

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." 

$\frac{1}{\mathrm{11,25}}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{1}{\mathrm{7,5}}\cdot t\phantom{\rule{0.12em}{0ex}}=1\cdot \mathrm{11,25}\cdot \mathrm{7,5}$ $\mathrm{7,5}t\phantom{\rule{0.12em}{0ex}}+\mathrm{11,25}t\phantom{\rule{0.12em}{0ex}}=\mathrm{84,375}$ $\mathrm{18,75}t\phantom{\rule{0.12em}{0ex}}=\mathrm{84,375}$ $t\phantom{\rule{0.12em}{0ex}}=\frac{\mathrm{84,375}}{\mathrm{18,75}}=\mathrm{4,5}$ 

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 

alternative: $\frac{1}{\mathrm{11,25}}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{1}{\mathrm{7,5}}\cdot t\phantom{\rule{0.12em}{0ex}}=1\cdot \mathrm{22,5}$ The main denominator is $\mathrm{22,5}=2\cdot \mathrm{11,25}=3\cdot \mathrm{7,5}$ $2t\phantom{\rule{0.12em}{0ex}}+3t\phantom{\rule{0.12em}{0ex}}=\mathrm{22,5}$ $5t\phantom{\rule{0.12em}{0ex}}=\mathrm{22,5}$ $t\phantom{\rule{0.12em}{0ex}}=\mathrm{4,5}$ 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. $\frac{1}{\frac{45}{4}}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{1}{\frac{30}{4}\cdot t\phantom{\rule{0.12em}{0ex}}}=1$ $\frac{4}{45}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{4}{30}\cdot t\phantom{\rule{0.12em}{0ex}}=1$ $\frac{8}{90}\cdot t\phantom{\rule{0.12em}{0ex}}+\frac{12}{90}\cdot t\phantom{\rule{0.12em}{0ex}}=1$ $\frac{20}{90}\cdot t\phantom{\rule{0.12em}{0ex}}=1$ $t\phantom{\rule{0.12em}{0ex}}=1\cdot \frac{90}{20}=\frac{9}{2}=\mathrm{4,5}$ As you can see: There are several roads leading to Rome as so often in mathematical affairs. 

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. 

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. 

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. 

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. 

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 

Which $4,$ which 2 do you mean? 

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 

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 