Multiplying Integers

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

That's why it is strongly recommended, that you read first Multiplying Whole Numbers!!!

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

Example 1. Find $$${46}\times{\left(-{21}\right)}$$$.

We find $$${46}\times{21}={966}$$$ and then place minus in front of result: $$$-{966}$$$.

So, $$${46}\times{\left(-{21}\right)}=-{966}$$$ .

Next example.

Example 2. Find $$$-{35}\times{21}$$$.

We find $$${35}\times{21}={735}$$$ and then place minus in front of the result: $$$-{735}$$$.

So, $$$-{35}\times{21}=-{735}$$$.

  • If you multiply two positive numbers, you're actually multiplying whole numbers.
  • If you multiply two negative numbers, multiply numbers ignoring minuses, i.e. $$${\color{green}{{-{a}\times{\left(-{b}\right)}={a}\times{b}}}}$$$.

Example 3. Find $$${23}\times{51}$$$.


Another example.

Example 4. Find $$$-{48}\times{\left(-{19}\right)}$$$.


So, $$$-{48}\times{\left(-{19}\right)}={912}$$$ .

Final example shows how to multiple more than two integers.

Example 5. Find $$$-{4}\times{\left(-{2}\right)}\times{\left(-{15}\right)}$$$.

We do such problems step-by-step.

First find $$$-{4}\times{\left(-{2}\right)}$$$. $$$-{4}\times{\left(-{2}\right)}={4}\times{2}={8}$$$.

Now we are left with $$${8}\times{\left(-{15}\right)}$$$. $$${8}\times{\left(-{15}\right)}=-{8}\times{15}=-{120}$$$.

So, $$$-{4}\times{\left(-{2}\right)}\times{\left(-{15}\right)}=-{120}$$$.

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

Exercise 1. Find $$${36}\times{\left(-{21}\right)}$$$.

Answer: -756.

Exercise 2. Find $$$-{57}\times{60}$$$.

Answer: -3420.

Exercise 3. Find $$${6}\times{10}$$$.

Answer: 60.

Exercise 4. Find $$$-{5}\times{\left(-{20}\right)}$$$.

Answer: 100.

Exercise 5. Find $$${5}\times{\left(-{25}\right)}\times{\left(-{15}\right)}$$$.

Answer: 1875.