# Subtraction with Help from the Number Line

Subtraction and minus are two names for the same mathematical operation. Subtracting positive numbers from each other makes things smaller, and moves you towards the left on the number line.

Rule

### ImportantWordsandExpressions

When you are talking about subtraction, all the numbers you are subtracting from each other are called terms. When you subtract several terms from each other, the answer is called a difference.

 $\text{TERM}-\text{TERM}=\text{DIFFERENCE}$

It’s important to remember these names for different parts of a subtraction, so you should memorize them!

Remember that you can always use the number line to help you with subtraction. The number of jumps to the left you need to get the answer is equal to the number you are subtracting.

Example 1

Find $13-6=7$

In this case, $13$ and $6$ are our terms, and $7$ is their difference.

What do you think will happen when you try to subtract 0 from another number?

Absolutely nothing!

 $10-0=10\phantom{\rule{1em}{0ex}}100-0=100\phantom{\rule{1em}{0ex}}42-0=42$

This is because you are jumping $0$ steps to the left on the number line, so the number isn’t getting any smaller. Subtracting $0$ is the same as removing nothing.

Example 2

Find $48-25=23$

In this case, $48$ and $25$ are our terms, and $23$ is their difference.

Example 3

Find $67-24=43$

In this case, $67$ and $24$ are our terms, and $43$ is our difference.

You can use the number line to find this. The number you are subtracting shows how many jumps to the left you need, which in this case is 24.

Remember: Friends of $10$ are pairs of numbers that sum to $10$.

What happens if you subtract a friend of 10 from 10?

Because the friends of $10$ are the numbers that become $10$ when you add them together, the difference between $10$ and one friend would be the other friend of $10$. $\begin{array}{llll}\hfill 10-1& =9\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 10-8& =2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 10-3& =7\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 10-6& =4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 10-5& =5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Math Vault

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