Divide four-digit numbers

Share one place at a time

For 4368÷4, share four thousands between four groups: each gets one thousand. Share three hundreds: none of the groups gets a whole hundred, so write zero hundreds. Exchange the three hundreds for thirty tens. With the original six tens, share 36 tens: nine tens per group. Share eight ones: two ones per group.

The result is 1092. Check:

Writing 192 would lose the thousands place and cannot pass the multiplication check.

Keep the remainder smaller than the divisor

For 5279÷6:

• Five thousands cannot give a whole thousand to each group; use them with the hundreds as 52 hundreds.
• Eight hundreds per group use 48 hundreds, leaving four hundreds.
• Exchange those for forty tens; with seven tens, share 47 tens. Seven tens per group use 42 tens, leaving five tens.
• Exchange to fifty ones; with nine ones, share 59 ones. Nine ones per group use 54, leaving five.

The quotient is 879 remainder 5. Check 879 × 6 + 5 = 5279. Five is smaller than six, so no further full group can be formed.

Here is the same working after exchanging the five thousands for hundreds. The quantities in each row count that row’s place-value units.

Four hundreds left become forty tens before the original seven tens are included. Five tens left then become fifty ones before the original nine ones are included. A remainder moves to the next place by an exchange; it does not stay the same number of smaller units.

Check your understanding 1 Keep the empty place

Find 6048÷3.

Quotient

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2016. Check 2016 × 3 = 6048. The zero is needed between the thousands and tens.

Check what the answer counts

For 5279 tiles packed six per full box, 879 full boxes can be made and five tiles remain. To hold all tiles, 880 boxes are needed, with five tiles in the last one.

Check your understanding 2 Reverse a division

A division by seven gives quotient 406 and remainder three. What was the original whole number? Check that the remainder is allowed.

Your answer or drawing on paper

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The number is 406 × 7 + 3 = 2845. Three is smaller than seven, so it can be a remainder. The zero in 406 is still part of the place-value notation.

Choose an estimate to check the size, then use multiplication and the remainder to check the exact original amount.