Adding | Carrying and Borrowing |

Subtracting | More Practice |

The Number Line |

What’s so scary about a number? Let’s go counting…….

OK, so let’s start with the basics – *numbers. **I truly believe that if you can count on your fingers to add *$ 2$* plus $ 2$ to get $ 4$, you can progress to do the most difficult math problem ever *— *just by taking baby steps! *It all starts there!

Let’s talk about the different types of numbers. I believe there’s a reason we have $ 10$ fingers: so we can count! You can count to $ 10$ with your fingers and then start over again! Your first finger always ends with a $ 1$, and your last finger ends with a $ 0$.

**Even** numbers are ones that end with $ 0,2,4,6,\,\text{and }8$, and **odd** numbers are those that end with $ 1,3,5,7,\,\text{and }9$. Later we’ll see that the number $ 2$ “goes into” even numbers perfectly, but not odd numbers.

And it’s OK if you use your fingers to count!

## Adding

At this point, you’ll need to learn how to add and subtract. A little bit later, we’ll talk about “carrying” and “borrowing” (also called “regrouping”) when we add and subtract; we may need to do this when we are working with numbers greater than $ 10$.

Adding numbers is just like adding dresses, for example. If you have $ 4$ pink/purple dresses and $ 2$ green dresses, you have $ 6$ dresses total – it’s as simple as that.

The following chart is an addition table for adding numbers from $ 0$ to $ 10$. To use this table, pick a number on the left, add it to the number on the top, and you get the number where they both end up! The numbers that you add are called **addends**, and the answer is called the **sum**.

Practice with this table until you really know your addition facts. You might even want to buy some flash cards to help you.

And, remember, again, it’s OK to count on your fingers for now! Don’t be embarrassed by that. I know some very successful adults who still do this, but you’ll probably find you won’t need to for very long.

**Memorize your addition facts:**

If we start with the $ 4$ on the left side and look for the $ 2$ on the top, they both point to $ 6$! Thus, $ 4+2=6$. For a little more difficult problem, add $ 9$ and $ 7$ to get $ 16$. Thus, $ 9+7=16$.

Note that it doesn’t matter which number we start with: $ 4+2=2+4=6$.

Notice the special number $ 0$. If you add $ 0$** **to any number (which is sort of like adding “nothing”), you just end up with the same number.

**Again, learn these addition facts well – you will use them your entire life!**** **

## Subtracting

Subtracting is just taking away numbers from other numbers. So, getting back to dresses, let’s say you have $ 6$ dresses total, and you decide you don’t want to wear pink/purple anymore. You give the $ 4$** **pink/purple dresses to your mom to save for your little sister, and you have $ 2$ green dresses left. **If you can add and subtract numbers of dresses, you can do any addition and subtraction! **You should know your division facts from your multiplication facts (backwards!)

At this time, we’re only subtracting smaller (or the same) numbers from bigger numbers.

Here’s a subtraction table; notice that it’s the same as the addition table above, except you start from the **left** and subtract the **top**. The number you start with is called the **minuend**, the number you are subtracting is called the **subtrahend**, and the number you end up with after the subtraction is called the **difference**. Notice that subtraction just “undoes” addition; it’s like the opposite.

**Know your subtraction facts from your addition facts:**

To subtract $ 6-4$, start with the $ 6$ on the left and look for $ 4$ on the top and see where they meet – at $ 2$. Thus, $ 6-4=2$. For the little more difficult problem, to subtract $ 16-9$**, **start with the $ 16$** **on the left and look up for the $ 9$ and see where they meet – at $ 7$. Thus, $ 16-9=7$.

Note that now it **does** matter which one we start with (we need to start on the left hand side): $ 16-9$** does not equal **$ 9-16$!

Also note that there are some areas where we don’t have numbers. That’s because right now we’re only dealing with **subtracting** **smaller numbers** from either **larger numbers** (or the same number). Later we’ll work with what we call **Negative Numbers**, where we can actually subtract larger numbers from smaller numbers.

**Learn the subtraction facts well** – you may want to get flash cards to help with addition and subtraction.

## The Number Line

Another useful tool for adding and subtracting number is what we call the **number line**. The number line is just what is called: a line with tick marks with numbers under them.

We can think of adding as counting to the **right** on the **number line**** **below, and subtracting as counting to the **left **on the number line as in the following examples:

Later, we’ll work with the number line when dealing with **Negative Numbers** and other types of numbers.

## Carrying and Borrowing (Regrouping)

It does get a little more complicated when you have more than $ 10$ things to add or subtract.

If we’re **adding numbers** greater than $ 10$, we may have to start “carrying” and “borrowing” since we have more than one number across. We’ll learn more about decimals later, but the numbers to the very right are called the “ones” (since these represent regular numbers), then the next over to the left are “tens” (since these each represent $ 10$ each), then “hundreds” (since these each represent $ 100$ each), and so on.

Let’s demonstrate “carrying” and “borrowing” with money, and we’ll work with regular dollars first (without cents – we’ll cover that later when we talk about decimals).

Let’s go on a shopping trip. Let’s say we have $ \$87$ saved from babysitting, and another $ \$45$ from Grandma for our birthday. What is the total amount of money we have? See how the $ 8$ and $ 7$ in $ 87$ means you have $ \$80$ (the tens) plus $ \$7$ more (the ones)?

Let’s add the amounts to see how much money we have. It’s easiest to line up the numbers vertically, so we are adding the correct number places together. The numbers should be lined up perfectly on the **right** and don’t need to be perfectly lined up on the **left**.

We always add **down** and start on the **right** (I know; this is the opposite from reading – sorry!)

Do you see how when we added **down** with the $ 7$ and the $ 5$, though, we got $ 12$, which didn’t fit (we can only put one number in at a time). We had to **carry** the $ 1$ from the $ 12$** **on the bottom to the **top** of the next (the tens). Then we added $ 1$, $ 8$, and the $ 4$ to get $ 13$. Since we are done at this point, we can just leave the $ 13$ (we don’t have to carry more). The final answer is $ 132$.

Think “start from the right”, “carry left”; it’s as simple as that! Sometimes you have to carry more than once, but now you can add **any numbers**!

Now let’s try a little** subtraction**, or “take away” with larger numbers. Sometimes we have to “borrow” when we try to subtract a larger number from a smaller one in a column.

Let’s say we go to the mall with $ \$64$ and buy a shirt for $ \$35$. How much money do we have left? (We’ll work on figuring out the tax later in the **Percentages, Ratios, and Proportions** section.)

Here’s how this works. Since we can’t subtract $ 5$ from $ 4$, we need to **borrow **$ 10$ from the next digit (the $ 6$). Then we have $ 14$ $ -$ $ 5$ $ =$ $ 9$. Since we borrowed from the $ 6$ in the tens place, we have to turn it into a $ 5$. Then, $ 5$ $ -$ $ 3$ $ =$ $ 2$. The answer is $ \$29$.

Do you see how, if we have to borrow, we are always lowering the number in the next column to the left? Sometimes we have to borrow more than once, but now you can subtract any number from a larger number!

It’s always a good idea to check your subtraction by **adding** the last two numbers to make sure you get the top number. For example,

**Learn these rules and practice, practice, practice!**

We’ll do a lot more adding and subtracting in the** Decimals **section.

**For Practice**: Use the **Mathway** widget below to try a **Describe an Addition **problem. Click on **Submit** (the blue arrow to the right of the problem) and click on **Describe the Transformation** to see the answer.

You can also type in your own problem, or click on the three dots in the upper right hand corner and click on “Examples” to drill down by topic.

If you click on **Tap to view steps**, or **Click Here**, you can register at **Mathway** for a **free trial**, and then upgrade to a paid subscription at any time (to get any type of math problem solved!).

On to **Multiplying and Dividing, including GCF and LCM **– you are ready!!