Long Division Calculator

How the Long Division Calculator works

Long division breaks a big division into a run of small ones. You work from the left of the dividend, asking how many times the divisor fits into the part you have so far, writing that digit in the answer, and carrying what is left over into the next digit. Every step uses only times tables and subtraction.

How the long division calculator works

The formula behind each step is: number so far = divisor × answer digit + remainder. The calculator starts with the first part of the dividend that the divisor fits into, writes how many times it goes in, multiplies back, subtracts, and brings down the next digit. In decimal mode it keeps bringing down zeros after the point until the remainder is 0, or until a remainder repeats, which means the digits from there on repeat for ever. A decimal divisor is turned into a whole number first by multiplying both numbers by 10, 100 or 1000.

First example. 7249 ÷ 6. Six goes into 7 once, leaving 1. Bring down 2 to make 12, which 6 goes into twice exactly. Bring down 4; 6 does not fit, so write 0. Bring down 9 to make 49, which 6 goes into 8 times, leaving 1. The answer is 1208 remainder 1.

Second example. 45.6 ÷ 1.2. Multiply both by 10 to get 456 ÷ 12. Twelve goes into 45 three times, leaving 9; bring down 6 to make 96, which is exactly 8 twelves. The answer is 38.

How many minibuses of 14 do 250 pupils need? 250 ÷ 14 is 17 remainder 12, so 17 full buses leave 12 pupils over, and you need 18.

Each step of 7249 ÷ 6 by long division

1,000 divided by every number from 2 to 25, as a quotient with remainder and as a decimal

Tips

• Check with multiplication. Quotient × divisor + remainder should give back the dividend.
• Write the zeros. When the divisor does not fit, put a 0 in the answer before bringing down the next digit.
• Remainder or decimal? Use a remainder for sharing whole things, a decimal for money or measurements.

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