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There's a question in a book,

16 2/3% of 600 gm - 33 1/3% of 180 gm

I was solving it like regular method which i use to find x% of a number, for eg.

20% of 200 =1/5*200=40.

But, when I convert mixed fraction (16 2/3%) into improper fraction (50/3), and then multiply it by 600 the result I get is wrong.

The book has a different formula of solving it:

[(50/3) * (1/100) * (600)] - [(100/3) * (1/3) * (180)]

I cant understand why should I add (1/100) in between the (50/30) and 600.

And why is there (1/3) in between (100/3) and 180.

Thanks in advance

Rishabh
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    $x$% of 600 gm is $\frac{x}{100}\times 600$gm. Now substitute $x=50/3$. Do the same thing for the next term. –  May 20 '19 at 09:35

1 Answers1

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$16 \frac{2}{3}\% \text{ of } 600 \text{gm} - 33 \frac{1}{3}\% \text{ of } 180 \text {gm}$

$\frac{50}{3}\% \text{ of } 600 \text{gm} - \frac{100}{3}\% \text{ of } 180 \text {gm}$

$\frac{50}{3}\% \times 600 \text{gm} - \frac{100}{3}\% \times 180 \text {gm}$

$\frac{50}{3} \times \frac{600}{\textbf{100}} \text{gm} - \frac{100}{3} \times \frac{180}{\textbf{100}} \text {gm}$

$\frac{50}{3} \times 6 \text{gm} - \frac{180}{3} \text {gm}$

$100 \text{gm} - 60 \text {gm} =\boxed{40\text{gm}}$.

To answer your query: whenever you remove the $\%$ you have to divide by $\textbf{100}$.

Vineet
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  • I noticed that 1/5 can be directly multiplied by the number to get the percentage of a number, but when there is an improper fraction (50/3 in our case) we have to first divide (50/3) by 100 and then multiply with the number, am I correct? – Rishabh May 20 '19 at 16:16
  • No Rishabh, you cannotjust multiply any number by $1/5$ to get the percentage. Consider this -- In a test of 40 marks you got 20. What is % of marks: According to your technique multiplying $20\times\frac{1}{5}=4%$ which is wrong. Percentage would be $\frac{20}{40}\times 100 = 50%$ – Vineet May 20 '19 at 16:30
  • Thank you @Vineet Kumar, got it! – Rishabh May 20 '19 at 17:46