Long Division

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Long Division: meaning, method and solved example (6th Grade) – Maths PDF

In short: Long division is a written method that splits a big number into equal groups one digit at a time, repeating divide, multiply, subtract and bring down until nothing is left.

6th GradeNumbers and Operations6.NS.B.2

What is Long Division?

When a division is too large to do in your head, long division breaks it into a chain of small, easy steps. Each step handles one digit of the dividend and records how many groups fit so far.

Precisely, it computes the quotient \(q\) and the remainder \(r\) of \(n \div d\) with \(d \neq 0\), so that \(n = d \cdot q + r\) and \(0 \le r < d\). When \(r = 0\), the divisor goes into the dividend exactly.

How to spot it

  • A division involves a divisor with two or more digits, such as 1,092 divided by 13.
  • You must share a large total into equal groups and cannot spot the answer from a times table.
  • A question asks for a decimal answer, so the process continues past the ones place.
  • A check calls for the quotient and any remainder written out in full.

The method

  1. Divide: see how many times the divisor fits in the first digits of the dividend, and write that digit above.
  2. Multiply: multiply the digit by the divisor and write the product under the digits you used.
  3. Subtract: subtract to find what is left, and make sure it is smaller than the divisor.
  4. Bring down the next digit and repeat; end when no digits remain, then check with multiplication.
131092841045252013 goes into 109 eight times8 x 13 = 104109 – 104 = 5, bring down 24 x 13 = 52, remainder 0
1,092 divided by 13 is 84 with no remainder.

Long Division: solved example

Problem

A hardware store packs 1,092 screws into boxes of 13. How many boxes does it fill?

Solution

Divide: 13 fits into 109 eight times, since \(8 \times 13 = 104\). Subtract: \(109 – 104 = 5\). Bring down the 2 to make 52.

Next, \(52 \div 13 = 4\) with remainder 0. The quotient reads 84, so the store fills 84 boxes. Check: \(84 \times 13 = 1{,}092\).

Try it

Question 1

Divide 3,405 by 15 and give the quotient.

Show the answer

15 into 34 is 2 (30, rem 4); bring down 0 for 40, 15 into 40 is 2 (30, rem 10); bring down 5 for 105, 15 into 105 is 7. The quotient is 227.

Question 2

Divide 95 by 4. Write the whole-number quotient and the remainder.

Show the answer

\(4 \times 23 = 92\) and \(95 – 92 = 3\), so the answer is 23 with remainder 3.

Long Division vs. Quotient

Long division is the written procedure with its repeating cycle of steps. The quotient is only the final answer the procedure produces, the number written on top of the bracket.

Quotient

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