2. Use column subtraction to check your answers in Question 1. 3. Use the column method to find the answers to the following question a. $$ 345765-202387 $$ b. $$ 766219-34387 $$ c. $$ 334938-231493 $$ 4. Use column addition to check your answers in Question 3 . 5. Complete these number sentences. Check each by substitution. a. $$ 23405+\ldots+350000=500000 $$ b. c. $$ -45347=950000 $$

Question

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Let's solve the problems step by step.

### Question 3: Column Subtraction

#### a. $$ 345765 - 202387 $$

We will perform the subtraction using the column method:

```
   345765
-  202387
__________
```

Starting from the rightmost column:

1. **Units**: $$ 5 - 7 $$ → We need to borrow. So, $$ 15 - 7 = 8 $$ (borrow 1 from the next column).
2. **Tens**: $$ 6 - 8 $$ → After borrowing, it becomes $$ 5 - 8 $$ → We need to borrow again. So, $$ 15 - 8 = 7 $$.
3. **Hundreds**: $$ 7 - 3 = 4 $$.
4. **Thousands**: $$ 5 - 2 = 3 $$.
5. **Ten Thousands**: $$ 4 - 0 = 4 $$.
6. **Hundred Thousands**: $$ 3 - 2 = 1 $$.

Putting it all together, we get:

```
   345765
-  202387
__________
   143378
```

#### b. $$ 766219 - 34387 $$

Using the column method:

```
   766219
-   34387
__________
```

1. **Units**: $$ 9 - 7 = 2 $$.
2. **Tens**: $$ 1 - 8 $$ → We need to borrow. So, $$ 11 - 8 = 3 $$.
3. **Hundreds**: $$ 2 - 3 $$ → We need to borrow. So, $$ 12 - 3 = 9 $$.
4. **Thousands**: $$ 6 - 4 = 2 $$.
5. **Ten Thousands**: $$ 6 - 0 = 6 $$.
6. **Hundred Thousands**: $$ 7 - 0 = 7 $$.

Putting it all together, we get:

```
   766219
-   34387
__________
   731832
```

#### c. $$ 334938 - 231493 $$

Using the column method:

```
   334938
-  231493
__________
```

1. **Units**: $$ 8 - 3 = 5 $$.
2. **Tens**: $$ 3 - 9 $$ → We need to borrow. So, $$ 13 - 9 = 4 $$.
3. **Hundreds**: $$ 9 - 4 = 5 $$.
4. **Thousands**: $$ 4 - 1 = 3 $$.
5. **Ten Thousands**: $$ 3 - 3 = 0 $$.
6. **Hundred Thousands**: $$ 3 - 2 = 1 $$.

Putting it all together, we get:

```
   334938
-  231493
__________
   103445
```

### Question 4: Column Addition to Check Answers

Now, let's check the answers from Question 3 using column addition.

#### a. Check $$ 143378 + 202387 $$

```
   143378
+  202387
__________
```

1. **Units**: $$ 8 + 7 = 15 $$ (write 5, carry 1).
2. **Tens**: $$ 7 + 8 + 1 = 16 $$ (write 6, carry 1).
3. **Hundreds**: $$ 4 + 3 + 1 = 8 $$.
4. **Thousands**: $$ 3 + 2 = 5 $$.
5. **Ten Thousands**: $$ 4 + 0 = 4 $$.
6. **Hundred Thousands**: $$ 1 + 2 = 3 $$.

Putting it all together, we get:

```
   143378
+  202387
__________
   345765
```

#### b. Check $$ 731832 + 34387 $$

```
   731832
+   34387
__________
```

1. **Units**: $$ 2 + 7 = 9 $$.
2. **Tens**: $$ 3 + 8 = 11 $$ (write 1, carry 1).
3. **Hundreds**: $$ 9 + 3 + 1 = 13 $$ (write 3, carry 1).
4. **Thousands**: $$ 2 + 4 + 1 = 7 $$.
5. **Ten Thousands**: $$ 6 + 0 = 6 $$.
6. **Hundred Thousands**: $$ 7 + 0 = 7 $$.

Putting it all together, we get:

```
   731832
+   34387
__________
   766219
```

#### c. Check $$ 103445 + 231493 $$

```
   103445
+  231493
__________
```

1. **Units**: $$ 5 + 3 = 8 $$.
2. **Tens**: $$ 4 + 9 = 13 $$ (write 3, carry 1).
3. **Hundreds**: $$ 4 + 4 + 1 = 9 $$.
4. **Thousands**: $$ 3 + 1 = 4 $$.
5. **Ten Thousands**: $$ 0 + 3 = 3 $$.
6. **Hundred Thousands**: $$ 1 + 2 = 3 $$.

Putting it all together, we get:

```
   103445
+  231493
__________
   334938
```

### Question 5: Complete Number Sentences

#### a. $$ 23405 + \ldots + 350000 = 500000 $$

To find the missing number, we can rearrange the equation:

$$
\ldots = 500000 - 23405 - 350000
$$

Calculating this:

$$
\ldots = 500000 - 350000 - 23405 = 126595
$$

So, the complete sentence is:

$$
23405 + 126595 + 350000 = 500000
$$

#### b. (This part is missing in the original question. Please provide the equation to complete.)

#### c. $$ -45347 = 950000 $$

To check this, we can rearrange it:

$$
950000 + 45347 = 0
$$

Calculating this:

$$
950000 + 45347 = 995347
$$

So, the complete sentence is:

$$
-45347 + 995347 = 950000
$$

### Summary of Answers
- **Question 3 Results**:
  - a. $$ 143378 $$
  - b. $$ 731832 $$
  - c. $$ 103445 $$

-
- **Question 3 Results**: - a. $$ 143378 $$ - b. $$ 731832 $$ - c. $$ 103445 $$ - **Question 4 Checks**: - a. $$ 345765 $$ - b. $$ 766219 $$ - c. $$ 334938 $$ - **Question 5 Solutions**: - a. $$ 23405 + 126595 + 350000 = 500000 $$ - c. $$ -45347 + 995347 = 950000 $$

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