Worked examples and common mistakes

Here are three fully solved problems, one per difficulty level. Each one follows the recipe from Step-by-step procedure.

Example 1 – 2-digit dividend (easy)

The whole number $95$ is our first chunk, because it is bigger than the divisor $14$. We are looking for how many times $14$ fits into $95$. Try $6\times 14=84$ — that fits, it is less than $95$. Try $7\times 14=98$ — that is already too much. So we write $6$ in the quotient. Subtract $95-84=11$. There are no more digits in $95$, so the remainder is $11$.

So $95:14=6$ remainder $11$. Check: $6\times 14+11=84+11=95$. ✓

Example 2 – 3-digit dividend (medium)

• First chunk is $56$. It is bigger than the divisor $23$, so we can divide. How many times does $23$ fit into $56$? Try $2\times 23=46$ — fits; $3\times 23=69$ is too much. We write $2$ in the quotient. Subtract $56-46=10$.
• Append the next digit of the dividend, $7$, to the difference $10$. The new chunk is $107$. How many times does $23$ fit into $107$? $4\times 23=92$ — fits; $5\times 23=115$ is too much. We write $4$. Subtract $107-92=15$.
• There are no more digits in the dividend, so the remainder is $15$.

So $567:23=24$ remainder $15$. Check: $24\times 23+15=552+15=567$. ✓

Example 3 – 4-digit dividend (hard)

• First chunk is $67$. It is bigger than $23$, so we divide. $2\times 23=46$ — fits; $3\times 23=69$ is too much. We write $2$. Subtract $67-46=21$.
• Append the next digit, $8$, to the difference $21$. The new chunk is $218$. How many times does $23$ fit into $218$? $9\times 23=207$ — that's the closest, still less than $218$. We write $9$. Subtract $218-207=11$.
• Append the last digit, $9$, to the difference $11$. The new chunk is $119$. $5\times 23=115$ — fits; $6\times 23=138$ is too much. We write $5$. Subtract $119-115=4$.
• There are no more digits in the dividend, so the remainder is $4$.

So $6789:23=295$ remainder $4$. Check: $295\times 23+4=6785+4=6789$. ✓

Common mistakes

Watch out for these — almost every wrong answer comes from one of them.

1. Quotient digit too small. If the difference after subtraction is larger than the divisor, you picked a quotient digit that was too small. The correct digit is one larger. (E.g. you wrote $5\times 14=70$ for $95:14$ and got $25$ as the difference — but $25>14$, so the correct digit is $6$.)

1. Quotient digit too large. If after multiplying you get a number bigger than the chunk you are dividing, the digit was too big. Try one smaller.

1. Forgetting to bring down a digit. Each step (after the first) uses exactly one new digit from the dividend. Skipping one will make the quotient too short.

1. Arithmetic slips during multiplication or subtraction. Double-check: the number you write below the chunk should equal the divisor times your quotient digit, and the difference after subtraction should be smaller than the divisor.

1. Final remainder is the same as or bigger than the divisor. If you finish and the remainder is at least the divisor, you missed a quotient digit — it could have been larger. Re-check the last step.

Self-check

A quick way to verify your answer:

If this equation holds, your division is correct.

Read more

• Division by a two-digit number – guide
• The principle of long division
• Step-by-step procedure

Practise

• Long division by a two-digit number