PolarMath Page

PolarMath Page!

The bears have been working hard at their math and want to share this cool math tricks with you.

1. Here is a method to multiply two-digit numbers in your head!!

This is how it works:

Example 1:

Let's say you want to multiply 14 x 18. We are going to use 10 as a base number.

1. Write down the uppers. (Well, actually you'd be doing this in your head...)
4 8

14 x 18 =

Since 14 is 4 more than 10, write "4" above 14. Since 18 is 8 more than 10, write 8 above 18.

2. Cross-add.
14 + 8 = 22

18 + 4 = 22

Think: 220

You can either add 14 + 8 or 18 + 4... the answer is 22 either way.

We are using 10 as a base, so "22" is really "220."

3. Multiply.

4 x 8 = 32

Multiply the uppers.

4. Add

220 + 32 = 252.

Add steps 2 and 3 together to find the answer!!

Example 2:

Let's say you want to multiply 9 x 19. Use 10 as the base again.

1. Write down the uppers.
-1 9

9 x 19 =

In this example, 9 is less than 10, so write -1 above the 9.

2. Cross-add.
9 + 9 = 18

-1 + 19 = 18

Think: 180

We are using 10 as a base, so "18" is really "180."

3. Multiply.

-1 x 9 = -9

Multiply the uppers.

4. Add

180 - 9 = 171

Add steps 2 and 3 together to find the answer!!

Pretty cool, huh?

2. Here's a quick way to do 11x questions!

If the number is less than 10, then double the digit.
11 x 3 = 33

11 x 8 = 88

If the number is less than 100, then add the digits and put it in the middle:
11 x 34 = ?

Split : 3_4
Add : 3 + 4 = 7
Answer: 374.

11 x 85 = ?

Split : 8_5
Add : 8 + 5 = 13
Answer: 935

34 is the number we want to multiply. Split the 3 and 4.

Add 3 + 4 and put the result between the 3 and 4. Hint: the "7" is really "70."

For larger numbers, you have to do some carrying when you insert. Hint: the "13" is really "130."

If the number is greater than 100, then use a calculator!

3. Here's a quick way to do 9x questions!

This is what your hands look like (as drawn by one of the bears):

If you are doing 9 x 4, then bend finger #4. That leaves 3 fingers on one side and 6 on the other.... so the answer is 36!

4. Here is another method for multiplying two-digit numbers in your head!!

This is how it works:

Example 1:

Let's say you want to multiply 14 x 32:

1. Visualize the question vertically.

14
x 32

2. Multiply the right-hand column.

14
x 32
8

4 x 2 = 8

3. Cross-multiply the two columns and add the results together.

14
x 32
48

1 x 2 = 2 and 4 x 3 = 12.
Add the results: 12 + 2 = 14

(Remember, we have to carry the "1")

4. Multiply the left-hand column (remember to add the "1" that we carried from step 3).

14
x 32
448

1 x 3 = 3, then add the "1" that was carried in step 3...
the result is 4.

So the answer is 448!

1. Write down the uppers. (Well, actually you'd be doing this in your head...)	4 8 14 x 18 =	Since 14 is 4 more than 10, write "4" above 14. Since 18 is 8 more than 10, write 8 above 18.
2. Cross-add.	14 + 8 = 22 18 + 4 = 22 Think: 220	You can either add 14 + 8 or 18 + 4... the answer is 22 either way. We are using 10 as a base, so "22" is really "220."
3. Multiply.	4 x 8 = 32	Multiply the uppers.
4. Add	220 + 32 = 252.	Add steps 2 and 3 together to find the answer!!

1. Write down the uppers.	-1 9 9 x 19 =	In this example, 9 is less than 10, so write -1 above the 9.
2. Cross-add.	9 + 9 = 18 -1 + 19 = 18 Think: 180	We are using 10 as a base, so "18" is really "180."
3. Multiply.	-1 x 9 = -9	Multiply the uppers.
4. Add	180 - 9 = 171	Add steps 2 and 3 together to find the answer!!

If the number is less than 10, then double the digit.	11 x 3 = 33 11 x 8 = 88
If the number is less than 100, then add the digits and put it in the middle:	11 x 34 = ? Split : 3_4 Add : 3 + 4 = 7 Answer: 374. 11 x 85 = ? Split : 8_5 Add : 8 + 5 = 13 Answer: 935	34 is the number we want to multiply. Split the 3 and 4. Add 3 + 4 and put the result between the 3 and 4. Hint: the "7" is really "70." For larger numbers, you have to do some carrying when you insert. Hint: the "13" is really "130."
If the number is greater than 100, then use a calculator!

1. Visualize the question vertically.	14 x 32
2. Multiply the right-hand column.	14 x 32 8	4 x 2 = 8
3. Cross-multiply the two columns and add the results together.	14 x 32 48	1 x 2 = 2 and 4 x 3 = 12. Add the results: 12 + 2 = 14 (Remember, we have to carry the "1")
4. Multiply the left-hand column (remember to add the "1" that we carried from step 3).	14 x 32 448	1 x 3 = 3, then add the "1" that was carried in step 3... the result is 4. So the answer is 448!