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 ${\color{red}{{\frac{{0}}{{a}}={0}}}}$ for any number ${a}$ . For example, $\frac{{0}}{{5}}={0}$ .

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 $\frac{{86}}{{-{2}}}$ .

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

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

Next example.

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

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

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

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

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

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

Another example.

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

Ignore signs, because we divide numbers with same signs:

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

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

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

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

Answer: -4.

Next exercise.

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

Answer: -15.

Next exercise.

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

Answer: 18.

Next exercise.

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

Answer: 68.

Final exercise.

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

Answer: 0.