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Use the standard division algorithm

The standard division algorithm represents division of multi-digit whole numbers by one- or multi-digit whole numbers through place-value regrouping: each quotient digit records how many groups of the divisor fit into the current partial dividend, with subtraction and bringing down preserving the value of the unprocessed remainder. The quotient and remainder satisfy dividend = divisor × quotient + remainder, with the remainder less than the divisor; estimates and multiplication provide checks. This scope excludes decimal divisors, decimal quotients, and symbolic polynomial division.

Detailed Explanation: Use the standard division algorithm

To divide using the standard division algorithm, work from left to right:

  1. Find how many times the divisor fits into the current partial dividend.
  2. Write that quotient digit above the correct place.
  3. Multiply and subtract.
  4. Bring down the next digit.
  5. Repeat until all digits have been used.

Example: Divide 1,3751{,}375 by 2424

We want to find

1,375÷24.1{,}375 \div 24.

The divisor 2424 does not fit into 11 or 1313, so start with 137137.

Step 1: Divide 137137 by 2424

2424 fits into 137137 5 times because

5×24=120.5 \times 24=120.

Write 55 in the quotient. Then subtract:

137−120=17.137-120=17.

Step 2: Bring down the next digit

Bring down the 55 from 1,3751{,}375. The 1717 remainder and the 55 make 175175.

Now divide 175175 by 2424:

7×24=168.7 \times 24=168.

Write 77 in the quotient and subtract:

175−168=7.175-168=7.

The work looks like this:

24)5724)1375‾24)12024)120‾24)17↓524)16824)168‾24)7\begin{array}{r} \phantom{24)}57\\ 24\overline{\smash{\big)1375}}\\ \phantom{24)}120\\ \phantom{24)}\underline{\phantom{120}}\\ \phantom{24)}17\downarrow 5\\ \phantom{24)}168\\ \phantom{24)}\underline{\phantom{168}}\\ \phantom{24)}7 \end{array}

Therefore,

1,375÷24=57 remainder 7.1{,}375\div24=57\text{ remainder }7.

Check the answer using multiplication:

24×57+7=1,368+7=1,375.24\times57+7=1{,}368+7=1{,}375.

The remainder 77 is less than the divisor 2424, so the answer is correct.

Learn by doing: Use the standard division algorithm

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