2
$\begingroup$

My friend asked me to help solve a problem in which she cannot use a calculator.

$$ \require{enclose} \begin{array}{r} 32.45 \enclose{longdiv}{253.11} \\[-3pt] \end{array} $$

What is the best method to approach this in an exam situation - i.e. relatively quickly?
Thanks for your help.

$\endgroup$
  • $\begingroup$ You can just focus on finding $$ \require{enclose} \begin{array}{r} 3245 \enclose{longdiv}{25311},\\ \end{array} $$ since $\frac{253.11}{32.45} =\frac{25311}{3245}$. By the way, is the exam multiple choice? And what type of answer does it want (decimal form, or remainder?)? $\endgroup$ – Minus One-Twelfth Mar 11 at 9:00
  • $\begingroup$ That is true. No, it is not multiple choice. With the answer in decimal form. $\endgroup$ – alicook Mar 11 at 9:06
  • $\begingroup$ This link might be helpful: mathlearners.com/vedic-mathematics/… $\endgroup$ – Paras Khosla Mar 11 at 9:15
  • 1
    $\begingroup$ +1 for figuring out how to display a long division using MathJax $\endgroup$ – bubba Mar 11 at 9:20
2
$\begingroup$

May be $$32.45=\frac{3245}{100}=\frac{5 \times 11 \times 59}{100}$$ $$253.11=\frac{25311}{100}=\frac{3 \times 11 \times 13 \times 59}{100}$$ could help to get $$\frac{32.45}{253.11}=\frac 5{39}$$ $$\frac{253.11}{32.45}=\frac {39}5=\frac {78}{10}=7.8$$

$\endgroup$
  • $\begingroup$ It was quite a good idea to factorise the numbers. $\endgroup$ – Henrik Mar 11 at 9:42
  • $\begingroup$ @Henrik. I suppose that this was the goal of the problem. Dividing by $5$ or by $11$ is simple mentally; by $13$, they used to teach it at my time (looooong time ago !). $\endgroup$ – Claude Leibovici Mar 11 at 9:45
  • $\begingroup$ That's great but how do you get to the factorisation? What is the thought process behind - if I can ask that? Do you just start with 5 or 10 usually? I can see as soon as you start doing that - it simplifies quickly. $\endgroup$ – alicook Mar 11 at 9:51
  • $\begingroup$ @alicook. Multiple both numbers by $100$ to kake them whole numbers; this does not change the ratio. Now, have a look at en.wikipedia.org/wiki/Divisibility_rule and use mental calculation. $\endgroup$ – Claude Leibovici Mar 11 at 9:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.