 ## Casting Out Nines

Mathematics, Operations (+, -, x, /, etc.), Problem Solving

### Objective

Students learn how to determine whether or not a division problem will have a remainder.

### Directions Some quotients (answers in division) have no remainders. You can tell before you do the problem if a division problem will have a remainder.
Rule: If the divisor is 9 and all of the digits in the dividend add up to 9 or a multiple of 9, there will be no remainder in the quotient.
Examples
 1. 63/9 6 plus 3 equals 9. The quotient is 7 with no remainder. 2. 4,536/9 Together the digits in the dividend add up to 18 (4 + 5 + 3 + 6), a multiple of 9. The quotient is 504 with no remainder. 3. 27,918/9 Together the digits in the dividend add up to 27, a multiple of 9. The quotient is 3,102 with no remainder. 4. 15,318/9 Together the digits add up to 18, a multiple of 9. The quotient is 1,702 with no remainder. 5. 3,617/9 Together the digits add up to 17, which is not a multiple of 9. The quotient is 401 with a remainder of 8. 6. 3,67_/9 What digit will go in the empty space to make this dividend divisible by 9? The answer is 2 because this will make the digit total in the dividend equal 18 which is a multiple of 9. 3,672/9 The quotient is 408.

### Resources

• Casting Out Nines activity pages
• pencils