>>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.