1.3 Subtract whole numbers

Use subtraction notation

Suppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference    . The notation we use to subtract $3$ from $7$ is

We read $7-3$ as seven minus three and the result is the difference of seven and three .

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 $10$ 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 $7-3=4$ .

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 $8-2=6$ .

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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.

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