Solving equations involving fractions

Solving equations involving fractions


>>Solving equations
involving fractions. There’s a couple
of little tricks. Well, there’s actually one trick
and it all comes from this. It’s Number Three right here. And it says to remove fractions
you multiply both sides by the LCD. Remember, from the
earlier videos, equations, whenever we solve them
we eliminate stuff. So you don’t want to
keep the fractions. You don’t have to find
a common denominator and make common denominators
and add them up. No. We eliminate it. So what we have to do to
eliminate the fractions is to multiply both
sides by the LCD. So the first thing you
have to find is an LCD. So I have two examples here. Let’s look at the first one. With all of our little
fractions we have there, we have thirds, six and halves. What is our common denominator? It’s six. So here’s
what we do with it. These are equations. So as long as you
multiply both sides by 6 it’s legal, both sides. Now remember whatever you do to the left you have
to do to the right. So here’s how we do it. We just distribute. 6 times 1 is 6. 6 divided by 3 is 2. And you notice no more fraction. Now you can multiply to
the top and then divide, or you could divide
and then multiply. Watch. 6 times 1 divided by 3. That’s 2. 6 divided by 3. That’s 2 times 1 is 2. Either way is fine. 6 times 5; 30. 30 divided 6. That’s 5. 6 divided by 6 is 1. 1 times 5 is 5. You get the idea. 6 times 3 is 18. 18 divided by 2 is 9. And then there is our
basic linear equation. Remember everything is going
to break down into these, these little basic
linear equations that we have right here, where
we get to do the subtract or add and then divide. So here’s our equation
and now we can solve it. So we minus 5 from both
sides and we get 2X equals 4 and then we divide
both sides by 2, and we end up with X equals 2. And then that’s the answer. All right. So let’s look at another one. LCD. What’s the LCD
for 5, 15, 3 and 5? And a lot of them
they’re very obvious. If you look at them,
we have 5 and 3, and when you multiply
together, you get 15. So that is our LCD. So we’re going to
multiply both sides by 15. Okay. 15 times 2 is 30. 30 divided by 5 is 6. If you notice, your
times tables need to be very strong
in order to do this. It’s a common thing with math. Multiplication tables
need to be strong. All right. I’m going to do the
division first. 15 divided by 15 is 1. 1 times 7 is 7. And we have to do this
side by 15 as well. Let me put that one in
red just so it matches because we’re supposed
to do this equally. Okay. 15 times X. So that’s
basically 15 divided by 3, which is 5, and then we
just bring down the X. So 15 times 11 is pretty big,
but 15 divided by 5 is 3. 3 times 11 is 33. And then there’s our equation. So this is like a two-sided
equation that we had here, just like these, which means
we need to pick an X side. So we’re going to put
all the X’s on the left because there’s more over there. I just like doing it that way. So we’re going to put
minus 5X minus 5 X’s. So 5X is on one side taken away,
and we’re going to take away 5 on the other; so
that gives us 1X. And then we can just
solve this one. Plus 7, plus 7. So X equals 40. And that’s it. So if you multiply by
the common denominator, it will get rid of
all the factions. You can only do this
with an equation because you need two sides. There are some practice
problems. Let’s do one more. I’ll get you started on it. I won’t do it. I’ll just get you started. All right. LCD here. Well, there’s
only one fraction. That’s 5. So let’s
rewrite our equation. [ Demonstration ] And then we’re going to multiply
both sides by that LCD of 5. So 5 times 3 is 15
divided by 5 is 3. And we also saw that the 5
and divided by 5 will be 1. You have to keep distributing. So 5 times 5. That’s 25. 5 times negative 2 is negative
10 minus 5 times X. Now it’s not going to cancel. It only cancels fractions. The rest of the numbers
just get multiplied. 5 and 5 is 25. It’s just normal distributing. There’s no real difference here. That’s all we’re doing is
distributing it to both sides. All right. And then we’re going to put
the X’s on the left side. So we’ll get rid
of those five X’s, but we have to add
five X’s over here. So that’s 8 X’s plus
25 equals negative 10. And then we just keep solving. Minus 25, minus 25. So 8X equals negative
35 divided by 8. So X equals negative
thirty-five eighths or negative four
and three-eighths. And then that’s the answer. Okay. So give the
other two a shot. Hit pause and try them. And when you un-pause them,
the answers will be there. Hit pause now. And there are your answers. So you should of
multiplied B by 15 and C by 4 and then solve the equation. Thank you.

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