By how much is the sum of 14.28 and 21.219 greater than their difference?

Options

A. `35.499`
B. ` 6.939`
C. `20.65`
D. `28.56`

Answer

To solve the problem, we need to find out how much greater the sum of 14.28 and 21.219 is than their difference. Let's break this down step by step.

### Step 1: Calculate the Sum
First, we need to find the sum of 14.28 and 21.219.

\[ \text{Sum} = 14.28 + 21.219 \]

To add these numbers, we can align them by their decimal points:

```
14.280
+ 21.219
---------
```

Now we can add them column by column:

- In the thousandths place: \(0 + 9 = 9\)
- In the hundredths place: \(8 + 1 = 9\)
- In the tenths place: \(2 + 2 = 4\)
- In the units place: \(4 + 1 = 5\)
- In the tens place: \(1 + 2 = 3\)

So, the sum is:

\[ \text{Sum} = 35.499 \]

### Step 2: Calculate the Difference
Next, we need to find the difference between 21.219 and 14.28.

\[ \text{Difference} = 21.219 - 14.28 \]

Aligning the numbers again:

```
21.219
- 14.280
---------
```

Now we subtract column by column:

- In the thousandths place: \(9 - 0 = 9\)
- In the hundredths place: \(1 - 8\) (we need to borrow, so it becomes \(11 - 8 = 3\))
- In the tenths place: \(2 - 2 = 0\)
- In the units place: \(1 - 4\) (we need to borrow again, so it becomes \(11 - 4 = 7\))
- In the tens place: \(2 - 1 = 1\)

So, the difference is:

\[ \text{Difference} = 6.939 \]

### Step 3: Find the Difference Between the Sum and the Difference
Now, we need to find out how much greater the sum is than the difference:

\[ \text{Result} = \text{Sum} - \text{Difference} \]

Substituting the values we found:

\[ \text{Result} = 35.499 - 6.939 \]

Aligning the numbers for subtraction:

```
35.499
- 6.939
---------
```

Now we subtract:

- In the thousandths place: \(9 - 9 = 0\)
- In the hundredths place: \(9 - 3 = 6\)
- In the tenths place: \(4 - 9\) (we need to borrow, so it becomes \(14 - 9 = 5\))
- In the units place: \(5 - 6\) (we need to borrow, so it becomes \(15 - 6 = 9\))
- In the tens place: \(2 - 0 = 2\)

So, the final result is:

\[ \text{Result} = 28.56 \]

### Final Answer
The sum of 14.28 and 21.219 is greater than their difference by **28.56**.

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