# How to divide by decimal quickly?

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?

• 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?)? – Minus One-Twelfth Mar 11 at 9:00
• That is true. No, it is not multiple choice. With the answer in decimal form. – alicook Mar 11 at 9:06
• This link might be helpful: mathlearners.com/vedic-mathematics/… – Paras Khosla Mar 11 at 9:15
• +1 for figuring out how to display a long division using MathJax – 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 $$\frac{32.45}{253.11}=\frac 5{39}$$ $$\frac{253.11}{32.45}=\frac {39}5=\frac {78}{10}=7.8$$
• @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 !). – Claude Leibovici Mar 11 at 9:45
• @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. – Claude Leibovici Mar 11 at 9:58