Dividing Integers

Integers are divided in the same fashion as whole numbers, except that certain rules should be applied.

Word of Caution. Remember, that we can't divide by 0.

Another interesting property is that 0a=0{\color{red}{{\frac{{0}}{{a}}={0}}}} for any number a{a}. For example, 05=0\frac{{0}}{{5}}={0}.

If you divide integers with different signs, i.e. one is positive and another is negative, then divide numbers ignoring minus and place minus in front of result.

Example 1. Find 862\frac{{86}}{{-{2}}}.

Ignore signs: 862=43\frac{{86}}{{2}}={43}. Since numbers have different signs then place minus in front of result: 43-{43}.

So, 862=43\frac{{86}}{{-{2}}}=-{43} .

Next example.

Example 2. Find 723\frac{{-{72}}}{{3}}.

Ignore signs: 723=24\frac{{72}}{{3}}={24}. Since numbers have different signs then place minus in front of the result: 24-{24}.

So, 723=24\frac{{-{72}}}{{3}}=-{24}.

  • If you divide two positive numbers, you're actually dividing whole numbers.
  • If you divide two negative numbers, multiply numbers ignoring minuses, i.e. ab=ab{\color{green}{{\frac{{-{a}}}{{-{b}}}=\frac{{a}}{{b}}}}}.

Example 3. Find 483\frac{{48}}{{3}}.

483=16\frac{{48}}{{3}}={16}.

Another example.

Example 4. Find 755\frac{{-{75}}}{{-{5}}}.

Ignore signs, because we divide numbers with same signs:

755=755=15\frac{{-{75}}}{{-{5}}}=\frac{{75}}{{5}}={15}.

So, 7515=5\frac{{-{75}}}{{-{15}}}={5} .

Now, it's your turn. Take pen and paper and solve following problems.

Exercise 1. Find 123\frac{{12}}{{-{3}}}.

Answer: -4.

Next exercise.

Exercise 2. Find 604\frac{{-{60}}}{{4}}.

Answer: -15.

Next exercise.

Exercise 3. Find 905\frac{{90}}{{5}}.

Answer: 18.

Next exercise.

Exercise 4. Find 163224\frac{{-{1632}}}{{-{24}}}.

Answer: 68.

Final exercise.

Exercise 5. Find 07\frac{{0}}{{-{7}}}.

Answer: 0.