Easy trick no one taught you

The ancient Egyptians used a division method we call "partial quotients." It's a quick an intuitive way to do division.

How ancient Egyptians multiplied numbers

The problem 30 divided by 2 1/2 is documented in the Rind Mathematical Papyrus, Problem 76. The document is from ~1650 BC, which is more than 3,600 years ago.

"The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook"

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[unknowngalaxy]

Didn't know I was using ancient Egypt.

[xp_pk]

#2 you can do mentally. #1 makes more sense to do on paper. For this problem, #2 is easier and doesn't require paper, but #1 is good to know since it will generally work for any real number problem and it can also be used for polynomial division.

[TheDigiWorld]

Another way to do this is using the fact that 4 of 25s is a 100, and 300 contains 3 of 100s so it contains 3 x 4 of 25s or 12 of 25s

[josephwilles]

There are more efficient methods for divide 25.

Divide 25 is × 4 ÷ 100.


300 ÷ 25 = 300 × 4 ÷ 100 = 3 × 4 = 12

[samparkins]

As a student I will say that my calculator is way faster than both of these methods

[GallingEssay]

We can also multiply and divide the top and bottom with 4. It will become 1200/100 = 12

[NeverMatter]

2nd method is harder than 1st.. u have to first find how to split 300 which will exactly be divisible by 25.. maybe in this particular case its easy, (as easy as usual method) think of something like 3145÷85?? You will take 2x times than simple division..like....
85×30=2550
85 × 7 = 595
2550+595=3145, so,
30 + 7 = 37 which is the answer..
Moreover it uses the same logical sense as normal division method i.e.
In video,
25 × (what gives(quotient)) = 300
25 × (10y + z) = 300[10y+z is the quotient]
250y + 25z = 300
250y + 25z = 250 + 50 [splitting 300 as (250 + 50) by conparing L.H.S terms]
y = 1, z = 2
10y+z = 10+2 = 12 which is the answer
The same concept is used in normal division if analysed deeply..
Still I admire the way you approach problems creatively and share new ideas of others... I felt this trick wouldn't be helpful until & unless we get simple numbers where division can be done in seconds.

[sharpnova]

modern students and ancient students both did it both ways. both of these are essentially number sense

[ionex]

That is just reverse of long division.
An easier way is to write 25 as 4/100
So it becomes 300*4/100
You can now cancel the zeroes and you're left with 3*4=12

[shambhav]

That's so obvious, lol. The reason you'd even bring out a paper and pen is if you needed a systematic approach when the numbers are too big, and can't go searching for perfectly aligned multiples.

[Waermelon]

Apparantly i was using the ancient egyptians method 😅

[creativeaj]

Todays schools are teaching more efficient!

[ninesevenpotatoes]

Method 1: Find multiples of 25 and use that to find ?x25=300.

Method 2: Find multiples of 25 and use that to find ?x25=300.

Every 1/60th of a minute you are writing a sentence a second passed in Chile.

[DCTOR-ZED]

One trick I like can often be applied to such methods and that is to realize that you don't need to make sure you have the optimum answer for each step as long as you allow both addition and subtraction as well as allowing the same digit place more than once. Sometimes it's easier to make a best guess and move forward than to make sure each step is exactly correct. The correct digit might be a 5, but if you don't know you might guess 6, plug that in then realize the result could have a -1 for the next step. Depending on the numbers involved, allowing yourself to guess and go is quicker than turning each step into it's own separate math problem to solve.

[lambda]

Ok but we want something like this: 432/17.5 what ancient Egypt says?

[dakeypunchar]

Just multiply by 4 and divide by 100

Edit: OMg, got some likes for the first time and comments as well. Mommy Daddy's friend's son is famous 😍😍😂

[SilntObsvr]

For divisions by 25 or 50, I multiply the hundreds column by four or two as appropriate, and done. Any remainder sort of "drops out".

[camerongray]

Or you just remember your multiplication rainbow facts.
When dividing by 25, times by 0.04
So only calculation you do is 3x4=12

[ashleyzinyk]

How is that "easier" than long division?

[bobh]

Method 2 is a short cut but requires a lot of insight and only is easy in certain situations.
From my experience, you can teach method 1 successfully to a vast majority of students. If they understand method 1, they may be able to use #2 as a shortcut. But if they can’t use #1, they usually don’t have the insight to break it up like #2.