23/10/2021
This turned up on a forum. 5+3x4 is 17 not 32. The reason is addition is kind of count in terms of 1 or unity, i,e., 5 may mean 5 dogs or 5 cows, etc. Multiplication on the other hand is a count in terms of groups, e.g., 3x4 means there are three groups and each group has 4 things (e.g., 4 dogs or 4 cows, etc.). Conversely, 3x4 may mean there are 4 groups each group having 3 things (i.e., 3 cows or 3 dogs etc.).
Unit count can't be added to group count directly.
When you add 5 to 3 in 5+3x4 the result is 8x4, which means 8 groups each group having 4 things (conversely, 4 groups each group having 8 things)...you have altered the meaning of the expression, which is wrong.
First convert 3x4 into unit count 12 then add with 5 (itself unit count)---answer is 17.
Addition imposes kind of a unit-structure on quantities; multiplication, a group structure.
It is better to know the reason for the rule instead of just memorizing the rule.
By Dr. Mohammad Naeem
UoP Peshawar
