I am in 9th grade in your educational system and I am actually a Secondary 3 student.(That doesn't mean 3rd grade, strange)
It is just all about distributive property of multiplication.
Distributive property of multiplication: \(a \times (b + c) = a \times b + a \times c\)
Example:
23 x 45
= (20 + 3) x (40 + 5)
= 40 x (20 + 3) + 5 x (20 + 3) <--- Distributive property of multiplication
= 40 x 20 + 40 x 3 + 5 x 20 + 5 x 3 <-- again Distributive property of multiplication
So that we do this when we are told to find the product with partial products.
In our country we use 23 x 40 + 23 x 5 though.
\(\begin{array}{rll}&2&3\\\times&4&5\\-&-&-\\20&\times&40=800\\3&\times&40=120\\20&\times&5\;\;=100\\3&\times&5\quad \!\!\!=15\\--&-&-----\end{array}\)
800 + 120 + 100 + 15 = 900 + 135 = 1035.
Check with this calculator: 23 x 45 = 1035
Tips: Use * for multiplication on this calculator!! :)
