Really not sure how to go about the two questions here and I have not been able to find something similar like this online. Would appreciate anyones help on how to answer the two questions! Thank you in advance.

This is the question:

  • $\begingroup$ the question tells you to do it by converting the decimals to fractions -- did you try that? $\endgroup$ – Matthew Towers Feb 10 '17 at 12:01
  • $\begingroup$ yeah I got 64/99 + 94/99 but i`m not sure if thats correct. $\endgroup$ – Alan Piggott Feb 10 '17 at 12:09
  • $\begingroup$ You can check if 94/99 is the same as.94949494... with the help of your calculator $\endgroup$ – Matthew Towers Feb 10 '17 at 12:50

When converting part a) to a fraction, you should get: $$\frac{67}{99}+\frac{94}{99}$$ If you divide by $99$, the digits on the numerator should repeat in the decimal form if the numerator is less than $100$ for positive integers.

Let me demonstrate why: $$\frac{67}{99}=\frac{67}{100}+\frac{67}{9900}=0.67+\frac{67}{9900}$$ We can continue this process: $$\frac{67}{9900}=\frac{67}{10000}+\frac{67}{990000}=0.0067+\frac{67}{990000}$$ $$\frac{67}{990000}=\frac{67}{1000000}+\frac{67}{99000000}=0.000067+\frac{67}{99000000}$$ Repeating this process infinitely gives: $$\frac{67}{99}=0.67+0.0067+0.000067\cdots=0.\dot{6}\dot{7}$$

So, try to convert the decimal forms you have into fractional form, and add the two fractions for part a) and multiply for part b).

If you wish, you can comment the answers you get below and I could verify them.


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