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.

  • $\begingroup$ 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

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 $$\frac{32.45}{253.11}=\frac 5{39}$$ $$\frac{253.11}{32.45}=\frac {39}5=\frac {78}{10}=7.8$$

  • $\begingroup$ 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

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