Here are some concepts
that will help.
Formula |
Example |
Answer |
x^2
– y^2 = (x + y)(x – y) | 20^2
– 18^2 = (38) (2) | 76
| (x + y)^2 = x^2 + 2xy
+ y^2 | 201^2 = (200 + 1)^2
= 40 000 + 400 + 1 | 40
401 | (x – y)^2 =
x^2 – 2xy + y^2 | 199^2 = (200
- 1)^2 = (40 000 - 400 + 1 | 39
601 | (n + 5)^2 = n (
n + 10 ) + 25 | 75^2 = (70) (80)
+ 25 = 5 600 + 25 | 5 625 |
Rules for Multiplying Multiplying by 11 Add ten times the
original number to the original number. Example: 248 x 11 = 2480 + 248 = 2728 Rules
for Divisibility Test for 2: A number is divisible by 2 if the last digit
is even. Example: 246 is divisible by 2. Test for 3: Sum the digits.
If the result is more than 1 digit, sum again. The result is called the digital
root of the number. If the digital root is divisible by three, so is the original
number. Example: 246: 2+4+6 = 12; 1+2 = 3, so 246 is divisible by 3. Test
for 4 The number is divisible by 4 if the last 2 numbers are divisible by
4. Example: 248: 48 is divisible by 4, so 248 is so divisible. Test
for 5 The number is divisible by 5 is the last digit is a 0 or 5. Example:
245 is divisible by 5 Test for 6 Test for divisibility by 2 and 3, the
factors of 6. The number must be even, and have a digital root divisible by 3.
Example: 246 is even, and the digital root is 3, so it is divisible by 6. Test
for 7 There are no simple tests for divisibility by 7. Test for 8
The number is divisible by 8 if the last three digits are divisible by 8. Example:
1248 is divisible by 8 Test for 9 The number is divisible by 9 if the
digital root is also divisible by 9. Example: 252: 2+5+2 = 9, so it is divisible
by 9. Test for 10 The number is divisible by 10 if the last digit is
0. Example: 240 is divisible by 10 Test for 11 Take the number in
reverse order, alternately subtracting and adding them. If the result is divisible
by 11, so is the original number. Example: 2948: 8–4+9–2 = 11,
so the number is divisible by 11. Test for 12 The number must be divisible
by 3 and by 4. Example: 252: The digital root is 9, so it is divisible
by 3. 52 is divisible by 4. So 252 is divisible by 12. |