This section covers:
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. First of all, 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, and 8, and odd numbers are those that end with 1, 3, 5, 7, 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!
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.
Let’s first talk about simple adding and subtracting. Adding numbers is just like adding dresses. Subtracting numbers is just like taking away dresses. 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! 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 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!
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 inside and move to the outside. 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.
Memorize your subtraction 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 lefton the number line as in the following examples:
Carrying and Borrowing (Regrouping)
Now, you probably noticed that it gets a little more complicated when you have more than 10 dresses (if you are so lucky!) to add or subtract. This is because we only have 10 fingers!
If we’re adding numbers greater than ten, 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 (this is a lot – I used to make 50 cents an hour, girls!), and another $45 from Grandma for our birthday. 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). So 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). So the final answer is 132.
Think “start from the right”, “carry left” (if you need to). It’s as simple as that! Sometimes you have to carry more than once, but now you can add any numbers!
So 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 on in a column.
Let’s say we go to the mall with $64 and buy a dress for $35 (we’ll work on figuring the tax later). How much money do we have left?
So here’s how this works. Since we can’t subtract 5 from 4, we need to borrow 10 from the next digit (the 6). So we have 14 – 5 = 9. Since we borrowed from the 6 in the tens place, we have to turn it into a 5. So 5 – 3 = 2. So 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!
So here’s how this works. Since we can’t subtract 5 from 4, we need to borrow 10 from the next digit (the 6). So we have 14 – 5 = 9. Since we borrowed from the 6 in the tens place, we have to turn it into a 5. So 5 – 3 = 2. So 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!
And the good thing about this type of borrowing is that we don’t have to return!
It’s always a good idea to check your subtraction by adding the last two numbers up to make sure you get the top number. For example,
We’ll do a lot more adding and subtracting in the Decimals section.
For Practice: Use the Mathway widget below to try a Describe a Transformation 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.
On to Multiplying and Dividing, including GCF and LCM – you are ready!!