Skill: Divide a 4-digit number by a 1-digit number

Explanation and Free Practice Resources

Division of a whole number from 1,000 through 9,999 by a one-digit divisor is understood as decomposing the dividend by place value into equal groups, using partial quotients or the standard algorithm to determine each quotient digit. The quotient may include zero in an intermediate place, and a remainder must be less than the divisor; results can be checked with divisor × quotient + remainder = dividend. This scope excludes decimal quotients, multi-digit divisors, and more advanced generalizations.

Detailed Explanation: Divide a 4-digit number by a 1-digit number

To divide a 4-digit number by a 1-digit number, divide one place-value digit at a time, starting on the left. Write each answer digit above the matching place.

Example: Find 4,032÷44{,}032 \div 4.

  1. Divide the thousands digit: 4÷4=14 \div 4=1. Write 11 in the thousands place.
  2. Bring down the hundreds digit, 00. Since 0÷4=00 \div 4=0, write 00 in the hundreds place.
  3. Bring down the tens digit, 33. Since 33 is less than 44, write 00 in the tens place. This zero is important because there are no groups of 44 in 33.
  4. Bring down the ones digit, 22. Now you have 3232. Divide: 32÷4=832 \div 4=8. Write 88 in the ones place.

So,

4,032÷4=1,0084{,}032 \div 4=1{,}008

You can check the answer:

4×1,008=4,0324 \times 1{,}008=4{,}032

Therefore, the quotient is 1,008\boxed{1{,}008}. If there is a remainder, it must be less than the divisor.

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Long Division - No Remainder 4 x 1


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