Addition and Subtraction - Introduction to Subtraction

What is subtraction?

Subtraction is taking things away. When you have an amount and you subtract from it, the amount becomes smaller. Subtraction happens a lot in real life.

For instance, imagine we have 8 eggs...
For instance, imagine we have 8 eggs...and we use a few. We're subtracting from the eggs we started with.
We can count the number of eggs to find out how many are left.
We can count the number of eggs to find out how many are left.
We can count the number of eggs to find out how many are left.
We can count the number of eggs to find out how many are left.
We can count the number of eggs to find out how many are left.
We can count the number of eggs to find out how many are left.
Five eggs are left. If you start with eight eggs and use three of them, then five eggs are left.

As we saw, if you have 8 eggs and subtract 3 of them, you'll have 5 eggs left. In other words:

8 - 3 = 5

8 - 3 = 5 is a mathematical equation . You could read it like this: five minus three equals two. As we learned in Introduction to Addition , a mathematical equation is basically a math sentence that uses numbers and symbols . When we write a subtraction equation, we use two symbols: - and = .

The minus sign ( - ) means one thing is being subtracted from another. This is why we put it after the first group of eggs — we had 8 eggs and subtracted 5 of them.

Try This!

Fill in the blanks in the expressions below.

The Equals Sign

The other symbol in our equation is the equals sign ( = ). As we learned in Introduction to Addition , the equals sign means two numbers or expressions are equivalent , or equal . Even though they might look different, they mean the same thing .

In our eggs example, since 3 eggs were left, we wrote 3 to the right of the equals sign. That shows each side means 3. 3 eggs on the left, and the number 3 on the right. Both sides are equal.

Writing Expressions

As you become more comfortable with reading and writing mathematical expressions, you might notice they are useful for seeing the amount you start with and what you're subtracting.

Any subtraction problem can be turned into a written expression . For instance, let's say your tomato plant has seven tomatoes and you pick four. To figure out the number of tomatoes that are left on the plant, you might write an expression like this:

7 - 4

The expression is just another way of describing the situation: seven tomatoes minus four that were picked.

Try This!

Write these situations as mathematical expressions. Don't solve the problems yet — simply set them up.

You have a pie with eight pieces. You eat two pieces.

You have nine cans of soup and you donate seven to the food bank.

You've gathered six sticks for your campfire. You throw three sticks on the fire.

Solving Problems

In Introduction to Addition , you learned how to use counting to solve addition problems. That skill can also be used to solve subtraction problems.

Ways to Count

We're going to take a look at two ways you can use counting to subtract. First we'll count with objects .

To count with objects, use the objects to show the first number in the expression.
Let's try it with this expression, 9 - 4 .
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We'll start by showing the number 9 . We'll need 9 objects.
We're subtracting 4 , so we'll take away 4 of the objects.
We're subtracting 4 , so we'll take away 4 of the objects.
We're subtracting 4 , so we'll take away 4 of the objects.
We're subtracting 4 , so we'll take away 4 of the objects.
We're subtracting 4 , so we'll take away 4 of the objects.
Now we can finish this expression. All we have to do is count the remaining objects.
Now we can finish this expression. All we have to do is count the remaining objects.
Now we can finish this expression. All we have to do is count the remaining objects.
Now we can finish this expression. All we have to do is count the remaining objects.
Now we can finish this expression. All we have to do is count the remaining objects.
Now we can finish this expression. All we have to do is count the remaining objects.
There are 5 objects left, so our answer is 5 .
To finish, we'll write 5 to the right of the equals sign.

Try This!

Solve these expressions.

7 - 2 =

6 - 3 =

5 - 4 =

Number Lines

Another way to solve subtraction problems is to use a number line .

Subtracting with a number line is simple.
When you subtract, you count by moving left one number at a time.
When you subtract, you count by moving left one number at a time.
When you subtract, you count by moving left one number at a time.
Let's practice subtracting with a number line.
We need to start counting from the first number in our expression.
Here, that number is 9 ...
Here, that number is 9 ...So, we'll start counting at the 9 mark on the number line.
The second number in our expression is how much we're subtracting.
Here, that number is 4 ...
Here, that number is 4 ...So, we'll move to the left 4 times.
Here, that number is 4 ...So, we'll move to the left 4 times.
Here, that number is 4 ...So, we'll move to the left 4 times.
Here, that number is 4 ...So, we'll move to the left 4 times.
We landed on 5 . This means that 9 - 4 = 5 .
We'll write 5 to the right of the equals sign. Our expression is complete!