable

Problem: Solve the missing numbers using long division.

The worksheet asks us to solve for the missing numbers in each division problem. Let's go through each problem step by step.

---

#### Problem 1: \( 9,016 \div 184 = \)
We need to divide 9,016 by 184.

1. Set up the division:
```
____
184 | 9016
```

2. Divide:
- How many times does 184 go into 901?
\( 184 \times 5 = 920 \) (too large), so try 4.
\( 184 \times 4 = 736 \).
Write 4 above the line. Subtract 736 from 901:
\( 901 - 736 = 165 \).

3. Bring down the next digit:
Bring down the 6 to make it 1656.

4. Divide again:
- How many times does 184 go into 1656?
\( 184 \times 9 = 1656 \).
Write 9 above the line. Subtract 1656 from 1656:
\( 1656 - 1656 = 0 \).

5. Result:
The quotient is 49.
```
49
184 | 9016
-736
------
1656
-1656
------
0
```

Answer: \( 9,016 \div 184 = 49 \)

---

#### Problem 2: \( 30,756 \div ? = 66 \)
We need to find the divisor when the dividend is 30,756 and the quotient is 66.

1. Set up the equation:
\[
\text{Dividend} = \text{Divisor} \times \text{Quotient}
\]
\[
30,756 = \text{Divisor} \times 66
\]

2. Solve for the divisor:
\[
\text{Divisor} = \frac{30,756}{66}
\]

3. Perform the division:
```
____
66 | 30756
```

- How many times does 66 go into 307?
\( 66 \times 4 = 264 \).
Write 4 above the line. Subtract 264 from 307:
\( 307 - 264 = 43 \).

- Bring down the next digit (5):
Make it 435.

- How many times does 66 go into 435?
\( 66 \times 6 = 396 \).
Write 6 above the line. Subtract 396 from 435:
\( 435 - 396 = 39 \).

- Bring down the next digit (6):
Make it 396.

- How many times does 66 go into 396?
\( 66 \times 6 = 396 \).
Write 6 above the line. Subtract 396 from 396:
\( 396 - 396 = 0 \).

4. Result:
The divisor is 466.
```
466
66 | 30756
-264
------
435
-396
------
396
-396
------
0
```

Answer: \( 30,756 \div 466 = 66 \)

---

#### Problem 3: \( 37,125 \div ? = 45 \)
We need to find the divisor when the dividend is 37,125 and the quotient is 45.

1. Set up the equation:
\[
\text{Dividend} = \text{Divisor} \times \text{Quotient}
\]
\[
37,125 = \text{Divisor} \times 45
\]

2. Solve for the divisor:
\[
\text{Divisor} = \frac{37,125}{45}
\]

3. Perform the division:
```
____
45 | 37125
```

- How many times does 45 go into 371?
\( 45 \times 8 = 360 \).
Write 8 above the line. Subtract 360 from 371:
\( 371 - 360 = 11 \).

- Bring down the next digit (2):
Make it 112.

- How many times does 45 go into 112?
\( 45 \times 2 = 90 \).
Write 2 above the line. Subtract 90 from 112:
\( 112 - 90 = 22 \).

- Bring down the next digit (5):
Make it 225.

- How many times does 45 go into 225?
\( 45 \times 5 = 225 \).
Write 5 above the line. Subtract 225 from 225:
\( 225 - 225 = 0 \).

4. Result:
The divisor is 825.
```
825
45 | 37125
-360
------
112
- 90
------
225
-225
------
0
```

Answer: \( 37,125 \div 825 = 45 \)

---

#### Problem 4: \( 71,100 \div 900 = \)
We need to divide 71,100 by 900.

1. Set up the division:
```
____
900 | 71100
```

2. Divide:
- How many times does 900 go into 711?
\( 900 \times 0 = 0 \) (not enough digits yet).
Consider 7110 instead.

- How many times does 900 go into 7110?
\( 900 \times 7 = 6300 \).
Write 7 above the line. Subtract 6300 from 7110:
\( 7110 - 6300 = 810 \).

- Bring down the next digit (0):
Make it 8100.

- How many times does 900 go into 8100?
\( 900 \times 9 = 8100 \).
Write 9 above the line. Subtract 8100 from 8100:
\( 8100 - 8100 = 0 \).

3. Result:
The quotient is 79.
```
79
900 | 71100
-6300
------
8100
-8100
------
0
```

Answer: \( 71,100 \div 900 = 79 \)

---

#### Problem 5: \( 43,548 \div ? = 57 \)
We need to find the divisor when the dividend is 43,548 and the quotient is 57.

1. Set up the equation:
\[
\text{Dividend} = \text{Divisor} \times \text{Quotient}
\]
\[
43,548 = \text{Divisor} \times 57
\]

2. Solve for the divisor:
\[
\text{Divisor} = \frac{43,548}{57}
\]

3. Perform the division:
```
____
57 | 43548
```

- How many times does 57 go into 435?
\( 57 \times 7 = 399 \).
Write 7 above the line. Subtract 399 from 435:
\( 435 - 399 = 36 \).

- Bring down the next digit (4):
Make it 364.

- How many times does 57 go into 364?
\( 57 \times 6 = 342 \).
Write 6 above the line. Subtract 342 from 364:
\( 364 - 342 = 22 \).

- Bring down the next digit (8):
Make it 228.

- How many times does 57 go into 228?
\( 57 \times 4 = 228 \).
Write 4 above the line. Subtract 228 from 228:
\( 228 - 228 = 0 \).

4. Result:
The divisor is 764.
```
764
57 | 43548
-399
------
364
-342
------
228
-228
------
0
```

Answer: \( 43,548 \div 764 = 57 \)

---

Final Answers:

\[
\boxed{49, 466, 825, 79, 764}
\]