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RASTA

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23:11 Uhr, 23.07.2022

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tag!
I need help in understanding a step in solving an equation.
1/11.25 * t + 1/7.5 * t =1

0.0888 * t + 0.1333 * t =1


What is not clear to me is how we got the decimals. what operation had to be performed so I could get 0.0888 and 0.1333

I put the equation in a math solver and it gives this as the first step of the solution but I am lost about how the decimals were gotten.

Vielen Dank im Voraus,

Für alle, die mir helfen möchten (automatisch von OnlineMathe generiert):
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supporter

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03:51 Uhr, 24.07.2022

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111,25t+17,5t=1|11,257,5

7,5t+11,25t=84,375

18,75t=84,375

t=84,37518,75=4,5


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pivot

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04:08 Uhr, 24.07.2022

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Hi,

it seems that the solution is somehow generated by a computer system, which is not always an efficient way for a human. Nevertheless I show you how I would transform 1/11.25, for instance.

11.25=454. I've used 4 at the denominator since 0.25=14

111.25=1454=445=459=4519=0.819

Then I know by heart that 19=0.1¯=0.11111.... Thus 1/11.25=0.80.11111...=0.088888...

greetings,
pivot
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supporter

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06:19 Uhr, 24.07.2022

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alternative:

111,25t+17,5t=1|22,5

The main denominator is 22,5=211,25=37,5

2t+3t=22,5
5t=22,5
t=4,5

That is even easier to calculate, in my mind the easiest way of doing it.

PS:
You should not turn fractions into decimal figures until the end of the calculation,
particularily not if the figures have to be rounded!
As Pivot said : Use fractions instead to avoid rounding problems which
affect the best possible result.

1454t+1304t=1

445t+430t=1

890t+1290t=1

2090t=1

t=19020=92=4,5

As you can see: There are several roads leading to Rome as so often in mathematical affairs.




Antwort
N8eule

N8eule

08:34 Uhr, 24.07.2022

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To make a long story short:
If you use a calculator,
and input
1:11.25
the calculator will reasonably output
0.08888888

"What operation...?"
It's a division.

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RASTA

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15:50 Uhr, 24.07.2022

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thank you so much @ supporter, pivot and 8neule. Very interesting all that. I was particularly thrown by the 2 and 4 and how to get to those.
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RASTA

RASTA aktiv_icon

15:50 Uhr, 24.07.2022

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thank you so much @ supporter, pivot and 8neule. Very interesting all that. I was particularly thrown by the 2 and 4 and how to get to those.
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RASTA

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15:50 Uhr, 24.07.2022

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thank you so much @ supporter, pivot and 8neule. Very interesting all that. I was particularly thrown by the 2 and 4 and how to get to those.
RASTA

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16:04 Uhr, 24.07.2022

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I have already done it the way supporter showed. I had done it like this. But what I was in doubt was how to get the decimals and the 2 and 4 which you all explained so clearly.

1/11.25 x t + 1/7.5 x t =1
t/11.25 + t/7.5 =1
t/11.25 + t/7.5 =1
7.5t + 11.25t / 11.25 x 7.5 =1
7.5t + 11.25t / 11.25 x 7.5 =1
18.75t / 84.40 =1
18.75t / 84.40=1
84.40(18.75t)/(84.40)=84.40 x 1
84.40(18.75t)/(84.40)=84.40 x 1
18.75t =84.40
18.75t =84.40
18.75t/18.75 = 84.40/ 18.75
18.75t/18.75 =84.40 / 18.75
cancelling,
t= 4.5
Antwort
supporter

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17:18 Uhr, 24.07.2022

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Which 4, which 2 do you mean?
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RASTA

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17:40 Uhr, 24.07.2022

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the teacher gave this other way but it more complex.
I am attaching pic. that is why I ask how the 4 an d the 2 were gotten. But you explained it when you developed your example

rsz_20220724_113157
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RASTA

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17:44 Uhr, 24.07.2022

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I got it once you wrote that the decimal part .025 = 1/4. Right then and there I tumbled into it. and then the 2 because it was 7.5 so the decimal part was .5 which half of.. = 2.
That is how the 4 and the 2 came into the equation