Flashcards and Practice Resources

Subtracting Multi-Digit Numbers Using Place Value

Imagine subtracting 528 from 1000. First, visualize 1000 as a length and imagine removing 528 units from it. The remaining length is the result of the subtraction. To make this process clearer, we use a table with place values alongside the standard algorithm method.

Place Value Chart

1. Thousands Place:
   We have 1 thousand (1000).

2. Hundreds Place:
   Initially, there are 0 hundreds in 1000. In 528, there are 5 hundreds.

3. Tens Place:
   1000 has 0 tens, while 528 has 2 tens.

4. Ones Place:
   Both numbers have digits in the ones place: 0 for 1000 and 8 for 528.

To subtract using place values, we must regroup (or borrow) because we cannot subtract a larger digit from a smaller one directly.

Standard Algorithm for Subtraction

We write 1000 and 528 aligned by place values:

1000

-  528

Starting from the ones place, we cannot subtract 8 from 0. We need to borrow from the tens, but since tens are also 0, we move to the hundreds. We borrow from the thousands place, turning 1000 into 900 (in the hundreds place) and giving us 10 in the tens place. Borrowing from the tens place turns it into 9, leaving 10 in the ones place.

Now, we can subtract step-by-step:

1. Ones Place:
   10 - 8 = 2

2. Tens Place:
   9 - 2 = 7

3. Hundreds Place:
   9 - 5 = 4

Putting it all together, the result of 1000 - 528 is 472.

Regrouping Process

• Break 1000 into 10 hundreds.

• From 10 hundreds, borrow 1 hundred, converting it into 10 tens.

• Borrow 1 ten, converting it into 10 ones.

After these steps, subtraction becomes straightforward:

• Subtract ones: 10 - 8 = 2

• Subtract tens: 9 - 2 = 7

• Subtract hundreds: 9 - 5 = 4

This method ensures you understand not just the procedure but the reasoning behind it.