Back to Calculation Tips & Tricks
- even numbers 2 through selected 2-digit evens
- digits of square of repeating ones
- consecutive odds
- consecutive between 2 numbers
- sequence from 1 to selected 2-digit number
- sequence from 1 to selected 1-digit number and back
- sequences in the 10's
- sequences in the 20's
- sequences in the 30's
- sequences in the 40's
- sequences in the 50's
- sequences in the 60's
- sequences in the 70's
- sequences in the 80's
- series of doubles
- series of quadruples
- series of 10 numbers
- 1's repeating, divide by 9, subtract 21
- 8's repeating, divide by 9, subtract 10
- squares of two numbers
- reversing/adding/subtracting 3-digit numbers
- finding 2.5 percent
- finding 5 percent
- finding 15 percent
- finding 20 percent
- finding 25 percent
- finding 33 1/3 percent
- finding 40 percent
- finding 45 percent
- finding 55 percent
- finding 60 percent
- finding 70 percent
- finding 75 percent
from a repeating 1's number, divide
9, subtract 21
- Select a number between 2 and 10 digits made up of 1's.
- Subtract a number equal to the number of digits in the number you have selected.
- Divide by 9. The answer will have one less digit than the original number in
the series 123456789.
- Subtract 21.
- If the repeating number selected has 5 digits:11111:
- Subtract 5 (same as number of digits) and divide by 9. The answer will be 1234
- Subtract 21: 1234 - 21 = 1213.
- So (11111-5)/9 - 21 = 1213.
See the pattern?
- If the repeating number selected has 8 digits:11111111:
- Subtract 8 (same as number of digits) and divide by 9. The answer will be 1234567
- Subtract 21: 1234567 - 21 = 1234546.
- So (11111111-8)/9 - 21 = 1234546.
For those who enjoy extensions of these patterns:
(answers after the division by 9, step 3)
11 digit number, answer is 1234567900
12 digit number, answer is 12345679011
13 digit number, answer is 123456790122
14 digit number, answer is 1234567901233
15 digit number, answer is 12345679012344
Extend the exercises using this basic pattern by changing step 4 to add or subtract
© 1994- The Math Forum at NCTM. All rights reserved.
Home || The Math Library || Quick Reference || Search || Help
26 August 1996
Web page design by Sarah Seastone