Model Subtraction

Model Subtraction of Whole Numbers

A model can help us visualize the process of subtraction much as it did with addition. Again, we will use \(\text{base-10}\) blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, \(7-3.\)

We start by modeling the first number, 7.
Now take away the second number, 3. We'll circle 3 blocks to show that we are taking them away.
Count the number of blocks remaining.
There are 4 ones blocks left.	We have shown that \(7-3=4\).

Example

Model the subtraction: \(8-2.\)

Solution

\(8-2\) means the difference of 8 and 2.
Model the first, 8.
Take away the second number, 2.
Count the number of blocks remaining.
There are 6 ones blocks left.	We have shown that \(8-2=6\).

Extra:

Model: \(9-6.\)

Extra:

Model: \(6-1.\)

Example

Model the subtraction: \(13-8.\)

Solution

Model the first number, 13. We use 1 ten and 3 ones.
Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones.
Now we can take away 8 ones.
Count the blocks remaining.
There are five ones left.	We have shown that \(13-8=5\).

As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.

Extra:

Model the subtraction: \(12-7.\)

Extra:

Model the subtraction: \(14-8.\)

Example

Model the subtraction: \(43-26.\)

Solution

Because \(43-26\) means \(43\) take away \(26,\) we begin by modeling the \(43.\)

An image containing two items. The first item is 4 horizontal rods containing 10 blocks each. The second item is 3 individual blocks.

Now, we need to take away \(26,\) which is \(2\) tens and \(6\) ones. We cannot take away \(6\) ones from \(3\) ones. So, we exchange \(1\) ten for \(10\) ones.

This figure contains two groups. The first group on the left includes 3 rows of blue base 10 blocks and 1 red row of 10 blocks. This is labeled 4 tens. Alongside the first row of ten blocks are 3 individual blocks. This is labeled 3 ones. An arrow points to the right to the second group in which there are three rows of 10 base blocks labeled 3 tens. Next to this is a row of 3 blue individual blocks and two rows each with five individual blocks in red. This is labeled 13 ones.

Now we can take away \(2\) tens and \(6\) ones.

This image includes one row of base ten blocks at the top of the image; Next to it are seven individual blocks. Below this, is a group of two rows of base ten blocks, and two rows of 3 individual blocks with a circle around all. The arrow points to the right and shows one row of ten blocks and seven individual blocks underneath.

Count the number of blocks remaining. There is \(1\) ten and \(7\) ones, which is \(17.\)

\(43-26=17\)

Extra:

Model the subtraction: \(42-27.\)

Extra:

Model the subtraction: \(45-29.\)

Optional Video: Model Subtraction of Three Digit Whole Numbers Using Base Ten Blocks

This video below by Mathispower4u explains subtraction of three digit whole numbers by using base ten blocks.

This lesson is part of:

Introducing Numbers

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