Subtract 469 from 2007: Vertical Format Solution

Video Solution

Solution Steps

00:00 Solve

00:03 Each time we consider borrowing 2 digits, and then we'll place

00:06 7 is less than 9

00:09 The tens digit equals 0 so we can't borrow from it

00:12 The hundreds digit also equals 0 so we can't borrow from it either

00:15 We'll borrow a thousand from the thousands place for the hundreds

00:19 So now instead of 0, we'll have 10 in the hundreds!

00:22 And now we'll borrow ten from the hundreds for the tens

00:25 Which will change the hundreds from 10 to 9

00:29 So now instead of 0, we'll have 10 in the tens!

00:32 And now we'll borrow ten from the tens for the ones

00:35 Which will change the tens from 10 to 9

00:39 So now instead of 7, we'll have 17 in the ones!

00:42 Now we'll subtract ones from ones, and place in ones

00:45 Subtract tens from tens, and place in tens

00:49 Subtract hundreds from hundreds, and place in hundreds

00:57 Place 0 in the missing digits

00:59 Subtract thousands from thousands, and place in thousands

01:03 And that's the solution to the problem

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Now, let's work through each step:

Step 1: Set up the subtraction vertically:
$2007$
$- 469$

Step 2: Subtract starting from the rightmost digit:

In the one's place, we have $7 - 9$ . Since $7$ is smaller than $9$ , we need to borrow. However, $0$ has no value to lend, so we need to also borrow from the hundreds place.
In the tens place, $0$ becomes $10$ (after borrowing $1$ from the hundreds), but now we have to borrow $1$ for the ones place operation, leaving us with $9$ in the tens place. Thus, the ones place calculation becomes $17 - 9 = 8$ .
In the tens place, we subtract $6$ from the adjusted $9$ (due to earlier borrowing). Thus, $9 - 6 = 3$ .
In the hundreds place, initially $0$ , now we have $9$ (after borrowing from the thousands, so it effectively becomes $9$ ). Thus, $9 - 4 = 5$ .
Finally, the thousands place remains $1$ as we have already borrowed $1$ away, and we have no number to subtract from it. So, it remains $1$ .

The complete subtraction sequence gives us:

$2007$
$- 469$
$\overline{1538}$

Therefore, the solution to the problem is $1538$ .