Fun base 10 application (Grocery Woes)

[shadowboy13]

If you are having difficulty figuring out the percentage of an item and don't have a calculator, you may utilize this trick (which i still don't know how it came to be in my mind).

Let: $a$ be a fractional number (percentage) and $b$ a whole number.

If you make $a$ be a whole number as well,then:

$a\times b$$=$$ab$

Then proceed to divide the product $ab$ by 100: $ab/100$$=$$n$

where n is the percentage of said item.

Example: What is 16% of 24.31$ ?

$16 \times 24$=$384$
$384/100$$=$$3.84$

Now: $16\times31$=$496$
$496/100$$=$$4.96$
$4.96/100$$=$$0.0496$

$3.84+0.0496$$=$$3.8896$

Which can be approximated to: $\approx 3.89$

Hope i can help people with this :)

 

[QuantumCurt]

That strikes me as being overcomplicated.

.16 x 24.31 would work just as well. If you don't have a calculator handy, and you have trouble doing longhand multiplication involving decimals, just move the decimal point over.

That would simplify it to 16x2431, then just do the long hand multiplication and you get 38896.

Now, since you moved the two decimals each over 2 spaces, you just move the ending decimal point back to the left 4 spaces and get 3.8896, or 3.90

Your method certainly works, but if someone is having trouble figuring out how to do percentages, I honestly can't see this method making it any easier to remember...lol

 

[shadowboy13]

It probably looks complicated and most likely is complicated, i wouldn't even attempt to bother reading this mess, if i were somebody else.

But just look at that practical example if it helps, I'm sorry it's not as useful as i thought :(

Edit: You can simply use the distributive property to work through the multiplication.

 

[QuantumCurt]

It's still cool from the perspective that it gives you a deeper understanding of what you're actually doing. I always try to look at problems from as many different angles as I can.

A long time ago, I used to always find percentages in a weird way too.

For instance, if I was trying to find, 35% of $67, I would take 67/100, which equals .67, then I would multiply that by 35, giving me $23.45

There again though, it makes it more complicated than it needs to be. Multiplying .35 x 67 gets the same answer.

 

[cjl]

Generally, if I don't have a calculator and I'm just trying to figure out percentages on the fly, I don't need perfect accuracy. Thus, I can make it a lot faster and easier. For example, the original example: 16% of 24.31.

1) 10% of 24.31 is 2.43
2) Add in half again (I'll approximate it as 1.20) --> 2.43+1.20 = 3.63
3) Add in a bit more, since I wanted 16%, not 15%, and I rounded down in the last step --> 3.63 + 0.25 (a bit more than 1% of 24.31) = 3.88

In the end, I'm only off by 0.01, but it was fast and easy to do mentally.

 

[1MileCrash]

Generally, if I don't have a calculator and I'm just trying to figure out percentages on the fly, I don't need perfect accuracy. Thus, I can make it a lot faster and easier. For example, the original example: 16% of 24.31.

1) 10% of 24.31 is 2.43
2) Add in half again (I'll approximate it as 1.20) --> 2.43+1.20 = 3.63
3) Add in a bit more, since I wanted 16%, not 15%, and I rounded down in the last step --> 3.63 + 0.25 (a bit more than 1% of 24.31) = 3.88

In the end, I'm only off by 0.01, but it was fast and easy to do mentally.

This is exactly what I do.

 

[shadowboy13]

If i may end this thread concisely, was the presentation well written? (proof)

It was one of my first times writing something like this.

 

[Hepth]

This thread made ke realize that I don't know what 16% of 25 is, but I DO know what 25% of 16 is... I'm so used to just brute force multiplication I'm missing easy ways. 27% of 66, or 66% of 27, one is easy one is hard...