TenMarks teaches you how to add and subtract decimals.
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Learn about Addition and Subtraction of Decimals In this lesson, let’s learn about addition and subtraction of decimals. We are given three problems for us to evaluate one, two, and three. Let’s do them one by one. First one is adding two decimals, 1.2 with 3.45. Step A, we need to make sure that the decimals have equal number of digits after the decimal point. If not, we add zeroes. Here, we’ve got one digit. Here, we’ve got two. So, we need to write this as 1.20. A zero at the end after the decimal point has no meaning plus 3.45. This is the same. Now that we have both decimals having two digits we’re okay. Now, we can add them, 1.20 and 3.45. The key is aligning them. Step B is aligning them so that the decimal points match. If we want to add them, 0 and 5 is 5, 2+4 is 6, decimal point and 1+3 is 4. So, the result is 4.65. Let’s try the second problem which is 1.2-3.45. This is a subtraction operation. Again, instead of 1.2, we’ll write 1.20-3.45 for the reason given here. We need to always make sure that the numbers of digits after the decimal point are equal. It’s key thing to remember here. Point C is if it’s a subtraction operation, we subtract first the larger number. We put the larger number on top. I’ll show you how to do this. Here, 3.45 is the larger number when it’s compared to 1.20, so we put that on top, 3.45, -1.20. It doesn’t matter that we are trying to take away 3.45 from 1.20. We always put the larger number on top and then we subtract, 5-0 is 5, 4-2 is 2, 3-1 is 2. Point D is the sign of the result is sign of the larger number, not larger number in value because a negative number is always lower in value but larger among the decimals. So, the sign is the sign of the larger number, 3.45 was a negative sign, so the result will have a negative sign. Let’s try the third one which is -1.2-3.45. Here is point E, if both numbers have a negative sign or both have a positive sign, if both have the same sign, it’s an addition operation always. If both have different signs like this one, it’s always a subtraction operation. So, I can write this as, pull the negative out, 1.2+3.45, negative sign outside. Now, we follow the same principle, 1.2 becomes 1.20+3.45. To make sure that the number of digits after the decimal point are the same, we align them 1.20, 3.45 and we add, all of these have got a negative sign outside, 0+5 is 5, 2+4is 6, 1+3 is 4. So, the end result is -4.65. That’s the final answer that we’re looking for, -4.65. The key things that we’ve learned in this particular video is if we’re adding or subtracting decimals, we need to first make sure that the number of digits after the decimal point are always the same. It can’t be one and two. It has got to be two and two. We always align them with the decimal spot aligned on top. The larger number is always on top if it’s being subtracted in a subtraction operation and the net result of a subtraction operation is the sign of the larger number. So -3.45, since 3.45 is greater than 1.2, the negative sign rules and if we have two numbers, both with a negative sign or both with a positive sign, we always perform an addition operation like we did here by pulling out the negative sign but the end result is a positive or an addition operation and we copy the negative sign at the end.