Addition and Subtraction of Integers
Addition and Subtraction
Since this is an overview of all the foundational concepts, I want to devote a little bit of time to the four basic operations. In this video, I’m going to discuss how to perform addition and subtraction with large integers, decimals, and fractions. First, large integers. Let’s take, for instance, 248 and 135.
First, to add these together, what you want to do is you want to line things up at the decimal point. In this case, the numbers don’t have anything past the decimal point, so you just line them up at the ends. You then start from the right and you add vertically. We have 5 plus 8. That’s equal to 13.
We can’t fit 13 in this single decimal place here, so we’ll write a 3 and carry the 1. Now, when we go to add this column, we have three numbers in the column. We have to add 1, 4, and 3. Together, those are 8. Then, we add 2 and 1 in the final column to get 3. That’s addition. Let’s try out the same two numbers with subtraction.
We’ll have 248, but this time minus 135. We’ll subtract 5 from 8. 8 minus 5 is 3. Then, we move to the next column. 4 minus 3 is 1, and 2 minus 1 is 1. That’s subtraction with integers. Next, we’ll go ahead and move on to decimals.
Decimals are going to work largely the same way as integers, but with decimals you have to be careful to line up the decimal points so that you’re adding and subtracting in the right columns. Let’s take points .435 and we’ll add .019. I’ve already done it here, but if you don’t already have it lined up, what you want to do is line up with decimals as I was mentioning back here.
Line up the decimals vertically. That way, you know you have the right place values lined up. You’ll have 5 plus 9, which is 14. Again, we can’t put 14 down here, so we have to carry the 1. Now we have 1 plus 3 plus 1. That’s equal to five. Then, over here we just have 4 and 0, so we’ll write a 4.
Now that we’ve added these, we need to make sure the decimal point drops in the right spot. We’ll add a leading 0. This is the addition of decimals. We’ll once again take the same two decimals and do subtraction. .435 minus .019. Now we have 9 minus 5. Unfortunately, that’s a negative number, so we have to borrow a one from over here.
This 3 is going to become a 2 and this 5 is going to become a 15. Now we have 15 minus 9. That gives us 6. 1 minus 2, because we borrowed the 1 for the 15, 2 minus 1 is 1. 4 minus 0 is just going to be 4. Once again, we’ll drop the decimal and add the leading 0. This is integers and decimals, and those are both pretty straightforward.
Then we have fractions. Fractions are easy enough if the denominator is the same. If the denominator is not the same, you have to convert one or both of the fractions to a different denominator before you can add or subtract them. Let’s take, for instance, one third and one sixth. We’ll use these as our example this time.
One third plus one sixth. We can’t just add them together, because the denominators are different. What we have to do is get a common denominator between the two fractions. To do that, you find the least common multiple of both the denominators. In this case, the least common or the least common multiple is 6, because 6 and 3 both go into 6 evenly.
3 goes into 6 two times. We only to multiply one third by 2 over 2. That gives us 2 over 6. Now what we have is 2 over 6 plus 1 over 6. Now that the denominators are the same, all we have to do is add the numerators together. Then we retain the same denominator as both of the fractions. We have a 6 in the denominator and 2 plus 1 is equal to 3. We have 3 over 6. That’s addition.
We’ve already done the hard part of converting that the two fraction- or of achieving a common denominator between the two fractions. For subtraction, all we have to do is write the converted form.
We have two sixths minus one sixth. Just like we did above, we’ll retain the 6 in the denominator and then we’ll just use subtraction on the numerators. 2 minus 1 is 1. That is addition and subtraction for integers, decimals, and fractions.