TenMarks teaches you how to write and solve decimal equations by addition and subtraction.
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Learn about Decimal Equation by Addition and Subtraction In this track, let’s learn how to do addition and subtraction equations. We’re given two problems. The first problem asks us to solve the equation and for us to check our answer. The equation is p - 3.2 = 7.8. Let’s do this one first, and then we’ll come back to the second one. So the equation is p - 3.2 = 7.8. As we can see, this is a subtraction equation because we are subtracting a value from p. So this is a subtraction equation. So the first thing we’ve got to do is remember that subtraction and addition are inverse operations. What that means is if a number is subtracted, I can undo that by adding the same number to it. So since in this equation, 3.2 is subtracted from p, I can undo it by adding 3.2 to both sides. So what we will do is we’ll take the equation, p - 3.2 = 7.8 and I will add 3.2 to both sides to get the value of p. So when I add 3.2 to the left side, well of course p - 3.2 + 3.2 will give me p + 0, which is p, and on the right inside, I will get 7.8 + 3.2 which is 11.0. So p = 11.0 is the value that I get. Now, the question or the problem also asks us to check our answer. So let’s do that. Let’s take this particular equation and replace p with 11. So p - 3.2 will become 11.0 - 3.2 = 7.8. Since all I did was replace the value of p as 11 in this equation. Once I did that, let’s actually see if this is correct. 11 - 3.2 is actually equals 7.8. So the left side and the right side are equal, which means the answer is correct and the value of p is indeed 11.0. The second problem says that Zack bought a pen and a pencil. So he bought two things. His total bill was $12.50. The pen cost $10.30. We need to figure out how much that the pencil cost. So let’s do problem second. The cost of the pen plus pencil equals $12.50 or $12.5. We know that the cost of the pen equals $10.3. So what do I know? Let’s do this. Let’s have q be the cost of pencil. So what do I know? What I know is if the cost of pen plus pencil was $12.5 and the pen was $10.3 that means the cost of the pen, which is 10.30 plus cost of the pencil is q equal 12.50. That’s the equation we have. Now that I know that the equation is 10.3 + q = 12.5, notice that this is an addition equation. So what I should be able to do is write the equation down, 10.3 + q = 12.50. I should be able to subtract 10.3 from both sides to solve for q. So what I get is 0 + q = 12.5 - 10.3, which is equal to 2.2, which means q = 2.2 or cost of pencil equals $2.20. We can also double check our answer. Let’s do that a real quick. If the cost of pencil is $2.20, let’s substitute or replace that here and see what happens. So the cost of pen is 10.3 plus the cost of pencil is 2.2. Both of them should be equal to 12.5. Well the left side is 12.5 and the right side is 12.5, which is correct. So, what have we learned? What we’ve learned in this particular track or video is if we have an equation that has a subtraction in it, it’s a subtraction equation. And in order to solve for p, I should add the value that’s been subtracted. Remember to do it on the left side as well as the right side, and that will solve for p. And I can double check that by replacing the value. Similarly, if we have an addition equation where the cost of the pen plus pencil equals 12.5 and we’re given the cost of the pen, I can write it in the form of an equation. Now since this is an addition equation, I can undo it by subtracting the value that’s added from both sides that gives me the value of q which is the cost of the pencil.