Let's think about this problem this way:
I have a drone and I'm standing on a street next to an open manhole. I can fly the drone up into the sky and I can fly it down into the hole. I'm going to say that when the drone is flying above me, that's a positive number (so when it's flying 5 feet above me, that is +5 feet) and when it's below me down in the hole, that is a negative number (so when it's flying 5 feet down in the hole, that is -5 feet).
This means that up is positive and down is negative. This is not to mean that addition and subtraction mean automatically up and down - they merely indicate a type of change.
So let's work out the different ways we can do math on this scenario (I'll show the math, then explain what it means):
#"Start" color(white)(00000) "Operation" color(white)(00000) "Amount"color(white)(00000)"Result"#
#color(white)(00)color(blue)5 color(white)(0000000000) color(red)(+) color(white)(00000000000) color(green)(1)color(white)(0000000000)color(brown)(6)#
My drone #color(blue)("starts with 5 upward feet")# and I #color(red)("add")# #color(green)("1 upwards foot")# so that it's now at #color(brown)("6 upwards feet")# (It's above me and flying higher - farther from me)
#color(white)(00)color(blue)5 color(white)(0000000000) color(red)(-) color(white)(00000000000) color(green)(1)color(white)(0000000000)color(brown)(4)#
My drone #color(blue)("starts with 5 upward feet")# and I #color(red)("take away")# #color(green)("1 upwards foot")# so that it's now at #color(brown)("4 feet")# (It's above me and flying lower - closer to me)
#color(white)(00)color(blue)5 color(white)(0000000000) color(red)(+) color(white)(00000000000) color(green)(-1)color(white)(0000000000)color(brown)(4)#
My drone #color(blue)("starts with 5 upwards feet")# and I #color(red)("add")# #color(green)("1 downwards foot")# so that it's now at #color(brown)("4 upwards feet")# (It's above me and flying lower - closer to me)
#color(white)(00)color(blue)5 color(white)(0000000000) color(red)(-) color(white)(00000000000) color(green)(-1)color(white)(0000000000)color(brown)(6)#
My drone #color(blue)("starts with 5 upwards feet")# and I #color(red)("take away")# #color(green)("1 downwards foot")# so that it's now at #color(brown)("6 upwards feet")# (It's above me and flying higher - farther from me)
#color(white)(00)color(blue)-5 color(white)(00000000) color(red)(+) color(white)(00000000000) color(green)(1)color(white)(0000000000)color(brown)(-4)#
My drone #color(blue)("starts with 5 downwards feet")# and I #color(red)("add")# #color(green)("1 upwards foot")# so that it's now at #color(brown)("4 downwards feet")# (It's below me and flying higher - closer to me)
#color(white)(00)color(blue)-5 color(white)(00000000) color(red)(-) color(white)(00000000000) color(green)(1)color(white)(0000000000)color(brown)(-6)#
My drone #color(blue)("starts with 5 downwards feet")# and I #color(red)("take away")# #color(green)("1 upwards foot")# so that it's now at #color(brown)("6 downwards feet")# (It's below me and moved lower - farther from me)
#color(white)(00)color(blue)-5 color(white)(00000000) color(red)(+) color(white)(00000000000) color(green)(-1)color(white)(0000000000)color(brown)(-6)#
My drone #color(blue)("starts with 5 downwards feet")# and I #color(red)("add")# #color(green)("1 downwards foot")# so that it's now at #color(brown)("6 downwards feet")# (It's below me and moved lower - farther from me)
#color(white)(00)color(blue)-5 color(white)(00000000) color(red)(-) color(white)(00000000000) color(green)(-1)color(white)(0000000000)color(brown)(-4)#
My drone #color(blue)("starts with 5 downwards feet")# and I #color(red)("take away")# #color(green)("1 downwards foot")# so that it's now at #color(brown)("4 downwards feet")# (It's below me and moved higher - closer to me)
