Question

what is $5 \cdot (-7)$?
you can think of 5 groups of $-7$ as repeatedly counting by $-7$ to the left on the number line.
that is why multiplying a positive number by a negative number gives you a negative product.
$5 \cdot (-7) = \square$

Explanation:

Step1: Recall multiplication rule

When multiplying a positive number by a negative number, the product is negative. The formula for \(a \cdot (-b)\) (where \(a,b>0\)) is \(-(a \cdot b)\).

Step2: Calculate the product

For \(5 \cdot (-7)\), we first calculate \(5 \cdot 7 = 35\), then apply the sign rule. So \(5 \cdot (-7)= - (5 \cdot 7)= - 35\).

Answer:

\(-35\)