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Still don't see the difference.

Density times volume is mass. Volume times density is mass. Distance times force is work/energy...

"5 times I will connect 12 apples"

You're correct. The GP in incorrect about their dimensional analysis. 5 apples 12 times yields apples because it's apples times a dimensionless scalar (count). Newtons times meters is always Newton-meters, never Newtons or meters. Units are never magically dropped in dimensional analysis.

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