## Kiss those Math Headaches GOODBYE!

### 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,

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.

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

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)

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.

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.

A) 25 x 21
B) 25 x 26
C) 25 x 35
D) 25 x 42
E) 25 x 63
F) 25 x 81

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

### Multiplication Trick #3 — How to Multiply by 25 FAST!

Here’s the third in my series of multiplication tricks. The first was a trick for multiplying by 5. The second a trick for multiplying by 15, and now this one, a trick for multiplying by 25. Anyone see a pattern?

TRICK #3:

WHAT THE TRICK LETS YOU DO: Quickly multiply numbers by 25.

HOW YOU DO IT:  The key to multiplying by 25 is to think about quarters, as in “nickels, dimes, and quarters.”

Since four quarters make a dollar, and a dollar is worth 100 cents, the concept of quarters helps children see that 4 x 25 = 100.

Since four quarters make one dollar, children can see that twice that many quarters, 8, must make two dollars (200 cents). And from that fact children can see that 8 x 25 = 200.

Following this pattern, children can see that twelve quarters make three dollars (300 cents). So 12 x 25 = 300. And so on.

Fine. But how does all of this lead to a multiplication trick?

The trick is this. To multiply a number by 25, divide the number by 4 and then tack two 0s at the end, which is the same as multiplying by 100.

A few more examples:

16 x 25. Divide 16 by 4 to get 4, so the answer is 400. [In money terms, 16 quarters make \$4 = 400 cents.]

24 x 25. Divide 24 by 4 to get 6, so the answer is 600. [In money terms, 24 quarters make \$6 = 600 cents.]

48 x 25. Divide 48 by 4  to get 12, so the answer is 1200. [In money terms, 48 quarters make \$12 = 1200 cents.]

Try these for practice:

20 x 25

32 x 25

36 x 25

16 x 25

24 x 25

44 x 25

52 x 25

76 x 25

20 x 25  =  500

32 x 25  =  800

36 x 25  =  900

16 x 25  =  400

24 x 25  =  600

44 x 25  =  1100

52 x 25  =  1300

76 x 25  =  1900

But wait, you protest … what about all of the numbers that are not divisible by 4? Good question! But it turns out that there’s a workaround. You still divide by 4, but now you pay attention to the remainder.

If the remainder is 1, that’s like having 1 extra quarter, an additional 25 cents, so you add 25 to the answer.

Example:  17 x 25. Since 17 ÷ 4 = 4 remainder 1, the answer is 400 + 25 = 425.

If the remainder is 2, that’s like having 2 extra quarters, an additional 50 cents, so you add 50 to the answer.

Example: 26 x 25. Since 26 ÷ 4 = 6 remainder 2, the answer is 600 + 50 = 650.

If the remainder is 3, that’s like having 3 extra quarters, an additional 75 cents, so you add 75 to the answer.

Example:  51 x 25. Since 51 ÷ 4 = 12 remainder 3, the answer is 1200 + 75 = 1275.

Now try these for practice:

9 x 25

11 x 25

14 x 25

19 x 25

22 x 25

25 x 25

34 x 25

49 x 25

9 x 25  =  225

11 x 25  =  275

14 x 25  =  350

19 x 25  =  475

22 x 25  =  550

25 x 25  =  625

34 x 25  =  850

49 x 25  =  1225

Happy teaching!

—  Josh

Josh Rappaport is the author of five books on math, including the Parents Choice-award winning Algebra Survival Guide. If you like how Josh explains these problems, you’ll certainly  like the Algebra Survival Guide and companion Workbook, both of which are available on Amazon.com  Just click the links in the sidebar for more information!