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# algebra

## Tags: Mathematik

23:11 Uhr, 23.07.2022

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):
"Ich möchte die Lösung in Zusammenarbeit mit anderen erstellen."

03:51 Uhr, 24.07.2022

$\frac{1}{11,25}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{1}{7,5}\cdot t\phantom{\rule{0.12em}{0ex}}=1|\cdot 11,25\cdot 7,5$

$7,5t\phantom{\rule{0.12em}{0ex}}+11,25t\phantom{\rule{0.12em}{0ex}}=84,375$

$18,75t\phantom{\rule{0.12em}{0ex}}=84,375$

$t\phantom{\rule{0.12em}{0ex}}=\frac{84,375}{18,75}=4,5$

04:08 Uhr, 24.07.2022

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.

$11.25=\frac{45}{4}$. I've used 4 at the denominator since $0.25=\frac{1}{4}$

$\frac{1}{11.25}=\frac{1}{\frac{45}{4}}=\frac{4}{45}=\frac{4}{5\cdot 9}=\frac{4}{5}\cdot \frac{1}{9}=0.8\cdot \frac{1}{9}$

Then I know by heart that $\frac{1}{9}=0.\overline{1}=0.11111...$. Thus $1/11.25=0.8\cdot 0.11111...=0.088888...$

greetings,
pivot

06:19 Uhr, 24.07.2022

alternative:

$\frac{1}{11,25}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{1}{7,5}\cdot t\phantom{\rule{0.12em}{0ex}}=1|\cdot 22,5$

The main denominator is $22,5=2\cdot 11,25=3\cdot 7,5$

$2t\phantom{\rule{0.12em}{0ex}}+3t\phantom{\rule{0.12em}{0ex}}=22,5$
$5t\phantom{\rule{0.12em}{0ex}}=22,5$
$t\phantom{\rule{0.12em}{0ex}}=4,5$

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.

$\frac{1}{\frac{45}{4}}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{1}{\frac{30}{4}\cdot t\phantom{\rule{0.12em}{0ex}}}=1$

$\frac{4}{45}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{4}{30}\cdot t\phantom{\rule{0.12em}{0ex}}=1$

$\frac{8}{90}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{12}{90}\cdot t\phantom{\rule{0.12em}{0ex}}=1$

$\frac{20}{90}\cdot t\phantom{\rule{0.12em}{0ex}}=1$

$t\phantom{\rule{0.12em}{0ex}}=1\cdot \frac{90}{20}=\frac{9}{2}=4,5$

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

08:34 Uhr, 24.07.2022

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.

15:50 Uhr, 24.07.2022

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.

15:50 Uhr, 24.07.2022

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.

15:50 Uhr, 24.07.2022

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.

16:04 Uhr, 24.07.2022

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

17:18 Uhr, 24.07.2022

Which $4,$ which 2 do you mean?

17:40 Uhr, 24.07.2022

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

17:44 Uhr, 24.07.2022

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