Question

I need help.... DiPaloma University had a faculty reduction and lost 1/6 of its faculty. If 110 of its faculty were left after the reduction, how many faculty were there originally?

Answer 1

This equation will help you solve the problem. What if 1/6 is 110?

Answer 2

I am having a hard time figuring out 1/6 of 110

Answer 3

So, with problems like this, you want to set up an equation, with variables. What we WANT to know is the amount they originally had, so lets call that our variable, say 'x'. (there's nothing magical about x, but we're used to dealing with it!)

So, lets see what it is saying.....we started with x, then lost 1/6th of x, and ended up with 110. From there, you can set up your algebra equation:
\[x-\frac{ 1 }{ 6 }x=110\]
From there, solve for x.

Answer 4

why is there another x on the other side of 1/6

Answer 5

x is the starting amount. THen we subtract 1/6th OF x, so that's 1/6*x.

Answer 6

It's like if I said 1/6th of 18, you'd write that as \[\frac{ 1 }{ 6 }*18\]

Answer 7

(\[\frac{ 1 }{ 6 }x\] is just shorthand for \[\frac{ 1 }{ 6 }*x\]

Answer 8

how do I multiply a fraction by "x"?

Answer 9

x is just the variable, that we're treating as an "unknown" number. So, we re-write \[x=1*x=\frac{ 6 }{ 6 }*x\]

Answer 10

so, you get \[x-\frac{ 1 }{ 6 }x=\frac{ 6 }{ 6 }x-\frac{ 1 }{ 6 }x=\frac{ 5 }{ 6 }x\]

Answer 11

Follow so far?

Answer 12

kind of... I just feel lost I do not understand how to come up with what you have so far.

Answer 13

What you did on one side you did on the other?

Answer 14

Correct....so originally, we had a starting amount of some unknown amount, and we're taking away a sixth of that amount, so we end up with 5/6th of that amount. All the symbols are is a way of saying that in shorthand, which is what math is
Make sense now?

Answer 15

5/6 because we subtract 1/6 from 6/6?

Answer 16

correct, because a whole is the same as 6/6th

Answer 17

ok I understand that part

Answer 18

So, we're left with 5/6th of our original is equal to 110, or in math, \[\frac{ 5 }{ 6 }x=110\]

Answer 19

Now, we WANT to know x, not 5/6th of x. So to fix that, we use the rule that we can multiply both sides of an equation by the same number. To get x out of 5/6th x, we need to multiply by the RECIPRICOL of 5/6th, which is 6/5th (Because 5/6*6/5=1)

Answer 20

Make sense?

Answer 21

because they cancel eachother out?

Answer 22

Correct.

So, in\[\frac{ 6 }{ 5 }*\frac{ 5 }{ 6 }x=\frac{ 6 }{ 5 }*110\] math, we get

Answer 23

550/6 and then simplify?

Answer 24

Npe.....660/5th

Answer 25

\[\frac{ 6 }{ 5 }*110=\frac{ 6 }{ 5 }*\frac{ 110 }{ 1 }=\frac{ 6*110 }{ 5*`1 }\]

Answer 26

132?

Answer 27

Yep

Answer 28

gosh I feel dumb lol thank you

Answer 29

No problem, good luck!

Answer 30

thank you