Use a Zero Quotient Digit in Long Division
Divide, multiply, subtract, and bring down the next digit in sequence.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For 1632÷16, the first sixteen gives one hundred in the quotient.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
The standard division algorithm follows place value from left to right. A zero quotient digit is required when a brought-down amount contains no complete divisor at that place. Omitting it shifts later digits and changes the quotient. The product plus remainder identity provides an exact check.
Divide, multiply, subtract, and bring down the next digit in sequence. Record a zero when a quotient place has no complete group. Check divisor × quotient + remainder = dividend and ensure any remainder is smaller than the divisor.
Keep one quotient place for each required place in the process. A missing zero can shift a correct final digit into the wrong place. Use labeled quotient-place columns and show each subtraction and brought-down digit.
- Use labeled quotient-place columns and show each subtraction and brought-down digit.
- Work through the supplied example and label what each number or attribute represents.
- Divide, multiply, subtract, and bring down the next digit in sequence.
- Answer the check, then try the three changed-input practice questions and explain one correction.
See the method in action
For 1632÷16, the first sixteen gives one hundred in the quotient. The next three cannot contain sixteen, so record zero tens. Bringing down two gives thirty-two and two ones. The quotient is 102, and 16×102=1632 verifies the placeholder. Keep one quotient place for each required place in the process. A missing zero can shift a correct final digit into the wrong place. Use labeled quotient-place columns and show each subtraction and brought-down digit.
Check your reasoning
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Helpful tips
- Keep one quotient place for each required place in the process.
- A missing zero can shift a correct final digit into the wrong place.
See the answer and explanation
104
Preserve every quotient place, including zero tens where required. The result is 104.
Take it further
Find 2448÷24. Expected: 102.
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