Question

Solve $\left( -5 \right)\times \left( -7 \right)$.

Answer 1

Hint: We have to find the product when (-5) is multiplied by (-7). First simply determine the product of the modulus value of the integers involved then for finding the sign of the product use
$''-''\times ''-''=''+''\left( i.e.\ negative\ \times \ negative\ =\ positive \right)$

Complete step-by-step answer:
According to the question, we have to find the value of $\left( -5 \right)\times \left( -7 \right)$.
Step 1: First simply determine the product of modulus values of integers involved.
Modulus values = values of the integers with positive sign.
Modulus value of (-5) $=\left| -5 \right|=+5$
Modulus value of (-7) $=\left| -7 \right|=+7$
Product of modulus values $\left( +5 \right)\times \left( +7 \right)$
= 35.
We have found the modulus value of the required product. Now we have to find the sign of the product.
Step 2: Check the sign of the two integers involved and find the product of their signs to get the sign of the required product.
Sign of (-5) = “ – “ (i.e. negative)
Sign of (-7) = “ – “ (i.e. negative)
We know $''-''\times ''-''=''+''\left( i.e.\ negative\ \times \ negative\ =\ positive \right)$
So, the sign of the product will be positive.
Thus, we have found the modulus value of product to be 35 and sign of the product to be + (positive).
Hence, the required product will be +35. i.e. $\left( -7 \right)\times \left( -5 \right)=+35$.

Note: The following sign multiplications are used:
$\begin{align}
  & \left( +ve \right)\times \left( +ve \right)=\left( +ve \right) \\
 & \left( -ve \right)\times \left( -ve \right)=\left( +ve \right) \\
 & \left( -ve \right)\times \left( +ve \right)=\left( -ve \right) \\
 & \left( +ve \right)\times \left( -ve \right)=\left( -ve \right) \\
\end{align}$
In short, we can say that when two numbers with the same sign are multiplied we get positive sign in product and when two numbers with opposite signs are multiplied, we get negative sign in product.