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1–7
Name
Date
Prove It!
Rule: A number is a multiple of 9 if the sum of its digits is 9. Prove it!
Write five digits whose sum is 9.
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⫹
⫹
⫹
⫽
Use the five digits in any order to create a five-digit number.
Divide that number by 9. Is there a remainder?
Now write six digits whose sum is 9.
⫹
⫹
⫹
⫹
⫹
⫽
Use the six digits in any order to create a six-digit number.
Copyright © Houghton Mifflin Company. All rights reserved.
Divide that number by 9. Is there a remainder?
1.
Use the rule above to write a seven-digit number that is a multiple of 9.
2.
Does the order of digits matter in the rule for 9? Explain.
3.
Is there any digit 0–9 that CANNOT be the final digit in a number that is a multiple of 9?
Why or why not?
1–7
Name
Date
Prove It!
Rule: A number is a multiple of 9 if the sum of its digits is 9. Prove it!
Write five digits whose sum is 9.
⫹
⫹
Check students’ work.
⫹
⫹
⫽
Use the five digits in any order to create a five-digit number.
Divide that number by 9. Is there a remainder?
Now write six digits whose sum is 9.
⫹
⫹
⫹
⫹
⫹
⫽
Use the six digits in any order to create a six-digit number.
Divide that number by 9. Is there a remainder?
1.
Use the rule above to write a seven-digit number that is a multiple of 9.
Check students’ work. The sum of the number’s
digits must be divisible by 9.
2.
Does the order of digits matter in the rule for 9? Explain.
No; No matter how you rotate the digits, the
number will still be divisible by 9.
3.
Is there any digit 0–9 that CANNOT be the final digit in a number that is a multiple of 9?
Why or why not?
No; 0 9 0, 1 9 9, 2 9 18, 3 9 27,
4 9 36, 5 9 45, 6 9 54, 7 9 63,
8 9 72, and 9 9 81, so every possible ones
digit is a potential part of a multiple of 9.