Stop with a remainder
Record the whole-number quotient and the remainder from the last original digit.
985 ÷ 4 = 246 remainder 1
Before this page: know the multiplication tables to 12 × 12 and understand the value of each digit from place value.
Sharing one place at a time
Short division breaks 984 ÷ 4 into smaller divisions, working from hundreds to tens to ones. Each answer digit goes above the place it counts.
For a two-digit divisor, recording the subtractions can help. That gives the method called long division; a decimal divisor is first made a whole number, by the method on dividing by decimals.
Exchanging the remainder
In 984 ÷ 4, the 9 is 9 hundreds. Shared into 4, they give 2 hundreds each, with 1 hundred left that cannot be shared as a hundred:
-
1 hundred
10 tens
10 tens and the next 8 tens make 18 tens: 18 ÷ 4 = 4 tens, with 2 tens left.
-
2 tens
20 ones
20 ones and the next 4 ones make 24 ones: 24 ÷ 4 = 6.
The small carried numerals record those exchanges: the 1 written before the 8 is the 1 hundred remainder renamed as 10 tens, and 984 itself is unchanged.
984 ÷ 4
Set out 984 ÷ 4
984 is 9 hundreds, 8 tens and 4 ones.
The short-division method
Work from the greatest place to the smallest
- 1
Divide the current amount by the divisor.
- 2
Write the whole-number result directly above that place.
- 3
Carry any remainder in front of the next digit.
- 4
Move right and repeat until every written digit has been used.
Keeping zeros in the quotient
After the first answer digit has been written, each remaining dividend digit must produce a digit in the quotient, even when that digit is 0:
6,048 ÷ 6
Set out 6,048 ÷ 6
6,048 is 6 thousands, 0 hundreds, 4 tens and 8 ones.
Dividing a decimal
The decimal point is not divided or carried. Put the point in the quotient directly above the point in the dividend, then continue through the decimal places with the same routine. If the quotient is below 1, write a zero before its decimal point.
18.9 ÷ 7
Set out 18.9 ÷ 7
18.9 is 1 ten, 8 ones and 9 tenths.
Remainder or decimal
First use every digit already written in the dividend. If the final remainder is zero, the division is complete. If it is not, the question says which to give: the answer with a remainder, or an exact decimal. For a worded problem the context decides, as on interpreting remainders.
Continue as a decimal
Exchange the remainder into the next decimal place and carry on dividing.
985 ÷ 4 = 246.25
Continuing into decimals
If the original digits run out and the question requires an exact decimal, extend the dividend with a zero after its decimal point. Add the point first if the dividend is a whole number. This does not change its value: 13 = 13.0 = 13.00 = 13.000.
Example: calculate 13 ÷ 8 exactly
13 ÷ 8
Set out 13 ÷ 8
13 is 1 ten and 3 ones.
13 ÷ 8 is terminating because the remainder reaches zero. If the remainder never reaches zero the decimal repeats instead: 13 ÷ 3 = 4.333…, written in recurring-decimal notation.
Explore short division
Set out 327.6 ÷ 6
327.6 is 3 hundreds, 2 tens, 7 ones and 6 tenths.
Checking by multiplication
Multiply the quotient by the divisor
- For an exact answer: 246 × 4 = 984 and 1.625 × 8 = 13.
- For an integer remainder, add it back: 246 × 4 + 1 = 985.
Multiplication checks both the digits and their places. For example, 5,035 ÷ 5 = 1,007, and 1,007 × 5 = 5,035. If we dropped both zeros and wrote 17, multiplying back would give only 85.
Key points
- Divide from left to right, keeping each quotient digit in its place.
- Exchange a remainder into the next smaller place before continuing.
- Keep any internal zeros, and place the quotient’s decimal point above the dividend’s.
- Zeros after the decimal point let an unfinished division continue.