Mental Math Multiplying Tricks Tricks to mentally multiply 10, 20, 30, 100, 1,000, etc.
Somewhere in themathlab.com, locked with a secret password, is a treasure page. This page has over 10 FREE gifts for you. You are now looking at the TREASURE FINDER page that will lead you to this password.

Read through the page below and do what it says. Write down any parts of the password as you find them.

You will need paper and pencil to keep track of your mental math results.

This treasure page's password has eleven letters in it, arranged in order from left to right as below. GOOD LUCK.

 1 2 3 4 5 6 7 8 9 10 11

The easiest number in the world to multiply by is !
doesn't change anything! Any number times is the number itself.

In math when an operation is done and nothing changes, this is known as an identity. So is the multiplication identity or the "multiplicative identity", if you want to be very correct.

Using this identity, we can grow into the second easiest number on the face of the Earth to multiply by. That number is !

Now ten is just a one with a zero attached at the end. So multiplying a whole number by is easy, you just multiply by and attach a zero at the end. In other words, the number stays the same except you place a zero at the end.

Ex 1: 10 x 5 = 50
Ex 2: 10 x 27 = 270
Ex 3: 10 x 3.5 = RED ALERT This is not a WHOLE number. We definitely have a decimal portion here.

Now if we place a zero after the 5 in 3.5, it will look like 3.50 and will not change the VALUE of the number at all!

But this number needs to be TEN TIMES BIGGER! You see, by placing at the far right of the number AFTER the decimal point we have added ZERO hundredths or NOTHING.

Have no fear though, the good part is coming now. The wonderful part about our number system is that it is BASED on ten numbers only. They are: , , , , , , , , ,and . Now we can create any number we want with just those digits. The numbers will be created according to which COLUMN we place the digits.

Now each column stands for a group of TEN. Each time we add a column before the decimal point, the number gets TEN TIMES BIGGER.

If we move that decimal over one column to the right, we have created 35 which is ten times bigger than 3.5

So for short we say that any time you multiply by TEN, simply move your decimal over one place to the right.

This concept also works for multiples of TEN like
,

,, and

, etc..
The number of zeros after the ONE tells you how many decimal places you should move the decimal TO THE RIGHT.

100 means move two places right.

1,000 means move three places right.

10,000 means move four places right, etc.

(note: remember that all whole numbers have a decimal point at their rightmost end, EVEN IF YOU DON'T SEE IT.
Ex: 13 can be written 13., or 13.0, or even 13.00
P
lacing zeros after a decimal point is adding NOTHING to the number. That is why whole numbers are usually written without their decimal point. It is the number's shortest form. Math people just assume you know it is there even though you can't see it.
)

Here, let's try a few. Click on the ? to see if you are correct. *Only works in Internet Explorer Browsers

1. 12.3 x 10 = ?
2. 345 x 100 = ?
3. 0.45 x 1,000 = ?
4. 6 x 10,000 = ?

NOW once you know how to multiply by TEN and 100 and 1,000 etc.,
you can easily multiply by TWENTY and 200 and 2,000 etc. and by THIRTY and 300 and 3,000 etc.. HERE"S HOW.

To multiply by TWENTY simply multiply by ten, and then DOUBLE your answer. This works because twenty is twice as big as ten.

Ex 1a: 14 x 20 = (ten times 14 = 140; double this to get 280)

*Some people prefer to double the number FIRST, and then multiply by ten.

Ex 1b: 14 x 20 = (double 14 and get 28; then multiply by ten = 280)

*This will work with 200 and 2000 also. Watch:

Ex 2a: 14 x 200 = (double 14 and get 28; then multiply by 100 = 2,800)

Ex 2b: 14 x 2,000 =(double 14 and get 28; then multiply by 1,000 = 28,000)

These can also be done by multiplying by 100 or 1,000 FIRST, then doubling.

Ex 2c: 14 x 200 =(14 times 100 = 1,400; double this to get 2,800)

Ex 2d: 14 x 2,000 =(14 times 1,000 = 14,000; double this to get 28,000)

To multiply by THIRTY,

EX 3a: 15 x 30 = (triple 15 to get 45, then multiplying by 10 = 450)

Ex 3b: 15 x 300 =(triple 15 to get 45, then multiply by 100 = 4,500)

Ex 3c: 15 x 3,000 =(triple 15 to get 45, then multiply by 1,000 = 45,000)

NOTE* as you might have guessed, this approach will work for 40, 50, 60, 70 80, 90 etc. as well.

Here, you try a few. Click on the ? to see if you are correct. *Only works in Internet Explorer Browsers

1. 13 x 20 = ?
2. 2.4 x 200 = ?
3. 0.6 x 30 = ?
4. 10.5 x 2,000 =?
5. 1.25 x 300 = ?

If you got those right, you are ready to find the treasure!

Below are eleven groups of multiplication problems.
Mentally multiply, and write down the answer to each problem in each group.

Add the numbers you get in each group. (You may use paper and pencil to add.)

Look for that sum in the DECODER BOX. It will give you a letter of the password.

 Group 1: 23.5 x 100 = \$0.15 x 10 = 4 x 1,000 = Group 2: 13.5 x 10 = 152 x 100 = \$5.62 x 10 = Group 3: 0.006 x 10,000 = 1.2 x 1,000 = 13.904 x 100 = Group 4: 5 x 30 = 15 x 20 = 3.2 x 30 = Group 5: \$13.50 x 20 = 2.4 x 40 = 0.6 x 30 = Group 6: 15.2 x 20 = 0.342 x 20 = 1.681 x 20 = Group 7: 2.34 x 2,000 = 3.2 x 3,000 = \$0.45 x 200 = Group 8: 31 x 40 = 47 X 200 = 5.8 X 30 = Group 9: 123 x 30 = 0.0089 x 100 = 5 x 3,000 = Group 10: 41 x 50 = 84 x 300 = 0.16 x 2,000 = Group 11: 3.9 x 20 = 7.08 x 200 = 24 x 300 = DECODER BOX

To learn even more of these mental math tricks try the book .

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