Multiply Up to 20X20 In Your Head

This is an strategy to multiply from 11 to 20 in your head easily.

Try this:

1. Take 15 x 13 for an example.

2. Always place the larger number of the two on top in your mind.

3. Then add the bigger number with the last digit of the smaller number. So add 15 + 3 = 18

4. Then multiply it by 10 to get 180.

5. Multiply the covered lower 3 from the 13 by the single digit above it the "5" (3x5= 15)

6. Add 180 + 15 = 195.

This works only with numbers from 11-20.

discovered by Helen

Congruent Triangles

Introducing the FANTASTIC:

Congruent Triangles

Congruent Triangles are just a fancy mathematical term for two completely equal triangles this need to be proven for it to work, there are formulas to prove congruent triangles here are them: SSS SAS ASA HL.

Example:

If AB=A'B' and ∠BAC=∠B'A'C' (∠stands for angle)and AC=A'C'

Are triangle A and B congruent Triangles? 

Answer:

Because of the information given above the SAS works for this triangle because S stands for side and A stands for angle. Side Angle Side look at the triangles above AB and A'B' are a side and so are AC and A'C', with the angles BAC and B'A'C' tucked in the middle (that is important not to get any other angles)

HL is a little bit more complicated here is an example:

CB=C'B' AB=A'B'

Answers: The answer to this we can use the formula HL the H is hypotenuse

which is an angle that doesn't touch the right angle and the L stands for leg which is a side that touches the right angle, if a hypotenuse and a leg is equal in right angle triangles then they are congruent triangles.

I have just covered a tiny bit to solving congruent triangle problems, there are more complicated problems that involves other strategies and formulae. Hope you get the basic understanding of what congruent triangles are!

discovered by Ben Z

Division Rules

1: Any number is divisible by one.

2: Numbers that end with 0, 2, 4, 6, or 8 is divisible by two.

3: Add up the sum of the numbers digits, and if that is divisible by 3 then the number is divisible by 3.

4: If the last two digits in the number is divisible by four then the number is divisible by four.

5: Numbers that end with 5 and 0 can be divided by 5.

6: If the number is divisible by 2 and three, the number is divisible by 6.

7: Remove the last digit, double the last digit, then subtract the doubled number from the digits left. If the number is still too big, repeat the process.
eg. If you want to find out if 348 is divisible by 7 take out the last digit which is 8 then double it which become 16. Subtract 16 by 34 (the remaining digits) which gives you 18. Which means 348 is not divisible by 7.

8: If the last 3 digits of the number is divisible by 8 then the number is divisible by 8.

9: If the sum of the number’s digit is divisible by 9 then the number is divisible by nine.

10: Any number that ends with 0 is divisible by 10.

Discovered by Yiwen

A Little Mind Reading Trick

1.   Get a friend to write down any three digit number, but all the numbers must be different.  Tell them not to let you see what they write.
2.   Write the number again backwards.
3.   Minus the small number from the big number.
4.   Ask him/her what the first digit of the final answer is.
5.   If the first digit is a ... 1 - then the final answer they have is 198, 2 - then their final answers is 297, 3 - 396, 4 - 495, 5 - 594, 6 - 693, 7 - 792, 8 - 891, 9 - 99. e.g. 123 > 321, 321-123=198.   198 begins with a ` so their answer must be 198!

TIP: If the first number is 1-8, the second number is always 9.  The first and last number's sum is always 9.
e.g. 198 1+8=9

Amaze your friends!

discovered by Lucia

Welcome to the Mathex class of 2011

We are a new mathex group this year and we are eagerly making our new discoveries.

Follow our maths discoveries here – we hope you are as excited as we are.