Question

Why the product of plus and minus is minus always?

Answer 1

People have suggested many ways of picturing what is going on when a negative number is multiplied by a negative number. It's not easy to do, however, and there doesn't seem to be a visualization that works for everyone.

Answer 2

$Let\ two\ positive\ numbers\ be\ x\ \&\ y. \\ \\ Putting\ negative\ symbol\ on\ y\ makes\ it\ negative,\ i.\ e.,\ -y. \\ \\ (Had\ taken\ two\ positives\ x\ \&\ y\ for\ comfort.) \\ \\ \\ x \times (-y)\ means\ (-y)\ is\ added\ x\ times. \\ \\ So\ it\ can\ be\ written\ as, \\ \\ x \times (-y) \\ \\ = \{(-y) + (-y) + (-y) +......\}x\ times \\ \\ = \{-y-y-y-......\}x\ times \\ \\ = -\{(y + y + y + ......)\}x\ times \\ \\ = -(xy)$

$\\ \\ Here,\ the\ product\ is\ negative. \\ \\ \therefore\ Negative\ times\ positive\ is\ negative. \\ \\ \\ There\ is\ another\ way. This\ way\ can\ be\ easily\ understood \\ if\ you\ imagine\ a\ number\ line. \\ \\ x\ can\ be\ written\ as\ (x - 0). \\ \\ (-y)\ can\ be\ written\ as\ (0 - y).\ (Right?!) \\ \\ \therefore\ x \times (-y) \\ \\ = (x - 0)(0 - y) \\ \\ = (x \times 0) + (x \times (-y)) + ((-0) \times 0) + ((-0) \times (-y)) \\ \\ = 0 - xy - 0 + 0 \\ \\ = 0 - xy \\ \\ = -xy$

$\\ \\ Here,\ the\ product\ is\ negative. \\ \\ \therefore\ Negative\ times\ positive\ is\ negative. \\ \\ \\ Hope\ this\ may\ be\ helpful. \\ \\ Please\ mark\ my\ answer\ as\ the\ \bold{brainliest}\ if\ this\ may\ be\ helpful. \\ \\ Thank\ you.\ Have\ a\ nice\ day. \\ \\ \\ \#adithyasajeevan$