Multiplication Trick: x 25

This is a simple trick that anyone can easily learn. It is just a trick for
multiplying a number by 25.

If someone asked you what 25 times 36 equals, you’d probably be tempted
to reach for a calculator and start punching buttons. But remarkably, you’d
probably be able to work it out even faster in your head.

Since 25 is one-fourth of 100, multiplying by 25 is the same thing as
multiplying by 100 and dividing by 4. Or, even more simply:
first divide by 4,
then add two zeros.

Here’s the example:

Problem: 36 x 25
First divide 36 by 4 to get 9.
Then add two zeros to get: 900.
That, amazingly enough, is the answer.

Another example: 88 x 25
First divide 88 by 4 to get 22.
Then add two zeros to get: 2,200.

Now try these problems in your head:

a) 25 x 12
b) 25 x 28
c) 25 x 48
d) 25 x 60
e) 25 x 84
f) 25 x 96

Here are the answers:
a) 300
b) 700
c) 1,200
d) 1,500
e) 2,100
f) 2,400

But, you say, what if the number you start with is not divisible by 4.
No problem. Just use this fact:
if the remainder is 1, that is the same as 1/4 or .25
if the remainder is 2, that is the same as 2/4 or .50
if the remainder is 3, that is the same as 3/4 or .75

So take a problem like this: 25 x 17
dividing 17 by 4, you get 4 remainder 1.
But that is the same as 4.25
Now just move the decimal right two places (same as multiplying by 100)
Answer is: 425

Another example: 25 x 18
dividing 18 by 4, you get 4 remainder 2.
But that is the same as 4.50
Now move the decimal right two places.
Answer: 450

Another example: 25 x 19
dividing 19 by 4, you get 4 remainder 3.
But that is the same as 4.75
Now move the decimal two places to the right.
Answer is: 475

Now try these in your head:
A) 25 x 21
B) 25 x 26
C) 25 x 35
D) 25 x 42
E) 25 x 63
F) 25 x 81

And here are the answers:

A) 525
B) 650
C) 875
D) 1,050
E) 1,575
F) 2,025

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8 Responses to “Multiplication Trick: x 25”

  1. Tracy Arnt says:

    I often post inspiration for the day, quirky bits of this and that to get my students engaged at the beginning of class. This is great! We talk about what it looks like as money all the time, so how many quarters in a dollar. . .
    Thanks, Tracy Arnt

  2. Evelyn Saenz says:

    I have loved your blog for years and now that I am again homeschooling a teen I look forward to lots more exciting math adventures.

    Just wanted to let you know that I recommended this blog to my Celebrating Teachable Moments Facebook Fan Club today.

  3. Scott says:

    This mental math trick is just what some of my students need. I plan on using it next week in class and then teach the skill to my class. I predict that they will be quizzing the rest of the school and their parents for days with this.

    Do you know where I can find more of these tricks/skills. Thank you.

  4. fahad says:

    This is an amazing trick. I surely will write a post about it now. Great job :)

  5. Garret says:

    Great trick. Thanks. Now whenever I need to multiply by 25 I will be able to quickly do it in my head.

    math games for the classroom
    Learning is more than just merely filling a cup it is the lighting of a fire!

  6. Garret says:

    Just added your rss feed. I look forward to your upcoming posts.

    Thanks again!

  7. Liliana says:

    But of course 0.AAA just CAN’T equal 1 by your logic, since there’s a reamnider of 1 that’s infinitely small. So you seriously just tried to prove that one tenth multiplied ten times, resulting in ten tenths or simply one, is not actually one because there’s the irreducible unreachable r1 . ERGO, 0.999 is 1, or ten tenths IS NOT 1. YOU DECIDE. And THAT, folks, is how you jam mathematical proofs into the skull of the uneducated. ? Any questions???? You’ve just been MATH’D.