6 machines can produce : 270 bottles?

Question

I always confuse a concept .....here i am posting it as a math problem.

suppose,

In 1 min, 6 machines can produce : 270 bottles

Then
In 1 min, 1 machine can produce :

(1)270/6

(2)270 *6 bottles ?

which is correct ? i confuse whether i need to multiply or divide .

It seems here i need to divide because obviously 1 machine will produce less number of bottles ...............BUT i have noticed in some problems we multiply .....i dont understand when to multiply and when to divide ................can anybody explain this stuff with some example ?

Thank you

Answer 1

Ask yourself, based on common sense and everyday experience, whether the answer will be greater or less than the number you are given.

Machines producing bottles: Fewer machines mean fewer bottles. You are right.
Time taken to dig a garden: more people digging means less time needed.

1 person takes 12 hours to dig a garden. How long will 4 people take?
Obviously less time than one person. So the answer has to be 12 / 4 = 3 hours, and not 12 * 4 = 48 hours.

Answer 2

6 Machines make 270 bottles
If you only have 1 of those machines, you can only make what 1 machine could do.
The answer is 270/6=45 bottles.
It makes sense that 1 machine makes less than 6 machines, right?

Now, to explain this better as to why you divide here, it is because we had 6 machines, now only 1, which is 1/6 the work power you had before, so there are going to be less bottles made. If we take 45 (the amount of bottles that 1 machine can produce in 1 min) and multiple that number by 6(the total amount of machines in the first part) we would get 270 bottles, working backwards.

Answer 3

When two things are compared, the result is something known as a "rate". A rate is always a ratio of two observations. In physics, speed is the best example. A car going 30 MPH involves the measurement of distance (miles) and the measurement of time(hours).

Ratios are essentially fractions. "Per" is the English language equivalent of the Math language term "divided by". Therefore, if 6 machines produce 270 bottles in 1 minute, then this is 6 machines per 1 minute per 270 bottles. The ratio is then expressed mathematically as 6/1/270.

NOTE: this is a very unusual fraction, but read on ....

However, just as the facts can be reworded, the ratio can be re-cast. If 270 bottles are being produced in 1 minute by 6 machines, then the ratio is now 270 per 1 per 6 or 270/1/6.

The importance of this is "units". A unit is the physical thing the rate is describing. In the speed example, the units were miles and hours. Keeping track of units is CRITICAL when solving rate problems. The reason for this is one of the fundamental rules of algebra which states:

anything/anything = 1.0000

For example:

If a car is going 30MPH, then figure out how far it travels in two hours. The English answer is obvious, but the math answer isn't.

What happens is

30 Miles
---------- times 2 hour = 30*Mile* 2*hour/1*hour
1 hour

this is 60*mile*hour/hour

remember however, that hour/hour = 1.000, so the answer is clearly 60 mile(s)

/////////////////////////////// therefore ///////////////////////////////////////////

Beware the dark side. It has filled your teacher with pride and your teacher is therefore trying to confuse you with fractions of the form minutes/machines/hours. Fractions are not expressed in terms of 1/6/270. However, there is hope young apprectice.

Another mathematical rule is that A/B/C = A*C/B

Therefore, 1 min/6 machines/270 bottles is really 270 bottle*minutes/6 machines. Can you see that to use this particular form of the rate to solve for "bottles" one has to develop a rate in terms of machines/minutes? Next, all ones needs to do is multiply the two rates. The answer then takes the form:

(270 bottles*min/6 machines) times (1 machine/1 min) =
(270*bottles*min*1*machine)/(6*machine*1*min) =
(270*bottles*1*1*1)/(6) = 45 bottles

(since min/min and machine/machine = 1.0000)

The answer is obvious in terms of English, of course. If six bottle driods are all producing 45 bottles per minute then all six driods will produce 270 bottles in total.

Hope this helps, and beware the dark side of the force ....

Answer 4

Use cancelation of units which you found out in Chemistry or Physics: entire Bottles (to be produced in 4 minutes) = [(270 Bottles/6 Machines)/Minute ] x [10 Machines] x [4 Minute] Machines will cancel out. Minute will cancell out. Leaving Bottles because of the fact the unit. for this reason: entire Bottles = (270/6) x (10) x (4) entire Bottles = 40 5 x 40 entire Bottles = a million,800 (answer) hint: that's a miles better answer somewhat than using stepwise ratio and share. stable success!

Answer 5

to get what each machine produces: 270/6 = 45
if the question was saying: "if every machine produces 45 bottles and we have 6 machines, then what is the total number of bottles produced??", the answer would be 45*6 = 270
Another example, let's say i have 5 apples and i want to ''divide'' them on 5 persons that they will all have equal amounts then ofcourse every one will take just one apple, to put this in a mathematical equation it will be as the following 5/5 = 1
multiplication is the opposite of division, if i told you that i gave EACH of my 5 friends an apple then what is the total numbers of apples we have??? ofcourse it will be 5*1 = 5
which is also 1+1+1+1+1 = 5
if there is something u don't understand from what i wrote, plz feel free to ask

Answer 6

(1)
6 machines = 270 bottles
1 machine= 270/6
=45 bottles
1 machine produces 45 bottles

Answer 7

Maybe this will help...

6 machines = 270 bottles

to get one machine, divide both sides by 6...
(6/6) machine = (270/6) bottles
1 machine = 45 bottles

Answer 8

you must divide. Simply thinking whitout maths, one machine must produce less than 6 machines!
Answer 270/6 =45 bottles

Answer 9

1)270/6