Find the product.
$(-45)(-3)$
$(-45)(-3)$
Find the product.
$(-45)(-3)$
We are asked to find the product of two negative integers, \(-45\) and \(-3\). Multiplication is a fundamental arithmetic operation that combines two numbers into a single product. When dealing with negative numbers, we must follow the rules of signs. For multiplication, the product of two negative numbers is always a positive number. Specifically, for any positive real numbers \(a\) and \(b\), the product of their negatives is given by \((-a) \times (-b) = a \times b\).
Given the expression \((-45)(-3)\), we can identify \(a=45\) and \(b=3\). According to the rule of signs, we can rewrite the product as:
\[(-45) \times (-3) = 45 \times 3\]
Now, we simply need to calculate the product of 45 and 3.
Calculating this:
\[45 \times 3 = (40 + 5) \times 3 = (40 \times 3) + (5 \times 3) = 120 + 15 = 135\]
Thus, the product of \(-45\) and \(-3\) is \(135\).
By applying the sign rule for multiplication and performing the multiplication of the positive factors, we have determined that the product of \(-45\) and \(-3\) is \(\boxed{135}\).
Imagine you have an automated budget app that tracks your spending. If you set a rule where every time you make a withdrawal of \$45 from your account (represented as -45), it is tracked three times due to a synchronization error, or perhaps you are reversing three separate \$45 unauthorized charges (reversing a negative is like multiplying by a negative), the total adjustment to your balance would be \( (-45) \times (-3) = \$135 \). This calculation helps in understanding how reversing debt or negative transactions can positively impact a financial balance.