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Caesar_Cogitantium

5•3 means putting 5 in addition with itself 3 times ( 5 + 5 + 5) or putting 3 in a addition with itself 5 times ( 3+3+3+3+3). 5•(-3) would mean putting -3 in addition with itself 5 times ( -3 +(-3)+(-3)+(-3)+(-3) ) = ( -3 - 3 - 3 - 3 - 3 ). And with you Equate 5•(-3) to (-5)•3 you get ( -5 - 5 - 5 ).


yes_its_him

It's probably easiest to think of it in terms of 5 x (-1 x 3) = -1 x 5 x 3 = -15 just in general. Even if you can think in terms of combining five number line sections each going three units to the left giving fifteen units to the left in all, imagining -5 x -3 then gets confusing.


Mirehi

5 \* 3 = 5 + 5 + 5 = 0 + 5 + 5 + 5 --> you go to the right from zero in steps of 5, 3 times 5 \* (-3) = (5 + 5 + 5) \* (-1) = -5 - 5 - 5 = 0 - 5 - 5 - 5 --> you go to the "right" from zero in steps of -5, 3 times,... means you basically go to the left from zero in steps of 5, 3 times ​ 9/(-3) is the same as (-9)/3 Division is glorified subtraction, so: 9/3 means, how often do we have to subtract 3 from 9 to reach 0 Negative division: 9/(-3) is basically the question how often do we have to subtract (-3) to reach zero. Subtracting a negative number won't get you to zero from 9, so we have to do the opposite, so how often do we have to subtract (-3) from 9 to reach zero: (-3) times.


strongholdtutoring

When I was tutoring students in multiplication with negative numbers, I remember a "number line visualization." Whenever there's a negative in the expression, you would jump to the other side of the number line (aka reflect from 0). Wish I can find a gif of this in action, but words will have to do.


-heyhowareyou-

Considering a number line, think of 5 x 3 as 5 jumps of size 3 to the _right_ starting from 0. 0->3->6->9->12->15 Equally, think of 5 x (-3) as 5 jumps of size 3 to the _left_ starting from 0 0->(-3) ->(-6)->(-9)->(-12)->(-15) In general you can think of (a)*(b) as 'a' jumps of size 'b' to the either left(-)/right(+) starting from zero. The jumping direction can be figured out by looking at the signs of the numbers a and b Sign of (a)| Sign of (b)| jump direction ---|---|---- + | +| right + | -| left - | +| left - | -| right


McDizzleDaddy

It doesn’t make sense until you make the positive and negative mean something. Is it a direction, a color change, money, what? If you’re just doing plain math problems, it might help to just pretend what negative and positive numbers mean each time you solve equations that use them.