TenMarks teaches you how to solve rational number equations.
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Learn About Rational Number Equations In this lesson, let’s learn about equations where we are adding or subtracting or multiplying fractions and decimals. We’re given three problems. Let’s do them one by one. First one says, y-17.5=11. So, it is a subtraction equation, y minus a decimal value equals another value. Now, the first thing we do is if it’s a subtraction equation, we will add the same value which is +17.5. Let’s add 17.5 to both sides. On this side is easy, y-17+5+17.5=y. On this side, we’ve got a whole number 11 being added to it, 11 can also be written as 11.0. So, when I’m adding them, I can now add the columns together which gives me 28.5, 0 and 5 is 5, 1 and 7 is 8, 1 and 1 is 2 so y=28.5. So, that’s the first equation. Second equation gives us a different problem which is t/7.5=4. This is a decimal, this is a whole number. Let’s try this one. T/7.5=4. Now, since the variable t is being divided by 7.5. In order to eliminate everything from the left hand side except the variable, I would multiply it by 7.5 but I will do it on both sides, the left side and the right side. Keys to remember; always to do it for both sides. So, the left side becomes t x 1 which is t and the right side is 4 x 7.5 which is 30. So t is 30, it’s the answer. Third problem is x+1/9=-4/9. Let’s write this down. Let me scroll back up to see the problem, x+1/9=-4/9. That’s what we’re given. So, we’ve got a variable added to a fraction equals another fraction. So, since this is an additive equation, on the left side I will subtract 1/9 and on the right side, we will subtract 1/9. So, what do I get? On the left side, I get x because 1/9-1/9 is 0. On the right side, I get -4/9-1/9. This is what we need to solve. Since these are like fractions, both have the same denominator. On top, we have -4, -1 which will give me -5/9. So x=-5/9 which is the answer we were looking for. So, the key thing that we’ve learned in this particular video is when we are subtracting or doing an equation that involves subtraction, multiplication, or addition, key thing to do is one, if there’s a whole number being added to a decimal, the whole number can be represented as 11.0 because any zero after the decimal point and there’s nothing beyond that doesn’t mean anything. So, 11.0 +17.5 will give me 28.5. And the rule we applied is if the variable has something being subtracted from it, we add that same value to both sides; left and right to solve it. Second problem, t/7.5=4, t is being divided by 7.5. So instead let’s multiply it as well, do it on both the left and right to solve for t. Third one, x+1/9 so fraction is being added, so we subtract the same fraction from both sides which we will get this value on the right and since these are like fractions, I can simply solve for x=-5/9.