Question

Find each of the following product:
\[\left( { - 30} \right) \times \left( { - 20} \right) \times \left( { - 5} \right)\]

Answer 1

Hint: To solve this question first we assume the answer of the given expression as a variable. Then first we multiply the first two terms and find the answer with the sign. Then we multiply that answer with the third and look at the answer whether that is positive or negative.

Complete step-by-step solution:
Let \[x = \left( { - 30} \right) \times \left( { - 20} \right) \times \left( { - 5} \right)\]
Using the rule of multiplication
If we multiply the negative number with a negative number then we get a positive number.
So using this rule we multiply the first two terms.
We know by using this rule \[\left( { - 30} \right) \times \left( { - 20} \right) = 600\]
 \[x = 600 \times \left( { - 5} \right)\]
If we multiply a negative number with a positive number we get negative number as a answer
On multiplying both the numbers and taking negative number
\[x = - 3000\]
Final answer:
The product of the given expression is
\[ \Rightarrow \left( { - 30} \right) \times \left( { - 20} \right) \times \left( { - 5} \right) = - 3000\]

Note:
> If we multiply a negative number with a negative number then we get a positive number.
> If we multiply a negative number with a positive number then we get a negative number.
> If we multiply a positive number with a negative number then we get a negative number.
> If we multiply a positive number with a positive number then we get a positive number.
The short trick used to decide the sign of the multiplication of numbers: i) if we multiply n negative number and here n is the even number then the answer is the positive number. And if n is odd then the answer is also negative. ii) if we multiply a positive number then the answer is always positive irrespective of the number of terms.